Once Upon A Time

Once Upon A Time
Once upon a time, son,
they used to laugh with their hearts
and laugh with their eyes:
but now they only laugh with their teeth,
while their ice-block-cold eyes
search behind my shadow.
By GABRIEL
OKARA
There was a time indeed
they used to shake hands with their hearts:
but that’s gone, son.
Now they shake hands without hearts:
while their left hands search
my empty pockets.
‘Feel at home’! ‘Come again’:
they say, and when I come
again and feel
at home, once, twice,
there will be no thrice –
for then I find doors shut on me.
So I have learned many things, son.
I have learned to wear many faces
like dresses – homeface,
officeface, streetface, hostface,
cocktailface, with all their conforming smiles
like a fixed portrait smile.
And I have learned too
to laugh with only my teeth
and shake hands without my heart.
I have also learned to say, ‘Goodbye’,
when I mean ‘Good-riddance’;
to say ‘Glad to meet you’,
without being glad; and to say ‘It’s been
nice talking to you’, after being bored.
But believe me, son.
I want to be what I used to be
when I was like you. I want
to unlearn all these muting things.
Most of all, I want to relearn
how to laugh, for my laugh in the mirror
shows only my teeth like a snake’s bare fangs!
So show me, son,
how to laugh; show me how
I used to laugh and smile
Pascal is often referred to as a ‘family’, forged with solid
ties, working in unison with the surrounding community. As
we bid a warm farewell to the graduates of 2011, we prepare
to welcome new members to follow in the footsteps of their
older peers who will continue to make us proud with
achievements that are still to come in years that will follow.
As Headmistress, I feel that our school, young as it is, has
established a commendable reputation on a local but also international scale due to the dedication and commitment of
teachers, heads of year groups, parents and students, of
course.
Honour and prowess is evoked in writing the Headmistress’
Note in each edition of Pascal Insight as I am urged to look
back in time but also to focus on the future. With schemes
like Comenius, educational trips abroad, university visits,
club days with destinations around the island, we have given
a first-hand impression of the essence of Pascal Larnaka, the
core of which is encapsulated within this magazine, hereby
presented to you.
Both the front cover and Okara’s poem deal with ageing
and both suggest a loss of innocence as we evolve and
adapt according to our exposure to the world surrounding us.
As children we take in, absorb, observe. As adults we
begin to give, influence and impact. Perhaps the focus
of Pascal Insight 2010-11 is to delineate the role we, as a
school community, play in each student’s path in trying
to maintain the natural goodness inherent in us all, for
our school is not only about learning, it is about learning
how to grow.
We hope that as you click through the electronic pages
that follow, you will savour many of the moments captured and upon reflecting, Okara’s words may even become apparent, that our students have as much to teach
us, as we have to teach them.
To end, we would like to dedicate this year’s edition to
all our students but in particular, to the graduating class
2010-11.
Chief Editor: Demos Kaoullas
Assistance from Christina Karaviotou
“The future belongs to those who prepare for it today”
Malcom X
“Once Upon a Time” is an emotional
poem about the story of a grown up
man—who
once was an innocent child.
His adult world has lost the charm of his
childhood years. The poet describes how
the
process of growing up transforms the innocence of childhood. After entering the
adult
world, the young adults will gradually
forget how to “laugh with their hearts.”
While growing up, the cold world intimidated our main character. He used to
sense
people’s insincerity and their superficial
laughs, because “they only laugh[ed] with
their
teeth,/while their ice-block-cold eyes/
search[ed] behind [his] shadow”.
It is a vicious circle: once someone has
entered the adult world, he will change—
then
change others. Our character will learn
how to say things that he doesn’t really
mean: “I
have also learned to say, “Goodbye,”/
when I mean “Goodriddance”;/to say
“Glad to meet
you,”/without being glad; and to say “It’s
been/nice talking to you,” after being
bored”
Like everyone else, our main character
was forced to grow up—in order to
adapt to the
adult world: “I have learned to wear
many faces/like dresses—homeface,/
officeface,
streetface, hostface, cock-/tail face,
with all their conforming smiles/like a
fixed portrait
smile”.
In this selfish world, our character
learned how to adapt; he adapted a little
too well. He
now can play the adult role without any
problem.
However, once he became a parent,
parenthood seems to have helped him
to remember
the innocent world of his childhood.
Because of his son, he wants to re-learn
how to be
sincere. His son holds the key to this
old, forgotten world.
What a wonderful poem! It presents in
such a simple manner, such a complicated subject:
the pain of growing up, and the loss of
innocence.
1A
First Row: Alexander Vikentiou, Charalambos Phokou, Alan Whittingham, Margarita Georgiadis, Ioanna
Arkadiou, Donya Ebrahim, Maxwell Kilner, Lewis Jenkins, Nash Passiades.
Second Row: Mrs Aspasia Manti, Maritsa Havadjia, Satya Christodoulou, Marina Koupparis, Eleni
Koumi, Ifigenia Kleanthous, Frederiki Soteriou, Andrey Sesyuk, Mrs Evy Pistola.
Back Row: Andreas Dinglis, Louiza Artemi, Antonia Diakou, Eleni Patsalos, Natasia Petrou, Alexander
Demetriou, Adrian Demetriou, Mahan Fathi, Armand Barle, Artem Osmolovsky.
1B
First Row: Kyriakos Stylianou , Averkios Nicolaou, Constantinos Ioannou, Thekla Georgiou, Anna
Savva, Marilena Papachrisodoulou, Erica Afxentiou, Kyriakos Pittas, Christodoulos Markides.
Second Row: Mrs Despina Kaittani, Giorgos Savvides, Nasia Charalambous, Alexandra Taratynova,
Paula Costa, Demetris Georgiou, Lazaros Pieri, Christoforos Kounes, Nicolas Tsaggaris,
Mrs. Evey Pistola
Back Row: Stelios Mavrides, Savvas Savva, Antreas Astraios, Christiana Lagou, Maria Manentzou,
Pantelis Georgiou, Olga Stylianou, Costas Costi, Christodoulos Louvia.
1C
First Row: Kypros Tilliros , Kousiappas Georgios ,Georgiou Michalia, Kounnas Constantinos, Michailas
Anastasis ,Anastasiou Marina, Moleski Charalambia ,Demetriou Theodoros
Second Row: Mr.Christoforos Alexandrou , Yiorka Stavriana , Kavalierou Marios ,Kafatari Constantinos , Procopiou Marios , Neoptolemou Vasilis , Anastasiou Panayiotis , Alambriti Loukia , Mrs.Evi Pistola
Back Row: Kyriacou Thekla , Kyriacou Michaella , Michael Savvas , Damianou Kyriakos ,Antoniou Antonis , Kemitzis Michalis , Efstathiou Ioannis , Sofokleous Odysseas
Absences: Paschali Maria
1D
First Row: Hadjiyianni Mikaella, Demetriou Demetra, Michaelidou Georgia, Poliviou Eleni, Cosma
Paris, Avgousti Chrysanthi, Papatheocharous Ioannis, Savva Constantinos, Toumazou Ioannis,
Second Row: Ms Maria Theophilou, Parperi Katerina, Popovidou Sara, Tambourla Antigoni (Noni),
Efthimiou Evdokia (Efi), Nikola Christos, Theodorou Xenios, Kadi Andria, Mrs Evey Pistola
Back Row: Konis Efraim, Karapitta Chrystalla, Ioulianou Christofora, Zachariou Georgia, Georgiou
Nicoletta, Panayi Alexandros, Zachariou Anastasis, Orthodoxou Margarita
2A
First Row: Koutra James, Pavlou Marios, Panayiotou Demetria, Passiadou Fiona, Stavrou Anastasios,
Zingis Paris, Pavlou Georgios, Xydias Constantinos.
Second Row: Mrs. Irene Petrou, Redpath Natalie, Agathokleous Marina, Hadjiyiannakou Andria, Solomonidou Rafaella, Constantinou Chrysostomos, Solomonides Andreas, Georgiou Antonis, Mr. Petros Kimitris.
Back Row: Xydia Nicoletta, Timm Elliot, Sutton Joshua, Karoullas Harry, Kakoullis Anastasios, Travkin
Philip, Iasonides Constantinos.
2B
First Row: Zorpides Christos, Georgiou Eleni, Elia Georgia, Costa Nicole, Kappelou Anastasia, Nicolaidou Andrea Rafaela, Kavourides Michalis.
Second Row: Christoforos Alexandrou (Form Teacher), Vassiliou Stalo, Vassiliou Maria, Charalambous
Sophia, Foka Andreas Georgios, Graham Savana, Evgeniou Andreas, Palate Danae, Tsappi Gavriella, Ms
Irene Petrou (HOY 2).
Back Row: Yiagkou Louiza, Demetriou Maria, Paschali Varvara, Kagkeli Maria, Frangou Charalambos,
Agathocleous Marios.
Absences:
2C
First Row: Spanou Rafaella, Foukkari Panagiota, Alexandrou Elena, Stavrou Pantelitsa, Papoulias Yiannis, Zachariou Constantinos, Todirica Alexandros.
Second Row: Miss Georgia Markadji, Marangou Elena, Kadi Kyriaki, Pirillos Panayitis, Kleopa Kleopas,
Sampson Costas, Zenonos Anastasis, Christou Panayiotis, Ms Irene Petrou.
Back Row: Shiantani Chrisanthi, Avraam Kalia, Foti Georgia, Sakka Nicoletta, Vrikki Nicoletta, Kittis
George, Shiantanis Antonis.
2D
First Row: Michael Demetris, Panayiotou Efthymia, Andronicou Anastasia, Georgiou Georgia, Charalambous Kyriaki, Panayi Nayia, Kyriacou Lazaros.
Second Row: Mrs Irene Petrou, Kafatari Iliana, Philipou Marina, Mavrou Kyriaki, Theodotou Andria, Mr
Socrates Petrides.
Back Row: Mouzouris Andreas, Sophocleous Andreas, Kyriacou George, Prodromou Lenos, Solomondas
Leonidas.
Absences: Helen Alexandrou, Stavrinos Constantinou, Demetris Demetriou, Christos Georgiou
2E
First Row: Zenonos Loizos, Anastasiou Marianna, Christou Maria, Pelide Electra, Stavrinou Thea, Vasiliou Kyriaki, Markou Lazaros.
Second Row: Mrs. Irene Petrou, Spirou Stefani, Apostolou Miranta, Charitonidou Constantina, Patziarou
Maria, Koudeli Sofia, Kiriakou Korina, Pelide Christina, Nikiforou Christiana, Mrs Myrto Michaila
Back Row: Petrides Evros, Ioannou Demetris, Solomou Demetris, Constantinou Nicolas, Antoniou Aggelos, Markou Stylianos, Stavrou Antonis, Efstathiou Alexandros.
3A
First Row: Stavrou Andreas, Eracleous Theodoros, Economides Andreas, Valeva Alexandrina, Michael
Michelle, Venizelou Mariam, Xiourouppa Charis, Hadjiyiasemi Kyriaki.
Second Row: Mr George Klokkaris, Thoma Christoforos, Mitsidou Christiana, Ourri Angelika, Hadjigeorgiou Stavri, Panayi Isabella, Antoniou Stavroulla, Alambriti Eleni, Ms Lena Mahdessian.
Back Row: Anastasi Petros, Valeev Marat, Shiantanis Antonis, Xiourouppas Michalis, Matsangos Rafael,
Zakheos Antonis, Graham Curtis, Shariari Arad.
Absences: Georgiadis Ioanna, Lappas Charalambos.
