Multimedia software “Archimedes and his work: a deepening path in

Multimedia software “Archimedes and his work: a deepening path in the
Arkimedeion Museum of Siracusa.
S. Merlino1, M. Bianucci1, C. Mantovani1, R. Fieschi2
1ISMAR-CNR, Forte Santa Teresa, Pozzuolo di Lerici, La Spezia, Italy
2Department of Physics, University of Parma, Viale delle Scienze 7/A, 43020 Parma, Italy
Abstract The distinctive feature of the Arkimedeion, the modern interactive Museum located in Siracusa, Sicily (Italy) - which
includes an exhibition of twenty-four interactive exhibits as well as a planetarium, is the "hands-on" approach, characteristic
of modern international science centres, strictly based on interactivity between visitors and the proposed exhibits, for an
active participation and a full intellectual involvement "minds on." (Bianucci et al. 2011a). Moreover, multimedia support
material is especially designed to allow visitors to get a self explaining tour of the museum: general information about
exhibits, historical news, mathematical demonstrations, and sources review are supplied by means of video and audiovisual
interactive material, very rich in pictures, diagrams and animations, structured in different deepening levels. The multimedia
software also provides visual examples, interactive models and virtual objects manipulation in a simple and very powerful
way. Such material has been designed and implemented by a CNR team of physicists with expertise in science
communication, in collaboration with some of the major Archimedes’ experts around the word, especially from like
Baltimora University, USA, and Pisa University, Italy. A special attention is given to interactive educational games.
Keywords
Scientific museum, science communication, teaching/learning strategies, educational games
Introduction
Mathematics and Physics are often abstract disciplines; thus we face some difficulties both in learning and teaching them.
For that it turns really helpful to take advantage of the modern multimedia technologies (Fieschi et al. 2003, Bussei et al.
2007), including hardware exhibits, that are really effective to explain concepts through visual examples, models, real
objects manipulation. Moreover new multimedia tools and modern exhibits allow us to try unexploited new teaching
strategies. The “Arkimedeion” is an Interactive Science and Technology Museum dedicated to the many-sided genius
Archimedes (287 B.C. – 212 B.C.) and to his work, and it is located in Siracusa, Italy (Bianucci et al. 2011b). A series of
interactive exhibits, movies and multimedia software on touch screen kiosks, guide visitors into the middle of Archimedes’
historical period and into the heart of his scientific work, making them discover and appreciate his great contribution to
Science, and in particular to his work on mathematics and physics.
The principle that inspired the authors, beyond rigorousness and accuracy, was the need for a good educational and
accessible approach. The museum contents and in particular the multimedia tools are structured in different levels of
complexity, allowing multiple levels of approach by visitors, depending on their background. We attempted to expose part
of the Archimedes’ original documents in an easy-to-understand way with the help of modern tools in order to facilitate the
understanding of complex mathematical demonstrations.
For this purpose, a special role is devoted to the mathematical and physical interactive games, considered as educational
spaces of play-learning (Merlino at al. 2003), and based on the many scientific discoveries and demonstrations of
Archimedes (Arkimedeion’s interactive laboratory and the Stomakion tool). Archimedes was, in fact, also one of the earliest
known brain-teaser enthusiasts, among which we mention: the Archimedes' cattle problem (or the problema bovinum); the
investigation about the number of grains of sand that the universe could contain, opportunity to introduce a system of
counting based on the myriad that anticipated our numeral positional system and the exponential notation; the Stomachion, a
dissection puzzle made of 14 pieces originally forming a square, presented in the Museum both as exhibit and educational
videogame.
We are aware that the playful moments stimulate the ability to abstract (Bondioli 2002, Gee 2007), and provides an
opportunity of de-contextualization compared to schoolwork, (Green and MacNeese 2007, Green and MacNeese 2011),
activating then personal learning processes (Michelini et.al 2008); in this way the game can become an important
opportunity for learning (Bateson 2002, Gee 2003)
Scientific path, exhibits and structure of multimedia
After an introductory presentation, focused on the discovery of the Palimpsest and on the importance of this event
(including interviews with famous historians and researchers), visitors follow a scientific path organized in four macroareas: Machines for Society, Equilibrium, Mathematics and Planetarium. Each area is equipped with several touch-screen
kiosks showing the multimedia contents related to this area. Multimedia are structured with different levels of detail and are
based on animation of graphical and textual elements helping to develop and illustrate concepts often abstract and not very
intuitive. Each macro-area is organized in few themes. In fig.1 and 2 we only show some examples, as the theme Give me
the place to stand, in the equilibrium macro-area.
Figure 1. Using a large lever the visitor can raise, with a little effort, a person sitting in the building that reproduces the
shape of the Earth; in this way we realize the famous Archimedes’ quote: “Give me the place to stand and I shall move
the Earth”
Figure 2. A sequence of two screenshots from the theme “Give me the place to stand”: it illustrates the visual approach to
mathematical demonstrations through animations related to the exhibit in fig.1
Figure 3. Another theme is the “geometry of position: the plane curves and the solids of revolution”. One of the
exhibits is composed by a big cone of Plexiglas and by a structure mounted on the wall (see Fig. 3). The structure
holds up four steerable laser projectors that generate plans of light. Every time one plane intersects the cone it
produces a conic section. It is possible to show four different conic sections at the same time: ellipse, circle, parabola
and hyperbola. Here the draft (on the left) and the exhibit (on the right). Figure 4. Screenshots of the animation used to visualize conic sections in an amusing and intuitive way. The
multimedia support of the theme “geometry of position: the plane curves and the solids of revolution”
deepens the concept of conic section and its importance in the history of Greek mathematics. It also discusses
the various methods used to obtain the four plane figures (ellipse, circle, parabola and hyperbole) and the
connections with the physical phenomena, such as orbits of planets and asteroids.
