The concept of treatment in thematic philately

The concept of treatment
in thematic philately
Mathematics,
a science between theory
and application
a) general challenges to
treatment in thematic philately
b) special challenges to
treatment caused by the theme
„mathematics“
________________________________________
Joachim Maas, Malmö, April 28, 2012
Title
Advances in mathematics:
- impetus by applications
- theoretic progress
Area of conflict:
Mathematics dominated by theory
or by application?
„a science between theory and
application“
This title defines the concept („red
thread“) of the treatment!
Plan
How to structure the theme?
g
e
disciplines -> o
m
e
t
r
periods;
y
progress within these periods
Early civilizations
(„mathematics“ support cultural
evolution)
Classical antiquity – Middle Ages
(exact fundamentals,
preservation of Greek knowledge)
15th – 16th century
(impetus by applications)
17th century to today
modern mathematical disciplines
today‘s presence of mathematics
.
a
r
i
t
h
m
e
t
i
c
s
a …
l
g
e
b
r
a
Plan
application
theory
g
e
o
m
e
t
r
y
disciplines ->
periods;
progress within these periods
Early civilizations
(„mathematics“ support cultural
evolution)
Classical antiquity – Middle Ages
(exact fundamentals,
preservation of Greek knowledge)
15th – 16th century
(impetus by applications)
17th century to today
modern mathematical disciplines
today‘s presence of mathematics
.
a
r
i
t
h
m
e
t
i
c
s
a …
l
g
e
b
r
a
Development: story concept
1. first two pages of 1.1:
man realizes geometric objects within
his natural surroundings
 man uses geometric figures for
decoration purpose
 man defines mathematical objects
exactly
2. first pages of 1.2:
steps to an abstract concept of numbers
3. „Pascal“ 4.2:
combination of a philatelic and a
thematic study
4. positioning of items strictly due to
the concept: Euclid‘s parallel postulate
5. mathematical aspects
 historical events
Illustration of abstract principles
Examples:
- positional systems of numbers (1.2)
- proof of Pythagoras‘ theorem (2.1)
- paradox (2.1)
- deductive method, Euclid (2.1)
- infinitesimal methods (2.1)
- numerical system (4.4)
- commutative law of addition (4.4)
- graph theory
Surprising items and
surprising positioning of items
- Numbers and musical harmony (2.1)
- Calculating machine (1.2)
Widest range of philatelic
material supporting the
thematic development
- Cape triangles (shape of stamps!)
- taxations with Roman nunbers
- printing errors
- philatelic importance vs. thematic
importance