3B
First Row: Athanasiou Vassiliki, Pashiourtidou Anna, Liperi Loukia, Kontos Panayiotis, Francis Lina,
Papamichael Joanne, Yiallouros Antonis.
Second Row: Mr. George Klokkaris, Alexandrou Christiana, Kavourides Katerina, Perikli Anastasia,
Maouri Chrystalla, Michael Paraskevi, Ogden Emma, Panayiotou Nikolas, Koumi Yiannis, Ms Christina
Karaviotou.
Back Row: Savva Savvas, Savva Stylianos, Solomou Miltos, Spanoudis Yiannis, Nicolaou Andreas, Takkas George, Anastasiou Panayiotis, Kemitzis Nicholas, Savvides Yiannakis.
Absences: Mavromatis Michalis.
3C
First Row: Mouzouris George, Andronikou Andronikos, Mavrolefterou Andrea, Stavrou Kyriaki,Elefthriou Evdokia, Papadopoulou Panayiota, Pitta Anna, Konnari Vicky.
Second Row: Fokas Zacharias, Kalli Marina, Papakyriakou George, Markou Markos, Nonis Stavros,
Antoniou Melina, Aresti Maria, Ms Maria Anastasiou.
Back Row: Mr George Klokkaris, Charous Andreas, Nicolaou Michael, Konatzi Efthymia, Ppasias
Panayiotis, Hadjimatheou Konstantinos, Fouli Vassiliki, Themistokleous Marios, Shambellas Panayioyis,
Charalambous Theodosis.
Absences: Thoupou Christina, Anastasiou Elena.
3D
First Row: Mr George Klokkaris, Stephanou Fotini, Theodorou Kyriaki, Polydorou Nikoletta , Tsikkos
Andreas , Loucaidou Stefanie , Kakoulli Stella , Yerolemou Tonia , Kounnas Kyriakos .
Second Row: Kyriakou Marios , Efraim Elena , Prastiti Andrea , Moyseos Maria , Nicolaou IreneChrysovalanto , Kyprianou Theodora , Kyriakou Katerina , Michael Irene , Ms Lyghia– Christina Jeronymides.
Back Row: Andreou Elina , Papamoyseos Moysis , Nicolaides Giorgos , Savva Andreas , Christou Vasilis, Andreou Panayiotis , Nicolaides Alexandros , Charalambous Maria .
Absences: Papacosta Avgousta, Loizou Natalie.
3E
First Row: Efthimiou Loukia , Patsalou Elena , Alexandrou Sotiris , Ioannou Georgia , Christofides Kyriakos , Solomou Christodoulos .
Second Row: Mr George Klokkaris, Constantinou Constantinos , Soteriou Gavriella, Nathanael Kalia ,
Theodorou Lambros, Panayi Thanasis, Vasiliou Vasilis, Ms Barbara Kounna.
Back Row: Malathoura Fotini, Georgiou Maria, Mallourides Constantinos, Christoforou Demetris, Psaras
Nicolas, Koukakis Nicolas, Demou Demetris.
Absences: Evangelou Chrisanthi, Athanasiou Kalliopi, Spyrou Kyriakos, Eleftheriou Andria.
4A
First Row: Iacovou George, Koumandari Vassilia, Andreas Andreou, Tatarian Pailag, Georgiou Demetra,
Clark Hayley, Panayiotou Marina, Timm Benjamin
Second Row: Stylianou Andreas, Eftychiou Achilleas, Ketsbaia Lida, Sutton Sam, Sandlers Georgiys
Back Row: Samouride Margarita, Georgiou Antreas, Sisou Varnavas, Petrou Stelios, Porfyriou Stephani,
Marottou Stephania, Jenkins Jack
Absences: Bothe Abbey, Joannou Jennifer, Cavendish Caomhe, Djurovic Iva, Kazantzis George, Petrou
Stylini
4B
First Row: Costi Kyriaki, Georgiou Terpsichori, Aristides Yiannos, Costa Eleni, Zimboulaki Danae,
Kasapis Stavros, Foukkari Loizos, Tingis Sophia, Nooraei Mona
Second Row:Mrs Athanasiou Panayiota, Papachristodoulou Andreas, Theodosi Mariana, Kotsapas Christina, Christou Stella, Xiourouppa Despina, Nicolaou Sergis, Hadjikakou Costas, Mrs Maria Evangelidou
Back Row: Parperi Savvas, Alexandrou George, Harris Sophie , Smith Chelsea, Hadjittoouli Nicolas,
Demetriou Sergios, Georgiou Panayiotis
Absences: Zachariou Elena
4C
First Row: Agathokleous Vasilia, Ioakim Eleni, Ioannou Panayiota, Sergi Maria, Kekkou Christina, Loizou Anna, Frangou Elli, Athanasiou Irene, Koshi Andriani, Erotokritou Antonia, Mrs Maria Evangelidou
Second Row: Ms Stella Charalambous, Adamou Andreas, Hadjimitsi Fivos, Alexandrou Panayiotis, Andreou Theodoros, Mavri Evgenios
Back Row: Demetriou Pavlos, Kyriacou Vasilis, Marangos Christos, Christoforou Timotheos, Pelides
Constantinos, Konomou Petros, Zachariou Minas, Tofias Haris
4D
First Row: Evangelou Elias, Avraam Marisa, Parpouna Vasia, Pafiti Constantina, Kyrpianou Ioanna, Antoniou Chrystalla, Kitsiou Constantinos, Kounnas E. Anastasis
Second Row: Ms.Zena Alambriti, Michael Michalis, Frangoudes Demetris, Hadjiandoni Pantelitsa, Theodorou Irene, Skalioti Anna, Varnava Charalambos, Mandridis Kleitos, Mrs. Maria Evangelidou
Back Row: Amirotos Christos, Efstathiou Efstathios, Ioannou Elias, Koudelis Antonis, Panayiotou Panayiotis,
Xiourouppa Pantelis, Gregoriades Constantinos, Ambiza Melinos
4E
First Row: Anastasiou Eleni, Papapanayiotou Elana ,Challouma Andry, Kassianou Marietta , Charalambous Louiza, Kyriacou Eleni, Hadjivassili Alexandra, Solomou Andreas
Second Row:Mr. Marios Thoma, Philippou Maria, Adamou Irene, Stavride Evanthia, Hadjiconstantinou
Demetris, Petrou Maria, Kanelis Rafael, Mrs. Maria Evangelidou
Back Row: Neokleous Neoklis, Kyriacou Andreas, Chrysaphi Kristianna, Michael Anastasis, Stylianou
Ioannis, Hadjiconstanti Andreas, Matsoukas Demetris, Christoforou Aristodemos, Christou Theofilos
5A
First Row: Mosfili Andria, Zachariou Fodini, Havadja Chrystalla, Shanina Alexandra, Christodoulou
Georgia, Flouri Magdalena Krolikowaska, Bothe Cassidy
Second Row: Demetriou Andreas, Demetriou Maria, Georgiou Giorgos, Kounna Irene, Manoli Marios, Ms
Eleni Malla
Back Row: Petrou Papi, Michalis Challoumas, Hadjichristou Constantinos, Zaouras Panayiotis, Tingis
Alexandros, Kavelis Zacharias, Apostolou Yiannis
Absences: Zachariou Christina
5B
First Row: Kleanthous Eleftherios, Kyprianou George, Assioti Savina, Lambrou Sophia, Psara Doinitsa,
Kounna Chrystalla, Savva Michaella, Elia Despo
Second Row: Mrs. Ioannou Eleni, David Patricia, Andronicou Theodora, Hadjiconstnti Kyriaki, Sidarok
Krystina, Christofi Katerina, Georgiou Rafael, Mrs. Maria Ioannou
Back Row:Kldiashvili Konstantin, Kldiashvili Kirill, Andreou Rafael, Kysela Petros, Menelaou Marios.
Patsalos Kyriakos, Kyriakou Michalis
5C
First Row: Savva Sotiris, Pavlou Chrystalla, Charalambous Maria, Michael Christianna, Poulli Natali,
Vasiliou Rafaela, Eftychiou Christianna, Kostikki Demetra
Second Row: Eleni Ioannou, Koumantaris George, Pavlou Anna, Petrides Alkeos, Ellinas Danae,
Demetriou Constantinos, Zourides George, Stylianou Zacharias, Kounnas Epiphanios, Sakkas Georgia,
Apostolou Angela
Back Row: Michael Antonis, Lappas Demetris, Alambritis Savvas, Zachariou Andreas, Manentzou Sokratis, Panayiotou George, Pasialountas Michalis, Charalambous Toumazos
5D
First Row: Tanos Christos, Eracleous Nicoletta, Stavrou Varvara, Makri Theodora, Constantinou Antri,
Gennadiou Michaella, Nicola Christina, Papoulias Emmanuel, Charalambous Nicholas
Second Row: Mrs. Eleni Ioannou, Ioannou Lucy, Kekkou Rafaela, Issa Stella, Papageorgiou Elena,
Timotheou Stavros, Zinonos Christoforos, Miss Maria Kkimitri
Back Row: Challoumas Alexandros, Pelides Constantinos, Valiantis Demetris, Louca Andreas, Pa
pacostas, Kyriacos, Hadjimatheou Giannis, Orphanides Giorgos, Vasiliou Stelios
6A
First Row: Ebrahim Sara, Xiourouppa Andri, Neophytou Elia, Kyriakou Maria, Christodoulou Irene,
Mrs Evrilia Kayia.
Second Row: Artemiou Panayiotis, Chasapis Yiannis, Georgallides Leonidas, Georgiou Pavlos, Pavlidou
Maria,
Back Row: Mr Michalis Ellinas, Mannouris Georgios, Valeev Marcel, Georgiou Christopher, Karaolis
George, Andreou Andreas, Demetriou Demetris, Michael Critchley Spencer, Challoumas
Michalis.
Absences: Joannou Krystie, Kazamia Gavriella, Kotsapas Paraskevi, Koutsofta Nicole, Petrou Jack,
Petrou Nicolletta, Hadjicostantinou Georgia.
6B
First Row: Matsangou Anastasia, Santi Andrea, Loucatzie Irene, Karagiorgi Elizabeth, Symeou Kallistheni, Palate Kleopas
Second Row: Mrs Frangesca Frangou, Theodorou Andreas, Shadarevian Demetra, Damianou Valentinos,
Phokou Theophanis, Michael Marios, Mrs Evrilia Kiayia
Back Row: Hadjisavas Georgios, Demetriou Christos, Papamichael Illane, Sergiou Sergios, Critchley
Alex
Absences: Pougioukka Constantinos, Demetriou Demetris, Samourides Andreas
6C
First Row: Theodorou Anastasia, Zimboulaki Faviola, Zinonos Niki, Christofidi Antri, Iacovou Marilena,
Erotokritou Despo
Second Row: Demetriou Gregoris, Toumazou Myrofora,Louka Thekli, Karagiorgi Marios, Athanasiou
Charalambos, Kyriacou George, Marinou Marinos, Panayi Theocharis, Evrilia Kiayia
Back Row: Patsalos Andreas, Georgiou Demetris, Alambritis Michalis, Ioulianou Andreas,
Iakovou Anastasis, Sofokleous Andreas, Andronicou Michalis
Absences: Iacovou Iacovina, Monoyios Christodoulos, Neophytou Andreas, Pittarides Gregoris,
From left to right:
First Row: Andri Pentari, George Georgiadis, Marios Hadjivasiliou, Despina Lioliou, Costas Costa, Soterios Panayi.
Second Row: Thegla Papastavrou, Stella Charalambous, Christina Thomaidou Pavlidou,
Despina Kaittani, Christina Karaviotou, Maria Zingi, Maria Kkimitri, Denise Evgeniou, Irene
Petrou, Aggela Venizelou, Eleni Ioannou, Michalis Ellinas
Third Row: Eleni Christodoulou, Constantia Papamarkou, Georgia Markadji, Barvara
Kounna, Lyghia-Christina Jeronymides, Maria Evangelidou, Joanna Panayi, Zena Alambritis, Andri Stavrou, Socratis Petrides.
Fourth Row: Frangesca Frangou, Panayiota Demetriou, Maria Anastasiou, Lena Mahdessian, Myrto Michailas, Maria Ioannou, Eleni Malla, Marios Thoma, George Klokkaris, Andri
Louca.
Back Row: Gregoris Demetriou, Andrea Myriantopoulou, Constantina Constantinou, Angela Apostolou, Panayiota Athanasiou, Evey Pistola, Evrilia Kiayia, Demosthenis Kaoullas,
Petros Kimitris, Michael Hielschler, Christoforos Alexandrou, Elpidoforos Anastasiou.
Absences: Elias Kamaratos, Andros Avraam, Maria Theophilou, Andrea Andreou, Iliana
Tsiapou, Elina Zevrou, Anna Shipettaris.
The PASCAL English School Larnaka Art
Club, for the academic year
2010-2011 aimed for another
exciting year of creative art activities.
The Archery Club this year was held differently to previous
years. Students of
all classes who truly
wished to learn to
The young art club enthusiasts
shoot a bow were
were challenged to construct
invited to enrol in
their own marionette puppets on
and train after school from 2-3:30 every
string. With modelling clay, paint, fabric,
Tuesday.
feather and other various art materials, the outThe few, but dedicated
athletes
showed great improvement during
the course of the
year, testimony to
which are the medals they have received at tournaments held
by the Cyprus Archery Federation.
Specifically, the athletes that distinguished
themselves,
are
Lefteris Kleanthous
(form 5), Michalis
Michail (form 5), Costas Hadjicakou (form
4),
Christoforos
Thoma (form 3) and Alexandra Taratynova
(form 1).
come was exceptionally creative.
One of the club days focused on lino printing,
where the students had the
opportunity to print their
designs on paper and fabric
which were later on sewn
into lavender scented
miniature pillows.
Art Club members also constructed Christmas
Charity Fundraising Ornaments. Every single little craft
was sold!
On the 4th Art club day, a
guest drama therapist, Roula
Demetriou was invited to conduct the session.
The aim…. for students to
experience and comprehend a different conceptual self awareness of art
Congratulations to them all and wishes for and body movement; a
means by which a self rean even better championship year next stricted barrier was broyear!
ken down encouraging the students to become
more expressive and confident.
Club Leaders: Elias Kamaratos
Club Leaders: Rodoula Anastasiou and
Anna Shepettari
Club Leaders:
Soterios Panayi, Giorgos Klokkaris
Members: 15
The aim of the club was to teach the basics of the game of Basketball to the
The aim of the
club
students of PES Larnaca.
was to enhance
team
spirit
to
stuStudents
that
regis- dents, help them develop bowling techtered for the niques and also compete with each
club
took other while at the same time, have fun!
part in learnWe had 35
ing how to
shoot, dribmembers
ble and dein our club.
fend within
During the
the rules of
6 club days
Basketball
we have
while teachvisited the
ers made an effort to teach students
how to be part of a team and how to
K max
take advantage of their skills in order to
Bowling
achieve the goal of winning a game of centre and Rock N’ Bowl (in Dekelia
Basketball.
road) three times .
During the 6 club days, members visited
the Larnaca Kinotiko Center, where they
were provided with a basketball court by
the Cyprus Sports Organisation. This
gave them the chance to practice every
aspect surrounding the game in a secure
environment, with a realistic impression
of how it feels to participate in a real
basketball game.
Students
spent their
time playing
and enjoying
games.
Students seemed to enjoy the time
spent on learning the fundamentals of
basketball and really had fun. The club Club Leaders:
coordinators were pleased with the behaviour and enthusiasm and promised Georgia Markadji, Lena Mahdessian,
that they would keep the club running Eleni Mala
for the following academic year!
Aim of club:
The aim of this club
was to make students
aware of the existence
of other cultural and
religious sites and monuments in the town
of Larnaca. The visit inspired a multicultural spirit that students should have when
attending an International World School.
Approximately there are 15 students in our
club.
Club day No1: Visit to
Angeloktisti Church and
Hala Sultan Tekke
Club day No2:
Visit to Aradippou
Municipality and
Larnaca Police Station
Club day No3: Larnaca Firestation and
EAC
Club day No4:
Pierides Museum, Ayios Lazaros church,
Larnaca’s castle
Club day No5: Ormideia Animal shelter
Club day No6: Aradippou Dog Shelter
Club Leaders : Andri Stavrou and
Thekla Papastavrou
The aim of the Dance
Club was to develop the
dancing skills of students in different genres
such as Hip Hop, Break,
Latin and Greek.
On each club day, students visited Mambo
Dance School and
learned a different
dance.
The club leaders are Eleni Christodoulou
and Christina Thomaides Pavlides,
with approximately 26 members, mainly
girls.
All members really enjoyed the grooves and
were eager to learn a new steps at every
session
THIS CLUB WAS EXCLUSIVE TO OUR GRADUATING YEAR 6 STUDENTS AND
OUR AIM WAS TO GIVE THEM WHAT THEY WANTED!
THEY WANTED SOMETHING DIFFERENT SO ON THE FIRST CLUB DAY, THE
‘ESC’ CLUB LEADERS CALLED THEIR BLUFF BY GOING CLIFF JUMPING AT
THE SPECTACULAR CAPE GRECO SITE. SOON AFTER, WE HIKED TO KONNOS BEACH, GIVING TIME FOR ADRENALINE TO RETURN TO NORMAL LEVELS!
ON THE SECOND DAY, WE TOOK THE SIX FORMERS TO
ALETHRICO WHERE THEY CHALLENGED TEACHERS AND
PEERS TO A PAINTBALL BATTLE...THEY PROVED RUTHLESS IN
ATTACK AND TOOK NO PRISONERS.
OUR FOLLOWING SESSION WAS TO ‘K.O’ GYM IN ARADIPPOU. STUDENTS
LEARNED BASIC MUAY THAI AND JUJITSU TECHNIQUES. THEY ALSO
LEARNED NO TO TAKE ON MR GREGORIS FROM THE SCIENCE DEPARTMENT WHO SOON HAD THEM SUBMITTING, FACE DOWN ON THE COLD,
GRIMY MATS.
OTHER CLUB DAYS INCLUDED VISITING THE SANTA MARINA RETREAT
WHICH OFFERED INDOOR CLIMBING STRUCTURES, A GOLF RANGE, A TOUR
AROUND THE FIELDS AND HORSE RIDING. AT THIS EVENT, EVEN THE
COACH DRIVER FOUND IT DIFFICULT TO KEEP UP WITH THE PACE.
WE CHILLED OUT AT ‘KOT’ BEACH FOR THE FINAL DAY AND PLAYED EXTREME VOLLEY BALL, IN EXTREMELY NICE CONDITIONS AND HAD AN EXTREMELY GREAT TIME!
NEEDLESS TO SAY, THERE WERE SOME PUPILS WHO OPTED NOT TO TAKE
PART (COULDN’T HANDLE IT) IN SOME OF THESE SESSIONS. PERHAPS
BOARD GAMES WOULD BE MORE FITTING FOR THEM, IF THERE WAS A NEXT
TIME. THOSE THAT WERE WILLING AND THOSE THAT WERE GAME, WILL
HAVE MANY MOMENTS TO REMEMBER. IN ANY CASE, WE WISH THE
GRADUATES OF 2011 THE VERY BEST IN THEIR POST PASCAL ENDEAVOURS.
CLUB LEADERS: PETROS KIMITRS, GREGORIS DEMETRIOU, ELPIDOFOROS
ANASTASIOU, DEMOS KAOULLAS, PANAGIOTA ATHANASIOU
Fitness
Name of club: “Fitness Explosion”
Aim of the club: The aim of the ‘fitness explosion’ club was to combine sports activities
along with music entertainment. Students joining us, came in their Pascal PE kit and chose
between gym, step aerobics classes (assisted
by Mrs Andri Louca), or even futsal games.
Club Leaders: Andri
Louca and Maria
Kkimitri
Members: 35-40 students
Description of club’s activities: During club
days we visited a local gym in Larnaca, where
students used the facilities for about an
hour, and then anyone
interested joined Mrs
Andri with her step
aerobics
session,
which usually lasted for
about 40-45 minutes. A
lunch break was mandatory, so after exhausting exercise we relaxed at the stadium’s cafeteria!
Feedback from students: There has been
very positive and encouraging
feedback
from the students involved in the fitness
club, as they had the
opportunity this year to take part in activities
that were not offered in previous years. Most
of the members of the club are well into sports
and gym practices so for them it was really
something they enjoyed doing.
We wanted to teach students
to appreciate nature and cultural historical sites so we
took to the outdoors. These
are some of the outstanding
sites we took in.
Places we Visited:





Stavrovouni
Seacaves
Nature reserve in Germasogia
Chirokitia & The Old Serai
Spilia Tis Athasias
...sometimes, words
just aren’t enough...
This year the horse-riding
The Jamming club was created to assemble
both school choir and school band in to one enwas under the guidance
semble.
of Ms. Angela AposIn order for a student to become a member of
tolou and Ms. Christina
this club, they had to pass an audition where
Karaviotou. The club’s
his/her talent was presented.
aim was to introduce students to the grace
Each member has a musical talent and the
and beauty of the equestrian sport.
whole club consists of 14 members: singers,
guitarists, violinists, bouzouki players, drummers and pianists.
All club days were spent
at the Salt Lake Stables
i
n
Dromolaxia where the
staff not only guided
and taught our students
how to ride but also how
to groom and care for the horses.
The aim of the club was to prepare for upcoming school events such as national celebrations,
Christmas, Valentine’s Day etc.
Besides preparing for school events, students
had the opportunity to perform their own music
choices as a group and exchange musical ideas
regarding different musical genres. They have
learned how to improvise music and realised
how much work needs to be dedicated in order
The highlight of the year was the Gym- for a musical group to be successful.
khana organized by the
staff on our last club They also had the opportunity to visit a local
radio station allowing them to talk on the air
day where the students
about their club activities and their school.
competed in many fun
activities.
According to some club members the Jamming
club has motivated and encouraged them to expand their musical interests. New ideas have
been proposed for future club activities on and
off school grounds which are going to be considered.
Club leaders: Andreas Avraam
Andrea Andreou
Jewellery
Mosaic
This year, the Mosaics Club students
worked with Ms.
Varvara Kounnas
and Ms. Denise
The Jewellery Making Club was formed Evgeniou on various projects where
they decorated artimainly for girls.
facts like mirrors,
We wanted to show the students simple, photo frames, tissue
clever and cheap ways to make their boxes and coasters
create
some
own jewellery by using different tech- to
lovely work for their
niques, tools and material.
personal use.
Students who chose the club gained not
only knowledge on how to create trendy,
cheap and beautiful jewellery for themselves or friends, but also enjoyed every
minute of it.
The first club day
involved students
visiting Helen’s Art
Studio where they
Irene Petrou was the leader of the
were shown how to
Club and Elina Zervou and Maria An- cut tiles with the special cutters, how
astasiou were the teachers who offered to glue and create designs on wood.
their valuable help. Our Club accommodated 22 wonderful ladies.
The following club
days were spent
working on projects,
grouting and shining
the finished products
The aim of the photography club was to
teach students the basics of photographic
composition, lightning, photographing people,
a
s
well
as
e s sentials
of image manipulation
a n d
correction
using
Adobe
Photoshop.
Our club was not only entertaining but also
very productive as each and every student has
managed to get a PADI certificate for open
water.
The
first
lessons
were about
learning
the theory
and applyM r .
E l i a s ing it in
Kamara- s w i m m i n g
tos, Ms Andri Pendari and Ms Constantia pools.
Papamarkou ran the club and they much
enjoyed the opposrtunity
of working with the students and showing
eachother the ins and outs of digital
photography.
There were approximately 15 students who
took an interest in this club and as well as
taking pictures around the school on the five
club days they also went on a trip to Faros
when the weather improved in April.
At Faros students took pictures of the lighthouse and the sea while at the same time
enjoyed the sunny day on the beach.
On the
d a y
worked
toshop
their
t o form a
of their
t h e
club days.
last club
students
on Phostitching
photos
gether to
collage
photos of
previous
Included are some these collages created by
the Photography club of 2010-2011.
Later on
we went
diving at
sea in
Protara.
Everyb o d y
enjoyed
it
and
had fun!
AIM OF CLUB: To improve students’ swimming techniques and to
introduce them to life saving skills in the water. The
first two club days were
spent practicing swimming skills such as entering the pool correctly, refining swimming strokes and turns.
On the third day we
found ourselves at the
L i f e
Saving
Unit in
L a r naca’s Marina where the
students enjoyed an interesting talk by three Life
Saving Instructors.
We carried on with a practical session on life
saving skills on our 4th day when students
practiced on each other. Our 5th day was
spent at the ΓΣΖ stadium as part of the
school’s sport day activities. We had great
fun on our last splash in the pool where the
students competed with each other in games.
GIRLS SELF DEFENCE
Many people think of selfdefence as a karate kick to
the groin or jab to the eyes
of an attacker.
But self
-defence actually means
doing everything possible
to avoid fighting someone
who threatens or attacks
you. Self-defence is all
about using your smarts,
not your fists. But if you cannot avoid a fight,
learn at least how to enjoy it!
T h i s
year we
had 26
g i r l s
w h o
really
enjoyed and learned lots of
techniques and this is the program that we followed throughout the year:
1st Club Day – GSZ Stadium Judo
2nd Club Day – GSZ Stadium Judo
3rd Club Day – Barbarian Gym – Kick Boxing
4th Club Day – Barbarian
Gym – Kick Boxing-yoga
5th
Club Day – Aspida
Team – Brazilian Jiu Jitsu
6th Club Day – GSZ Stadium - Judo
Club Leaders: Despina Kaitani, StellaClub Leaders: Marios Thoma, Aspasia
Charalambous
Manti, Lyghia Jeronymides
Also known as the ‘Ping-Pong’ club, Table Tennis
Hello,
we
Christina
Christoforos
are
Zingi
Maria- is a new club within the grounds of Pascal English
and School Larnaka. Its club leaders are Mr Michalis
Alexandrou
and we are responsible for the Tennis Club.
Ellinas and Mr Sokratis Petrides who are responsible for developing this new sport in school. The
main aim of the club is to teach members the basic
Our aims for the club
rules and techniques of the game and hopefully
were to teach our mem-
help them learn how to play.
bers how to play tennis
and to teach them basic
It is important to note that there was a great re-
techniques and hopefully we may have a Ten- sponse for joining the club and we managed to
nis Club in the future that can compete with
other schools.
serve the interest of around 50 pupils. Club activities were held on school premises during the six
club days. Two fully equipped rooms were created
in order to serve the club’s needs in which table
We have had six club days
tennis rules and techniques were successfully
taught and various in-school tournaments organ-
during which we taught the ized.
children how to use the tennis racquet
At last, it is important to stress the fact that most of
correctly and techniques in
the students were highly satisfied with the creation
both forehand and back-
of this new club and therefore we managed to re-
hand strokes. Members also
ceive positive feedback which was encouraging in
had a chance to learn the service, volley, slice helping us to decide on its running the following
and how to topspin the
ball.
All these skills were
taught and practiced during our club days and on our last day we held
a tournament where the students competed
academic year.
As club leaders we were aiming to
show our students what goes on behind closed curtains and what it takes
to put on a production.
There
were
15
members in our
club who showed
enthusiasm
and
genuine interest in
the whole process,
which can be exciting and extremely
rewarding though laborious at times.
During the six-day clubs programme,
the following occurred:
Actor-producer, Mr Xenios Xenofontos visited
us on school premises
and spoke to us about
the whole industry surrounding theatre in Cyprus.
‘Yoga’ means union between the mind, body
and soul. It is the perfect way to ensure overall health and physical
fitness.
The aim of the club is to help members
to create a balance between the body
and the mind, and to accomplish all of
the above.
In all, there were ten
members, and the club
leaders are Evrilia
Kiaya and Maria Evangelidou.
During club days we visited a yoga studio where
our
students
were
taught different postures
and exercises from an
Acting coach Mrs Flora excellent teacher.
Charalambous Pasavva
gave our members les- They loved it and most
sons and showed us of them will continue
how to use make up to practicing yoga, as
achieve a more mature
they found it really inlook. She also showed
us how to form realisti- teresting.
cally gruesome wounds. It goes without saying that students enjoyed these
sessions.
CLUB LEADERS: ANGELA VENIZELOU
ELENI IOANNOU
AND
The second of our two-year Comenius project involving schools from Germany,
Finland, Denmark, Turkey, Slovenia, France and Cyprus started with Mr Elias
Kamaratos and Mrs Maria Anastasiou taking Raphael Matsangos and Stella
Kakoulli of from 3 on a memorable trip to Germany. Visits to an open cut coal
mine, a glass factory and the Berlin wall stood out during this trip.
In February Mrs Denise Evgeniou and Ms Despina Kaittani travelled to Slovenia
with Elina Andreou and Tonia Yerolemou also of form 3. Although it was very cold
it remains an unforgettable experience for all as warm friendships were forged.
The Comenius Project drew to a close in April when Mr. Kamaratos and five students Charalambos Lappas, Joanna Georgiadis, Chrysanthi Evangelou, Christina
Thoupou and Kallia Athanasiou boarded a flight to Helsinki, Finland. It was the beginning of spring and the ice in bay of Helsinki was just beginning to melt. This
didn’t stop Charalambos however, from diving into the frozen waters after coming
out of a hot sauna. During the closing concert Joanna mesmerized the students
teachers and parents by singing at the closing concert.
Workshops, concerts and educational visits were in the programme for all the
Comenius trips and much credit must
go to the organizers for doing a
wonderful job as to the hosting families who made all students feel welcome and at home.
The Comenius Project is a wonderful
opportunity for students and teachers to make new friends and meet
new cultures. We look forward to
participating in more such projects in
the future.
Time: 1.30hrs
LASS M
ENAGERIE
TTHE
HEGGLASS
MENAGERIE
Date: 23rd March 2011
Directors: Mrs Angela Venizelou and Eleni Ioannou
This year, PASCAL English School Larnaka put on the theatrical play, ‘The
Glass Menangerie’ with great success. On the 23rd of May, the Founder’s Theatre was full to the brim with spectators waiting to watch this magical performance. Our actors were fantastic and got rave reviews. They included, Sergios
Sergiou, Irene Christodoulou, Mariam Venizelou, Andreas Sophokleous, Georgia Hadjiconstantionou. Other students that played an important role in the
making, are Michaella Gennadiou, Barbara Paschali, Stella Issa and Savvas
Alambritis. Back Stage hands were George Karaolis and Faviola Zimboulakis.
THE GLASS MENAGERIE is a memory play, and its action is
drawn from the memories of the narrator, Tom Wingfield. Tom
is a character in the play, which is set in St. Louis in 1937. He is
an aspiring poet who toils in a shoe warehouse to support his
mother, Amanda, and sister, Laura. Mr. Wingfield, Tom and
Laura’s father, ran off years ago and, except for one postcard, has
not been heard from since.
Tom confides to Jim that he has used the money for his family’s
electric bill to join the merchant marine and plans to leave his
job and family in search of adventure. Laura refuses to eat dinner with the others, feigning illness. Amanda, wearing an ostentatious dress from her glamorous youth, talks vivaciously with
Jim throughout the meal.
Amanda, originally from a genteel Southern family, regales her
children frequently with tales of her idyllic youth and the scores
of suitors who once pursued her. She is disappointed that Laura,
who wears a brace on her leg and is painfully shy, does not attract any gentlemen callers. She enrols Laura in a business college, hoping that she will make her own and the family’s fortune
through a business career. Weeks later, however, Amanda discovers that Laura’s crippling shyness has led her to drop out of
the class secretly and spend her days wandering the city alone.
Amanda then decides that Laura’s last hope must lie in marriage
and begins selling magazine subscriptions to earn the extra
money she believes will help to attract suitors for Laura. Meanwhile, Tom, who loathes his warehouse job, finds escape in liquor, movies, and literature, much to his mother’s chagrin. During
one of the frequent arguments between mother and son, Tom
accidentally breaks several of the glass animal figurines that are
Laura’s most prized possessions.
As dinner is ending, the lights go out as a consequence of the
unpaid electric bill. The characters light candles, and Amanda
encourages Jim to entertain Laura in the living room while she
and Tom clean up. Laura is at first paralyzed by Jim’s presence,
but his warm and open behaviour soon draws her out of her
shell. She confesses that she knew and liked him in high school
but was too shy to approach him. They continue talking, and
Laura reminds him of the nickname he had given her: “Blue
Roses,” an accidental corruption of pleurosis, an illness Laura
had in high school. He reproaches her for her shyness and low
self-esteem but praises her uniqueness. Laura then ventures to
show him her favorite glass animal, a unicorn. Jim dances with
her, but in the process, he accidentally knocks over the unicorn,
breaking off its horn. Laura is forgiving, noting that now the
unicorn is a normal horse. Jim then kisses her, but he quickly
draws back and apologizes, explaining that he was carried away
by the moment and that he actually has a serious girlfriend. Resigned, Laura offers him the broken unicorn as a souvenir.
Amanda and Tom discuss Laura’s prospects, and Amanda asks
Tom to keep an eye out for potential suitors at the warehouse.
Tom selects Jim O’Connor, a casual friend, and invites him to
dinner. Amanda quizzes Tom about Jim and is delighted to learn
that he is a driven young man with his mind set on career advancement. She prepares an elaborate dinner and insists that
Laura wear a new dress. At the last minute, Laura learns the
name of her caller; as it turns out, she had a devastating crush on
Jim in high school. When Jim arrives, Laura answers the door, on
Amanda’s orders, and then quickly disappears, leaving Tom and
Jim alone.
Amanda enters the living room, full of good cheer. Jim hastily
explains that he must leave because of an appointment with his
fiancée. Amanda sees him off warmly but, after he is gone, turns
on Tom, who had not known that Jim was engaged. Amanda
accuses Tom of being an inattentive, selfish dreamer and then
throws herself into comforting Laura. From the fire escape outside of their apartment, Tom watches the two women and explains that, not long after Jim’s visit, he gets fired from his job
and leaves Amanda and Laura behind. Years later, though he
travels far, he finds that he is unable to leave behind guilty
memories of Laura.
WINTER
ll things
a
s
r
e
v
o
c
Snow
l inside.
l
a
g
n
i
z
e
e
Fr
ite blanh
w
y
h
c
n
Like a cru
ke t
4A
Ben Timm
TIGER
Tiger wide awake
Lying watching in the brush
Waiting for dinner .
Abbey Bothe 4A
FEARF
E AR
The wi
nd i s w
hirling
No voi
ce, onl
y breat
The ma
h.
n is sle
eping,
I seek
a hideout
While m
y terrif
ying fe
Is trap
ar
pe d i n
my min
d
Demet
ra Geo
rgiou 4
A
TEARS
COLD
Such freezing weather
Cold, slippery ice.
Unpleasant, with a shiver
Sophia Tingi& Mona
Mooraei 4B
MUSIC
ic sounds
Song, melod
our heart
y
o
t
in
p
e
e
d
Drawn
g.
Exhilaratin
Stephanie
i&
r
a
d
n
a
m
u
VasiliaKo
4A
Porphyriou
Unchangeable pain
Drops of heartbroken pain Flowing
Bend my sanity.
Eleni Costa 4B
SALMON
Salmon in th
e
Fighting the ra stream
ging torrent
Fighting for it
s life.
George Sand
lers & Jack Je
nkins 4A
What is the point of living if everything you live for is gone?
The key rattled in the lock. ‘Stand back and face the wall,’ came the harsh voice of the security guard. He dumped
a brown lumpy stew in front of me, his brown eyes looking at me with hatred. The stew wafted towards me, making me gag on the putrid smell of rotten vegetables and old meat. The door slammed shut and I was locked up
once again.
The blank walls stared at me, making me feel like a caged animal. The bed groaned heavily as I sat down on it. I
looked up at the barred window. There was no breeze to cool the stifling air. I began to gasp for breath, feeling
claustrophobic; the air pressed in on me making the sweat marks on my shirt grow. I blinked once and then I saw
the flames.
They were hungrily devouring the houses. The acrid smell burnt my throat. I was screaming. My house was on
fire. Then the white walls of the prison cell came into view. I fell to the floor and rolled into a ball. Why was this
happening to me? Tears poured down my face. ‘I’m innocent!’ I screamed but no-one heard me. No-one answered. I was trapped!
I remember that night. I was walking down the dark road, laughing to myself. I might have drunk a bit more than
I had intended to, but it was a party after all. I skipped along the streets, in my own world, until I saw the strong
orange glow.
The cold night air hand suddenly hit me. I knew something was wrong. I began running towards the orange thing,
towards my house. I turned the corner and stared uncomprehendingly at the house on fire. It was mine! I had
jumped over the back fence and walked into my garden. ‘James!’ I screamed. My husband was in that house with
four of his friends. I was too late. I opened the back door choking on the fumes. I watched a photo of me and my
husband being eaten up by the flames. My feet crunched the pieces of debris and glass as I ran.
I knew I could die but I had to find him. Thick smoke came from the kitchen. There was fire everywhere; it was
burning my skin. I slammed into the kitchen door. The fire suddenly blew outwards, burning my face. Before I
ran, I glanced into the room. Five figures lay on the floor. I stared at one of them. I watched the fire lick away
my husband’s face. Then I ran.
I was accused of murder. Many witnesses had seen an almost drunk woman running out of the door. The parents
of the other victims had wanted justice. I was sent to prison. I was locked up. I was innocent.
I stared at the filthy floor. I had to escape from here. It is killing me, but I don’t have the key. In my mind, the
cell suddenly erupted in flames. I began screaming. ‘Give me the key! I’m innocent! GIVE ME THE KEY!’ My
nails began scratching the door. They became bloody stubs but I still continued. The fire was choking me. The
acrid smell burnt my throat.
‘Stand back and face the wall.’ I heard the words from a distance. My ears were ringing from the explosion that
made my house collapse. I suddenly knew how to escape. It wasn’t the cell key I needed. It was something better, stronger, more final. I stood backwards as the flames engulfed me. The guard came in, shouting and pointing.
I lunged at him.
I ripped the gun out of his holster, leaving bloody marks where my fingers had touched it. I pulled the gun towards
me. The cold metal touched my head. ‘This is my key to happiness,’ was my last thought before my fingers
closed around the trigger.
What is the point of living if everything you live for is gone?
By Katerina Kavourides 3B
(Winning Essay Competition story between all Pascal schools)
What was the Short-Term Significance of the Blitzkrieg Tactic?
The Blitzkrieg was a strategy used by the Germans
in World War 2 and even though they ultimately
suffered defeat its short term effects cannot be underestimated nor can its tactical ingenuity for that
time, proof of which can be found in the fact that it
was used in recent times during the Gulf Wars. The
Blitzkrieg was one of the pinnacle tools of Germany’s early success along with Hitler’s hold on
power and Germany’s economy. One could argue
that without it the course of the war would have
been drastically altered or ultimately prevented.
Earlier use of
a
smaller
scale Blitzkrieg
was
used by General Edmund
Allenby during the Battle
of Megiddo
in September
1918 . The
first
major
use of the
Blitzkrieg
was in 1939
when Poland
was invaded.
This of course forced Britain and France to declare
war on Germany but more importantly, this was the
first introduction of the Blitzkrieg and its use of
technology. This however has been argued by historians such as Matthew Cooper who stated that the
Blitzkrieg effects were, “only incidental by-products
of the traditional manoeuvres”. None the less, Poland’s downfall would not have been as swift had it
not been for the Blitzkrieg.
One could argue that had the Germans invaded more
“traditionally” this would have given time for
France and Britain to react and send help to Poland
making German fight a war on both fronts. This in
turn could have proved disastrous. However, the
Blitzkrieg gave the Germans victory to turn its attention on France with few loses.
The same claim can be made in France. The French
had established the Maginot line which was to be
used against the Germans. This can be seen as proof
that the French were expecting a trench war much
like World War 1. However, the Germans’ Blitz
allowed them to
bypass
the
Maginot
line
and surrounded
it by making a
daring advance
through the Ardennes region in
Belgium. It was
clear
that
through the use of the Blitzkrieg Germany was able
to completely out-manoeuvre and overwhelm
France, who were unprepared for this type of war.
This is shown in the French President (of the Ministerial Council) Reynaud’s speech who commented
on the collapse on 21 May 1940, “The truth is that
our classic conception of the conduct of war has
come up against a new conception…” One could
also argue that had the Germans not used Blitzkrieg
and invaded head on into the Maginot line the war
would have been drawn out and had given time for
the Allies to react and reorganize and possible defeat the Germans whose war potential was still developing. The Blitzkrieg also eliminated British
forces in France by advancing through Belgium and
eliminating the BEF. We can see that the main principle of Blitzkrieg, made clear in its detention of
“lighting war”,
was to eliminate
the enemy before it had time
to prepare and
plunge it into
chaos. By doing
this Hitler was
able to take control over Europe
and focus on the
USSR. It can be concluded that had it not been for
the blitzkrieg the whole invasion of Russia would
have been impossible due to fear of war on both
fronts.
Prior to the war the Nazi had secured their hold on
power. However, it was not absolute. There was
still opposition from the population which can be
seen from D.J.K.Peukert, who said, “…the longer
the regime lasted, the less popular it became.” The
Blitzkrieg helped change that as new, quick victories strengthened Hitler’s support among the population. This in turn allowed him to stay in power. Had
the war against France been prolonged, the regime’s
support would have faded away and opposition
would have used it to their advantage. In that scenario one could claim that the Blitzkrieg was the
main reason for the continuation of Hitler’s rule and
the support of the Nazi war machine. Blitzkrieg also
aided the German economy. Even though unemployment fell from 7.4 percent these were only due
to short term effects such as road building or construction. The Blitz helped stimulate the German
economy by increasing pressure on industrialization
and as Overy stated, “…by spring of 1940, the German economy was set on the path of full mobilization”.
The Blitzkrieg not only increased demand for industrial labour but also presented opportunity to capture
enemy goods from occupied countries and sending
them back to Germany to increase the wealth of the
population and strengthen support as well as decrease poverty. As Ian Kershaw stated, “…only
through expansion-impossible without war-would
Germany, and the national Socialist regime, survive” However a long war would put strain on both
the economy which had not fully recovered from the
First World War, as well as keeping the population
in place. As such it can be stated that through the
Blitzkrieg the war was able to continue and the Nazi
regime be maintained. Also, due to the British
blockage there was a large scarcity of resources. It
is unlikely that Germany would have been able, or
supported, to continue the war without the Blitzkrieg victories and foreign resources plunder. Had
it not been for an overwhelming defeat the Nazi
would have been forced to introduce rationalization
and one should not underestimate the extent of possible opposition within the early years of the regime.
During the blockade the German economy was
aided by Russian aid and Williamson stated that
“ironically, it was probably only Russian assistance
that prevented an early German economic collapse…”
One main benefit that Blitzkrieg brought was solidifying the partnership between the Nazi regime and
the German elite: the army. Hitler had strengthened
his hold on the army through the “night of the long
knives” and by the oath swore to him as well as
gaining support through rearmament .
However many still some still opposed Hitler’s
ambitions such as Field Marshal von Blomberg
and General von Fritsch who believed that Germany was unprepared. Both were eliminated.
However, this showed the army was still lacking
faith in Hitler. The Blitzkrieg fast victories over
France quickly earned Hitler the view of a tactical
genius and secured the army’s support. Had the
war not been won so quickly, opposition within the
army would have grown as it did when the tide
turned and in 1944 when a failed bomb plot was
carried out. As such if the Blitzkrieg had failed,
army opposition would have grown towards Hitler
and the German war effort would have been crippled. The blitz strengthened the Nazi resolve allowing it to push further into the war. This also
allowed the army to gain both the experience and
confidence it needed before attempting operation
Barbarossa in Soviet Russia.
Operation Barbarossa, which of course ended in
failure, was the combination of all the previous
tactics learned by the Nazi. As mentioned earlier
the Blitzkrieg eliminated the possibility of war on
two fronts and had created enough breathing space
to launch an attack against communist Russia. In
its early stages the operation was a success. German took large portions of Russian soil. Even
though some historians such as Kitchen state that,
“the army which was thrown against the Soviet
Union was only marginally larger…that which invaded France.” This again provided, yet limited
due to the policy of “scorched earth” , raw resources and economic aid. It also provided opportunity to introduce forced labour camps. More importantly the large areas taken via the Blitzkrieg
allowed the incarceration of the many Jews on the
west of Russia which was ultimately Hitler’s goal.
The Blitzkrieg allowed the Germans, as in France
and Poland, to eliminate the air force of the USSR
which in the short term, gave them a huge advantage over the enemy and paved the way to victory
while the enemy would have to rebuild their losses.
As we can see the Blitzkrieg did not focus on a
“fair” fight but rather the use of surprise and crippling the enemies counter attack power and machinery. As in the other cases had the Russians
been able to mount a successful counter attack of
defensive perimeter, the war would have taken a
different turn. However, Germany invaded without a declaration of war and the soviets were
caught unaware. This can be seen in a soviet
broadcast, “Today at 4 o'clock a.m., without any
claims having been presented to the Soviet Union,
without a declaration of war, German troops attacked our country.”
In the end however with the fall of winter, whereby
the soldiers were, “scarcely better equipped” than
in France, Germany was
pushed back and morale
sank as a German pilot,
Theodor Plotte wrote,
“the crew mutinied. They
didn’t want to fight anymore…”
The Blitzkrieg also
proved to be a valuable
show of power to potential allies such as Italy, although there tactical use can be questioned. They
provided support to Germany through the war until
their defeat in 1945 in the Spring offensive. However, it is doubtful that Italy would have joined the
war even though its dictator Benito Mussolini had
close relations to Hitler and political similarities.
Though the Blitzkrieg however Hitler was able to
bring Italy on its side and secure an alliance if the
two powers. Had the war again stretched out, Italia’s
involvement would have been unlikely.
Blitzkrieg didn’t only bring short term effects on
land and sea. In the battle of Britain Germany engaged in a Blitzkrieg
compromised solely of
Arial assaults and
bombing raids. The
Blitz here was intended
to destroy morale
through bombing raids.
However some claimed
that “No decisive success can be expected from terror attacks on residential areas.” One can argue that even if it did
strengthen morale in the short run it would have
been damaging to
the
populations
sense of security.
As one British politician
recalls
“Everyone is worried about the feeling in the East End,
where there is much bitterness” But it can be stated
that the blitz was more damaging to the Germans as
it failed in its main objective to bomb Britain into
submission and only served to divert its air forces
from the eastern front as well as suffering heavy
loses.
Many such as O’Neill stated,
“What makes this story worth
telling is the development of
one idea: the Blitzkrieg. The
German Army had a greater
grasp of the effects of technology on the battlefield, and
went on to develop a new
form of warfare by which its
rivals, when it came to the
test, were hopelessly outclassed.” However many others claimed, such as
German historian Karl-Heinz Frieser, that the notion of 'Blitzkrieg' was "a worldwide delusion."
The Blitzkrieg success was clearly due to the outdated tactics of the Allies particular the French
who underestimated the tactical use of tanks and
aircraft.
However one should not underestimate the Blitzkrieg as being simply a tool for war. It had a much
larger impact on politics back in Germany
as well as economic
effects and foreign support during the early
stages of the war.
These short terms ultimately lead to total war
which would have been
largely impossible without the use of the Blitzkrieg.
1089 ΚΑΙ ΟΛΑ ΑΥΤΑ
ΠΕΡΙΛΗΨΗ
Η εργασία αυτή έχει ως κύριο στόχο να αναδείξει την μαγεία των μαθηματικών που περικλείεται σε
όμορφα θεωρήματα, με υπέροχες αποδείξεις και σημαντικές εφαρμογές. Η εργασία μας χωρίζεται
σε δύο μέρη. Στο πρώτο μέρος τονίζουμε την σημασία και συνάμα την ομορφιά της απόδειξης στα
μαθηματικά. Στην προσπάθεια μας αυτή καταπιανόμαστε με αποδείξεις διαφορετικού τύπου κάποιων θεωρημάτων από την άλγεβρα και την γεωμετρία καθώς και κάποιας ενδιαφέρουσας ιδιότητας των τριψήφιων αριθμών σε σχέση με τον αριθμό 1089. Στο δεύτερο μέρος κάνουμε μια ιστορική
αναδρομή σε κάποιες από τις σημαντικότερες έννοιες των μαθηματικών όπως το π και το e δίνοντας ιδιαίτερη έμφαση στις εφαρμογές τους στην γεωμετρία, την τοπολογία, τις σειρές και τις πιθανότητες. Η εργασία μας βασίζεται στο εξαιρετικό βιβλίο “1089 and all that, a journey into mathematics” του διακεκριμένου μαθηματικού David Acheson.
Μέρος Α
Η επίλυση προβλημάτων και ασκήσεων στα μαθηματικά είναι από μόνη της μια πνευματική πρόκληση. Η έξυπνη χρήση των θεωρημάτων και ιδιοτήτων που οδηγούν στην επίλυση είναι μια δημιουργική εργασία που διεγείρει το μυαλό. Η ικανοποίηση της λύσης είναι μοναδική. Η απόδειξη
όμως είναι αυτό που σε κάνει να ενθουσιάζεσαι, να θαυμάζεις τα μαθηματικά, να τα ερωτεύεσαι!
Θα προσπαθήσουμε να αναδείξουμε το πιο πάνω, παρουσιάζοντας μερικές απλές αλλά πολύ κομψές
αποδείξεις κάποιων σημαντικών μαθηματικών εννοιών.
Α1.
.
Αν α,β και γ είναι οι πλευρές ενός ορθογωνίου τριγώνου και η γ είναι η μεγαλύτερη
πλευρά (υποτείνουσα) τότε
. Αυτό δεν είναι άλλο από το Πυθαγόρειο
θεώρημα, ένα από τα διασημότερα θεωρήματα των μαθηματικών.
Ενας όμορφος τρόπος να αποδείξουμε το θεώρημα γεωμετρικά είναι ο πιο κάτω.
Παίρνουμε ένα τετράγωνο με πλευρά α+β και δημιουργούμε εσωτερικά τέσσερα
τρίγωνα με πλευρες α,β,γ όπως φαίνεται στο σχήμα.
Ως αποτέλεσμα δημιουργείται ένα τετράγωνο με εμβαδόν
.
Τώρα ας σκεφτούμε ότι τα τρίγωνα είναι άσπρα χαλάκια σε
σκούρο πάτωμα. Η επιφάνεια του πατώματος που είναι ελεύθερη έχει έμβαδον
. Μετακινούμε τα τρίγωνα κατα τέτοιο τρόπο ώστε να κατάλαβουν τις νέες τους θέσεις όπως φαίνεται στο
σχήμα.
Το εμβαδόν του πατώματος που είναι ελεύθερο αποτελείται από δύο τετράγωνα. Το ένα έχει πλευρά
α και το άλλο πλευρα β, έτσι μαζί έχουν εμβαδον
τώρα έχει εμβαδόν
Άρα,
Αυτό σημαίνει ότι η ελεύθερη επιφάνεια
. Το εμβαδόν της ελεύθερης επιφάνειας όμως πρέπει να είναι το ίδιο.
.
Α2.
.
Στην άλγεβρα συναντάμε συχνά ταυτότητες οι οποίες είναι πολύ χρήσιμες στην
επίλυση εξισώσεων. Μια από αυτές είναι
Για παράδειγμα
Πιο κάτω παρουσιάζουμε μια γεωμετρική απόδειξη της ταυτότητας.
Σχηματίζουμε ένα τετράγωνο με πλευρα χ+α όπως φαίνεται στο σχήμα.
Το εσωτερικό του τετραγώνου μπορεί να χωριστεί σε τέσσερα μέρη:
2
x2 .
aa22 .
τετράγωνο με πλευρά α δίνοντας εμβαδόν
τετράγωνο με πλευρά χ δίνοντας εμβαδόν
ax
ax .
ax
ορθογώνιο με πλευρές χ και α δίνοντας εμβαδόν
.
2
22
2
2
x aa ax
ax ax
ax x  2ax  a
ορθογώνιο με πλευρές χ και α δίνοντας εμβαδόν
Άθροισμα εμβαδών στο εσωτερικό=
Εμβαδόν τετραγώνου με πλευρά
+
+
+
x  a ισούται με
Το εμβαδόν του τετραγώνου
ισούται με το αθροισμα των εμβαδών του εσωτερικού, άρα
=
.
( x  a )( x  a )  ( x  a ) 2 .
πρέπει να
.
Α3. Το
22 είναι άρρητος!
Όλοι οι αριθμοί που μπορούν να γραφτούν σαν λόγος δύο ακεραίων αριθμών ονομάζονται ρητοί. Όλοι οι άλλοι που δεν
μπορούν να γραφτούν με αυτό τον τρόπο ονομάζονται άρρητοι. Ένας από αυτούς είναι το
το
22
.Θα αποδείξουμε ότι
2 είναι άρρητος χρησιμοποιώντας την μέθοδο της εις άτοπον απαγωγής.
22 ΔΕΝ ΕΙΝΑΙ ΑΡΡΗΤΟΣ άρα μπορεί να γραφτεί σαν κλάσμα. Δηλαδή στην πιο απλοποιημένη
m
2
n
Υποθέτουμε ότι το
του μορφή γράφεται ως
όπου το m και το n είναι ακέραιοι χωρίς κοινούς παράγοντες.
m2
2 2
m22 22nn22.. Αυτό
n , δηλαδή m
Στη συνέχεια υψώνουμε στο τετράγωνο και τις δύο πλευρές και παίρνουμε
22
2
m
nn22
mm22
m
m
σημαίνει ότι το
είναι 2 φορές ένας ακέραιος αριθμός (
) άρα το
είναι ζυγός αριθμός. Όμως αν το
είναι ζυγός αυτό σημαίνει ότι το m είναι ζυγός γιατί
(μονός)  (μονός) = (μονός) ενώ (ζυγός)  (ζυγός) = (ζυγός).
Τώρα, αφού το
m είναι ζυγός σημαίνει ότι το m μπορεί να γραφτεί ώς 2r όπου το r είναι ακέραιος. Μα αυτό ση-
22rr2  2n22  4r22  n22  2r22 

2

2  22  2n  4r  n  2r  22
nn είναι ζυγός και επομένως το nn είναι ζυγός.
nn
μαίνει ότι
2
22
m
m
n
Δηλαδή σύμφωνα με την αρχική μας υπόθεση ότι το
δεν είναι άρρητος καταληγούμε ότι το
και το
είναι
ζυγοί αριθμοί. Αυτό όμως έρχεται σε αντίθεση με το ότι το m και το n είναι ακέραιοι χωρίς κοινούς παράγοντες γιατί
δύο ζυγοί παντα διαιρούνται με το 2. Αρα η αρχική μας υπόθεση είναι λανθασμένη που σημαίνει ότι το
είναι άρρητος!
22
Α4. 1089
Σκεφτείτε ένα τριψήφιο αριθμό όπου το πρώτο με το τελευταίο ψηφίο διαφέρουν κατά 2 ή περισσότερο ,(π.χ
732).
Τώρα αντιστρέψτε τον και αφαιρέστε τον μικρότερο από τον μεγαλύτερο, δηλαδή για παράδειγμα ,
732 – 237 = 495.
Τέλος αντιστρέψτε τον νέο τριψήφιο αριθμό και προσθέστε,
495 + 594= 1089.
Ας δούμε ακόμα ένα παράδειγμα,
613 – 316 = 297,
297 + 792 = 1089.
Και ακόμα ένα,
856 – 658 = 198,
198 + 891 = 1089.
Αυτό ισχύει για όλους τους τριψήφιους και εμείς θα το αποδείξουμε!
Κάθε τριψήφιος αριθμός όπου το πρώτο με το τελευταίο ψηφίο διαφέρουν κατά 2 ή περισσότερο μπορεί να γραφτεί ως εξής:
100(x+n) + 10y + x όπου x,y,n ακέραιοι και n  2.
Αντιστρέφουμε και αφαιρούμε,
100(x+n) + 10y + x - (100x + 10y +x+ n )
= 100x + 100n + 10y + x -100x-10y –x – n
= 99n.
Για,

n=2, 99n = 99  2=198
n=3, 99n = 99  3= 297

n=4, 99n = 99  4=396
Παρατηρούμε ότι το πρώτο ψηφίο ισούται πάντα με n-1 , τo μεσαίο με 9 και το τελευταίο με
10-n.
Άρα η διαφορά 99n μπορεί να γραφτεί ως 100(n-1)+10  9+ (10-n).
Αντιστρέφουμε και προσθέτουμε,

100(n-1)+10  9+ (10-n)
+
100(10-n)+10  9+ (n-1)
--------------------------------100n-100+90+10-n+1000-100n+90+n-1
= 1089!
Μέρος Β
Σε αυτό το μέρος θα ασχοληθούμε με δύο ιδιαίτερους αριθμούς στα μαθηματικά το π και το e που εμφανίζονται
σχεδόν συνέχεια σε διάφορους τομείς των μαθηματικών.
Το π το πρωτοσυναντούμε όταν μελετούμε την περιφέρεια και το εμβαδόν του κύκλου. Ο λόγος της περιφέρειας
ενός κύκλου προς την διάμετρο του ισούται πάντα με ένα σταθερό αριθμό, τον ίδιο για όλους τους κύκλους. Αυτός ο αριθμός είναι το π = 3.14159…. του οποίου τα ψηφία είναι άπειρα.
Αν συμβολίσουμε την περιφέρεια με C και την διάμετρο με d τότε
.
Αν συμβολίσουμε το εμβαδόν του κύκλου με Α και την ακτίνα του με r τότε
Το π λόγω της σχέσης του με τον κύκλο δε μας εκπλήσσει που εμφανίζεται στους διάφορους τύπους που μας
δίνουν τον όγκο και εμβαδόν παράπλευρης επιφάνειας διάφορων τρισδιάστατων σχημάτων με κυκλική βάση
όπως για παράδειγμα του κυλίνδρου :
r
h
2
όό
  rr 2hh
2

άά
 
άά
  22rr 2  22rh
rh
όπου r είναι η ακτίνα της βάσης και h το ύψος του κυλίνδρου.
Η αλήθεια είναι ότι το π δεν έχει να κάνει μόνο με κύκλους. Αν κάναμε ένα ταξίδι στον κόσμο των μαθηματικών
θα το συναντούσαμε σχεδόν παντού!
Το π δίνει το παρόν του πολύ συχνά στα αθροίσματα και τις σειρές. Ένα από τα διασημότερα αποτελέσματα σε
αυτή την κατηγορία είναι :

1 1 1
11 1  1  1 ...
...
44
33 55 77
Εδώ παρατηρούμε μια ιδιαίτερη σχέση που έχει το π με τους μονούς αριθμούς που σίγουρα μας γεννά το ερώτημα: υπάρχει σχέση ανάμεσα σε μονούς αριθμούς και τον κύκλο; Σίγουρα είναι μια απρόσμενη διασύνδεση, μια
από αυτές που κάνουν τα μαθηματικά να μας ενθουσιάζουν και να μας κινούν το ενδιαφέρον να τα εξερευνήσουμε. Η πιο πάνω σειρά απείρων όρων δημοσιεύτηκε από τον διάσημο μαθηματικό Leibniz το 1674.
Πριν το Leibniz προηγήθηκε ο Αρχιμήδης που χρησιμοποιώντας πολύγονα με 96 πλευρές μέσα και έξω από
10
1
33 10
33 1
71
71 και μικρότερο από το 77 καταλήγοντας
τον κύκλο απέδειξε ότι το π πρέπει να είναι μεγαλύτερο από το
22
7
στην προσέγγιση π =
.
2000 χρόνια αργότερα ο Viete το 1593 χρησιμοποιώντας πολύγωνα πάλι κατέληξε στο αποτέλεσμα:
22
2
2 2
2 2 2
 2  2  2  2  2  2 ...
...

22
22
22
το οποίο μας επέτρεψε να υπολογίσουμε το π σε 14 δεκαδικά ψηφία,
 33.1415926535
.14159265358979
8979
Μετά τον Viete έρχεται η σειρά του John Wallis to 1655 με ένα ακόμα τύπο απείρου γινομένου:

2 2 4 4 6 6
 2 2 4 4 6 6...
...
22 11 33 33 55 55 77
Το 1674 ήταν ο Leibniz με τον τύπο που είδαμε στην αρχή και μετά από αυτόν ο Euler to 1736 με τη διάσημη
σειρά απείρων όρων :
1
1
1
1
22
11 12  12  12  12 ......
66
22 2 332 44 2 552
Μέχρι την εποχή του Euler το π είχε υπολογιστεί με ακρίβεια περίπου 100 δεκαδικών ψηφίων με μεθόδους σειρών, αλλά το 1761 ο Lambert απέδειξε τελικά αυτό που πολλοί είχαν υποψιαστεί: το π είναι άρρητος δηλαδή δε
μπορεί να εκφραστεί ως λόγος δύο ακεραίων και άρα τα δεκαδικά του ψηφία δεν τελειώνουν ποτέ! Είναι αξιοσημείωτο ότι τώρα με την χρήση μοντέρνων υπολογιστών έχουμε καταφέρει να υπολογίσουμε το π με ακρίβεια
κάποιων δισεκατομμυρίων δεκαδικών ψηφίων.
Στην συνέχεια θα δούμε την σχέση του π με τις πιθανότητες. Μια πιο απλή και ίσως πιο διασκεδαστική προσέγγιση.
Παίρνουμε μια κόλλα χαρτί με οριζόντιες ευθύγραμμες γραμμές απόσταση d μεταξύ τους και ρίχνουμε πάνω
της μια βελόνα μήκους d . Η πιθανότητα η βελόνα να πέσει ακριβώς κατά μήκος μιας οποιασδήποτε γραμμής
22

είναι
.
Αν αντί βελόνες προτιμούμε τα νομίσματα, ρίχνουμε ένα νόμισμα 2ν φορές, όπου το ν είναι πολύ μεγάλο, η πι-
11
θανότητα να πάρουμε ακριβώς ν κορόνες και ακριβώς ν γράμματα είναι περίπου


.
Αν δεν μας αρέσουν ούτε τα νομίσματα, τότε αν ρωτήσουμε κάποιο φίλο μας να διαλέξει αρκετούς ακέραιους
αριθμούς η πιθανότητα να μας πει δύο θετικούς που να μην έχουν
66
κανένα κοινό διαιρέτη (εκτός από το 1) είναι
22
.
Μιλήσαμε αρκετά όμως για το π. Ας μελετήσουμε λίγο ένα άλλο εξίσου σημαντικό αριθμό με άπειρα δεκαδικά
ψηφία, το
ee22.7182818284
.718281828459
59......
Ας υποθέσουμε ότι δανείζουμε σε κάποιο 1 ευρώ με τόκο 100% το χρόνο. Μετά από ένα χρόνο θα πάρουμε
1+1= 2 ευρώ. Τώρα αν πείσουμε το δανειζόμενο να πληρώσει τόκο 50% στους 6 μήνες, δηλαδή μισό ποσοστό
1
11 1
22
διπλάσιες φορές, το αποτέλεσμα θα είναι το ίδιο στον ένα χρόνο; Όχι. Μετά από 6 μήνες θα πάρουμε
2
ευρώ και στους επόμενους 6 μήνες
 1 2
1  
 2
11
33
33
33
=2.25 ευρώ. Με τον ίδιο τρόπο αν πληρώνει
% στους 4 μή33
 11
.37
11  22.37
 33
. Λίγο περισσότερα δηλαδή. Αν συνεχίσουμε
νες (τρεις φορές το χρόνο δηλαδή) θα αποφέρει
να μειώνουμε το ποσοστό και να αυξάνουμε αντίστοιχα τις δόσεις που θα δώσει το χρόνο τότε που καταλήγουμε; σε μια περιουσία;
Η απάντηση είναι όχι, από κάποιο σημείο και μετά θα αρχίσει να κοντεύει σε ένα συγκεκριμένο αριθμό, ο αριθμός αυτός είναι το e!
To e εμφανίζεται πολύ συχνά σε διάφορες πτυχές των μαθηματικών και ιδιαίτερα εκεί όπου υπάρχει
ρυθμός με τον οποίο μεταβλητές αλλάζουν. Εμείς θα δούμε το e εν δράσει σε ένα πιο προσιτό θέμα.
Παίρνουμε 2 κανονικές τράπουλες, τις ανακατεύουμε και τις βάζουμε ανάποδα την μία δίπλα από την
άλλη. Τώρα διαλέγουμε τυχαία ένα χαρτί από κάθε τράπουλα. Η πιθανότητα τα δύο χαρτιά να είναι τα
ίδια είναι πολύ μικρή. Συνεχίζουμε να γυρίζουμε ζεύγη μέχρι να εξαντλήσουμε τις τράπουλες. H πιθα11
e
νότητα να μην βρούμε ούτε ένα ζεύγος το ίδιο αποδεικνύεται ότι είναι ίση με e δηλαδή λιγότερη από
1
2
(50%) και άρα θα μπορούσε να πει κάποιος ότι είναι αρκετά πιθανό να πετύχουμε ίδιο ζεύγος!
Το e όπως και το π που είδαμε πιο πάνω μπορεί να εκφραστεί ως άθροισμα απείρων όρων με τον ακόλουθο τρόπο:
1
1
11
ee1111 1  1 
...
...
22 2233 223344
Τόσο το π όσο και το e είναι δύο αριθμοί που θα μπορούσε κάποιος να τους ονομάσει μαγικούς διότι
έχουν την ικανότητα να εμφανίζονται σχεδόν παντού και να μας εκπλήσσουν!
Κάπου εδώ τελειώνει το μικρό μας ταξίδι στο κόσμο των μαθηματικών. Γευτήκαμε την μαγεία της απόδειξης κάποιων γνωστών μαθηματικών ιδεών, μελετήσαμε την ιδιότητα των τριψήφιων αριθμών σε
σχέση με το 1089 και την αποδείξαμε, κάναμε μια βόλτα στην ιστορία του π, γνωρίσαμε το e και διασκεδάσαμε με τις εφαρμογές τους.
«Πυθαγόρα, εύγε!»
Ποτέ μου δεν μπόρεσα να καταλάβω τους συμμαθητές μου, όπως αυτοί εμένα σχετικά με την άποψή
μας για τα Μαθηματικά. Ενώ εγώ τα λάτρευα και τώρα τα λατρεύω ακόμη περισσότερο, σε αυτούς
ποτέ μέχρι τώρα δεν άρεσαν. Μπορεί κάποιος με ευκολία να πει πως τα βαριόντουσαν μέχρι θανάτου,
μέσα από τον τρόπο που εκφράζονταν για αυτά, πιθανόν γιατί δεν τα καλοκαταλάβαιναν. Βέβαια και
οι καθηγητές που είχαμε, ούτε εμένα εντυπωσίαζαν με τον τρόπο και τις μεθόδους που δίδασκαν το
μάθημα των Μαθηματικών. Δεν έφταιγαν εκείνοι όμως που ο παραδοσιακός τρόπος διδασκαλίας, περιείχε μόνο στεγνές γνώσεις βγαλμένες από τα βιβλία. Τότε πώς να ενδιαφερθούν τα υπόλοιπα παιδιά
που απαιτούσαν κάτι πιο εντυπωσιακό;
Προς καλή τύχη όμως των καημένων και ανεκτίμητων Μαθηματικών, όταν βρισκόμουν στην τρίτη
τάξη του Λυκείου είχε έρθει ένας δάσκαλος Αθηναίος. Είχε σπουδάσει στο Πανεπιστήμιο Αθηνών,
εκεί όπου ο κάθε φοιτητής που κατάφερνε να περάσει γινόταν ένα πραγματικό στολίδι της κοινωνίας,
γεμάτο με γνώση και πάθος για τη σπουδή που είχε επιλέξει. Τέτοιος ήταν και ο κ. Πυθαγόρας, έτσι
φωνάζαμε τον καθηγητή αυτό. Στην πραγματικότητα, το αληθινό του όνομα ήταν Ευκλείδης, άλλο και
τούτο, όμως στο Πανεπιστήμιο όπου σπούδασε κι αργότερα στο σχολείο μας, του έβγαλαν αυτό το
παρατσούκλι, προς τιμή του μεγάλου μαθηματικού Πυθαγόρα. Όχι πως ο Ευκλείδης ήταν άξιος υποβιβασμού, αλίμονο, απλά για κάποιο λόγο ο καθηγητής μας έτρεφε λίγη περισσότερη αδυναμία στον
Πυθαγόρα.
Αυτός ήταν λοιπόν ο κ. Ευκλείδης. Ένας καλοσυνάτος και αξιαγάπητος γεροντάκος, που προερχόταν
από μια πλούσια γενιά με μαθηματικό μυαλό και είχε διδακτορικό στο επάγγελμά του. Ένας ηλικιωμένος άνθρωπος, ο οποίος δεν έκανε ιδιαίτερη εντύπωση με την πρώτη ματιά, που όμως έκρυβε μια ψυχή
παιδιού, ενθουσιασμένη και νεωτεριστική. Την πρώτη φορά που τον αντικρίσαμε, οι περισσότεροι
μάλλον είχαν σκεφτεί από μέσα τους: «Τι είναι τώρα αυτός; Ένας ξερόλας που θα μας κάνει τη ζωή
ποδήλατο;» Που να ξέραμε πως αυτός εδώ ο κύριος ήταν ένας πολύτιμος θησαυρός, μια κινούμενη
εγκυκλοπαίδεια, όπως αποκαλύφθηκε.
Εκείνη την πρώτη μέρα τη θυμάμαι σαν να ήταν χτες, κι ας έχουν περάσει τόσα χρόνια πια. Ανοίγει
την πόρτα και μπαίνει με ένα δήθεν σοβαρό ύφος στην τάξη για να μας πάρει, υποθέτω, τον αέρα. Γι’
αυτό και όλοι νομίσαμε πως θα ήταν αντιπαθής σε εμάς. Έβαλε την τσάντα του, η οποία από τα πολλά
βιβλία που περιείχε φάνταζε να ζυγίζει 100 κιλά, πάνω στην έδρα, και για μια στιγμή μας κοίταξε με
ένα διαπεραστικό βλέμμα που έκανε όλους να θέλουν να το αποφύγουν-σαν να ήθελε να μπει στην
ψυχή του καθενός μας και να την εξερευνήσει με μια ματιά. Σαν να ήθελε να καταλάβει τι είδους
άνθρωποι είμαστε. Όμως, αμέσως μετά από αυτή τη σύντομη σιωπή, το αυστηρό ύφος μετατράπηκε
σε ένα χαμόγελο και ο καθηγητής μας λέει:
«Καλημέρα σας παιδιά!»
«Καλημέρα.», απαντάει η τάξη βαριεστημένα και φοβισμένα μαζί.
«Με λένε κ. Ευκλείδη. Χαίρομαι πολύ που σας γνωρίζω! Είμαι σίγουρος πως θα περάσουμε πολύ
ευχάριστα μαζί!», μας απαντάει ο κ. Ευκλείδης με πολύ ευθυμία.
«Αφού εγώ σας έχω συστηθεί, θα απαιτήσω να κάνετε κι εσείς το ίδιο. Θα σηκωθείτε ένας-ένας
από το θρανίο σας, θα πείτε το όνομά, το επίθετό σας και μερικά λόγια για τον εαυτό σας».
Όλοι έμειναν έκπληκτοι από τα λόγια αυτά. Με όλους τους άλλους δασκάλους αρχίζαμε μεμιάς
το μάθημα. Έτσι λοιπόν ο καθένας συστήθηκε και μίλησε λίγο για τις ασχολίες του στον ελεύθερό του χρόνο.
Αλήθεια χωρίς λογική… Μια καμπάνα κτυπάει πένθιμα, ο ουρανός γεμίζει μαύρα σύννεφα Ένα παιδί τρέχει χωρίς πόδια και τα όνειρα του γίνονται συντρίμμια Έψαχνα στο σκοτάδι να βρω σπίρτα, στάθηκα στην πόρτα και σου έγνεψα μα εσύ μουρμούριζες πως δεν είδες ανθρώπους, μονάχα αγρίμια. ~ Τιναζόσουν κάθε λίγο απ΄τον ύπνο σου και μιλούσες για κόλαση, Γιατί τάχα πήγα στο μέτωπο; Γιατί είχα μάτια χωρίς όραση; Κλαίνε των χαμένων αιώνων οι ήρωες που ποτέ δεν δικαιώθηκαν για μάχες και ιδανικά που τα πάντα προδόθηκαν... ~ 'Ελαβα διαταγή απ΄την μεραρχία "Προς ολοταχώς", μα περπατούσα χωρίς ηγεσία και στο τέλος έμεινα μοναχός. Γυμνός από συναίσθημα και ιδεολογία σκοτώνω αδελφούς που μέσα απ' την πλάνη της προπαγάνδας, τους βλέπω σαν εχθρούς. ~ Αναρωτιέμαι αν θα βρω το θάρρος να κοιτάξω κατάματα το φως και να ψιθυρίσω την αλήθεια σαν μετουσιωμένος εαυτός. "Ο πόλεμος γυαλίζει σαν μαύρος χρυσός και μαριονέτα κατάντησε και πάλι ο λαός". Σταύρος Νόνη 3C Modern Greek Ποιοι παράγοντες επηρεάζουν την επιλογή δραστηριοτήτων
στον ελεύθερο χρόνο; Σχολιάστε.
Στη σημερινή εποχή του «τρέξε να προλάβεις», του άγχους και της αγωνίας, ο ελεύθερος χρόνος αποτελεί αναγκαιότητα για τον κάθε άνθρωπο αφού έτσι θα έχει μια
ανάπαυλα από την καθημερινή ρουτίνα.
Οι επιλογές όσον αφορά την αξιοποίηση του ελεύθερου χρόνου είναι πολλές και
εξαρτώνται κυρίως από εμάς τους ίδιους. Ίσως θελήσουμε να κάνουμε μια εθελοντική
εργασία που θα μας ικανοποιήσει πνευματικά και ψυχικά αφού έτσι θα συμβάλουμε
στους κοινωνικούς στόχους. Όμως, οι επιλογές της οικογένειάς μας αλλά και των φίλων
μας ίσως μας επηρεάσουν στην τελική μας επιλογή.
Παράλληλα, μπορούμε να αξιοποιούμε τον ελεύθερο μας χρόνο καλλιεργώντας
το ταλέντο μας, το οποίο μπορεί να αφορά τη ζωγραφική, το χορό, τη μουσική αλλά και
οτιδήποτε άλλο αυξάνει το ενδιαφέρον μας για τη ζωή. Παρ’ όλα αυτά, το αν θα επιλέξουμε να αναπτύξουμε το ταλέντο μας θα εξαρτηθεί από την οικονομική μας ευχέρεια
αλλά και από την ψυχολογική μας διάθεση. Τις πλείστες φορές η οικονομική άνεση μας
βοηθά να πετύχουμε τους στόχους μας.
Ακόμα, ο διαθέσιμος μας χρόνος δεν είναι ο μόνος παράγοντας που επηρεάζει τις
ενασχολήσεις μας. Σημαντικό ρόλο παίζει και το κατά πόσον η δραστηριότητα που θέλουμε να κάνουμε είναι εφικτή. Πιο συγκεκριμένα, οι κλιματολογικές συνθήκες επηρεάζουν τις επιλογές μας, καθώς πρέπει να τις ευνοούν. Για παράδειγμα, εάν θέλουμε
να ασχοληθούμε με κάποια δραστηριότητα όπως το κανό, τότε η βροχή θα αποτελούσε
ανασταλτικό παράγοντα.
Συνοψίζοντας, η ενασχόληση με κάποια δραστηριότητα αναπτύσσει τη φαντασία
και την κρίση μας. Ο ελεύθερος χρόνος είναι πολύτιμος, έτσι καλό θα ήταν να μην τον
αφήσουμε να πάει χαμένος. Το πιο σημαντικό είναι να επιλέγουμε σωστά και να αποφασίζουμε σύμφωνα με το τι θέλουμε εμείς οι ίδιοι.
Δήμητρα Γεωργίου
4Α
IGCSE Modern Greek
ALEXANDRA SHANINA: “MYSTERY AND
IMAGINATION”
ANDREAS KYRIACOU: “SHADOWS AND
SHADES”
ALEXANDRA SHANINA: “SAVAGE”
ANDRI CHRISTOFIDI: “SNOW
WHITE AND THE SEVEN DOORS”
ANASTASIS ANASTASI: “SHADOWS AND
SHADES”
DANAE ELLINA: “EXPRESSION THROUGH
HANDS”
MARCEL VALEEV: “INSANITY”
STEPHANY
PORFIRIOU:
“SHADOWS
AND SHADES”
VARVARA STAVROU: “EXPRESSION:
THE EYES”
MARGARITTA SAMOURIDES: “SHADOWS AND SHADES”
DESPINA XIOUROUPPA: “SHADOWS
AND SHADES”
BACKGROUND:SERGIOS DEMETRIOU: “THE SECRET OF THE SERPENT
ABOVE: MARIANNA THEODOSI: “SHADOWS AND SHADES”
NICOLE KOUTSOFTA : “SOULS”
MARCEL VALEEV:
“INSANITY”
STEPHANY PORFIRIOU: “SHADOWS
AND SHADES”
ELIA NEOPHYTOU: “SEVEN SEALS”
MARCEL VALEEV: “BALANCING
DUALITY”
MARCEL VALEEV: “BALANCING
DUALITY”
IRENE LOUCATZIE: “DISCOVERY AND
EXPLORATION”
SEPTEMBER 2010
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
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BACK TO SCHOOL!
EFFECTIVE HOME STUDY
FOR PARENTS OF YEAR 1
CLASS ELECTIONS
CLUB PRESENTATIONS
OCTOBER 2010
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NOVEMBER 2010
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Lecture on Options to Year 3 and on
IB to pupils in Year 4
1st Excursion
UK University trip
Careers Fair
Green Dot Lecture and visit
Commenius trip to Germany
Anti-cancer fund raiser
Radio Marathon
Overnight trip to Ayia Napa (Yr 2)
28th October Parade
Overnight trip to Agros
Artemis Halloween House Party
DECEMBER 2010
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Sports Day
Food Baskets collection and delivery
to homes
Christmas Carolling outside Debenhams
Staff Christmas party
JANUARY & FEBRUARY 2011
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Nicosia/Larnaca Indoor Archery Tournament
Comenius Trip to Slovenia
Valentine’s Day order/delivery of chocolates
and flowers organised by events committee
Tsiknopempti organised by Parent’s Association
MARCH 2011
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APRIL 2011
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Visit from Private School of Athens
The Cyprus Mathematics Olympiad
Tree Planting Week
Car Wash
Blood Donation for Parents
Educational Trip to Prague for Year 1
Easter Activities
Parent’s Association Fancy Dress
Pascal Discovery Day
School Play, ‘The Glass Menagerie’
National Holiday Parade
Entrance Exams
Sports Day
MAY & June 2011
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Hidden Talent’s Evening
Science Fair
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Art Exhibition at Kypriaki Gonia Gallery
Teacher’s Happy Hour
End of Year Ceremony
6th Formers Last Day
Graduation Ceremony
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Trip to Germany in July!