The Arkimedeion Virtual Laboratory.
The Archimedes’ Lab is an educational computer game intended for people of all ages and backgrounds. It’s inspired by
other famous games like the Incredible Machine computer game series (Jeff Tunnell - PushButton Labs), and many other
2D platform-like computer games where the player must arrange a given collection of objects in a needlessly complex
fashion so as to perform some simple task. In our case the task is to allow a ball moving in a vertical board to reach a given
target. The ball is affected by gravity, there are many obstacles disseminated on the board, and there are a lot of tools that
can be used to avoid/destroy the obstacles and to route the ball along the right path. Archimedes’ Lab is designed, like most of the computer games, with an increasing level of difficulty. Moreover, being an
educational game, it is also calibrated to allow users to gradually improve their knowledge, in this case about the physical
principles and results related to the Archimedes work.
In fact, the interacting objects on the game’s stage are strictly linked with the Archimedes opera, as they are levers,
parabolic mirrors, solids of revolution, catapults, etc., and they behave following physical laws, although in a simplified
way because represented in a 2D cartoon-style world. It means, for instance, that the player can balance a lever attaching
different solids of revolution to the edge of the lever, however this must be done according to the proportions between such
solids’ volume, as found by Archimedes. In general all the objects must be combined and placed in the correct position in
the stage so that, when the player starts the simulation, they can allow the ball to reach the target. In the most advanced
levels additional elements are added, e.g. the levers can be located underwater, involving in such way also the Archimedes’
principle about buoyancy.
The design of the Lab was mainly focused on developing a game easy to use, entertaining, and at the same time able to
force the player to manipulate and apply concepts related to the work of Archimedes. Application of the physical concepts
described in the game and in the museum, and immediate feedback in the result of the game, make players to understand
connections of the theory with the real world. By learning from their mistakes, players improve their ability to solve game
situations.
Moreover, in each level the path leading the ball to the goal is not unique, so that the tools to use, and the actions to be
performed, are not bounded: the player moves in a playing environment with many degrees of freedom. This fact gives the
chance to solve the same game level using different strategies, more or less efficient, contributing to a personalized learning
of concepts.
The Virtual Lab can also work as a game levels editor, promoting the user from a simple player to a game’s level designer,
i.e. giving the possibility to realize a customized versions of the game.
This editing mode not only stimulates and reinforces the learning of concepts related to the Archimedes’ work, but also
encourage personal manipulation of concepts, fantasy, improvement on game strategy and consequently on problem solving
ability.
Figure 5. Screenshots of the virtual Lab. This Lab is designed as a modern app, with a good playability and with an original cartoon-style
“drag and drop” GUI (graphical user interface). On the left we can see the menu where it is possible to enter the “Level Editor” mode.
Teaching and learning use of Archimedes’ lab and related pedagogical
Archimedes’ Lab has been designed in order to improve the science museum visiting experience, but it also represents an
useful educational tool for teaching and learning physics:
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in a museum context, it can be used both as a recreational game without educational purposes, and for
consolidating or assessing the learning of concepts related to the Archimedes’ work. Obviously, in the latter case it
is desirable to browse through the entire Archimedes’ multimedia before trying this game.
as teaching/learning tool, it can be used in the classroom to introduce or deepen knowledge in the field of physics,
such as the balance of forces, the laws of motion and gravity, buoyancy, and also the principles of geometrical
optics.
The question of how knowledge acquired during the game can be transferred into the real world reveals the Achilles’ heel of
digital gaming. We think that in our case the main limitation is the simplification of the simulation: needless to say, physical
laws used in the game are approximation of the real ones (for example, friction is not included in the simulation).
Figure 6. Screenshots of the virtual Lab. Using in a proper way some mirrors to focus sound waves (left) or light waves (right), and
catapults, the player should find the way to build a path for the ball to reach the goal. Simplifications and schematic representations of reality could also lead the player to miss the link between the game solving
strategy and the concepts about Archimedes’ work we would like him to learn through the game. In other words, a student
could become very able in solving the game levels, but then he could still find difficulties in solving simple problems of
statics in the classroom. Figure 7.Other screenshots of the virtual Lab where the player can place, move and set mirrors and catapults to build the right path for the
ball. The pedagogical question here is to determine in which real context players can apply what they have learnt and which
aspects can be transferred directly from the game.
A process of de-contextualization is required, in order to create correlation between learning accomplishments in play and
those in the real-life context. Once players/students have been made aware of the relevant content and their learning
accomplishments, a link between the virtual and the real domain must be created. Here is where the importance of the
teacher’s role is, when games are used – something that is underestimated to this day –. The learners require constructive
support to identify and consider, in the settings of the game, any aspect relevant to their learning process. External impetus
is therefore needed to direct attention to the potential of the games and to what has been learnt in them (Thai et al. 2009).
This is a meta perspective that teachers can and should adopt in order to foster the educational potential of games. If
teachers are able to create a link between the virtual and the real context, their action may make a transfer possible. This
educational role demands that teachers be interested and willing to engage with educational games (Klopfer et al. 2009).
Being aware of this, using games like the virtual Lab as didactic tools, can be well worthwhile, becoming a new learning
challenge for teachers.
Figure 8. Here the player should use some knowledge regarding the laws of the lever and the ratio between the volumes of different
solids of revolution. Stomachion game: the exhibit and the computer game
Every game begins with a challenge that motivates the players to put their knowledge and skills to the test. The challenge of
the game allows players to fail in an enjoyable way while encouraging them to learn and improve.
The players find out whether their abilities are sufficient to meet the requirements. Their own progress in the game gives
them the reassurance of having achieved and learnt something. In this sense, the game “Stomachion”, represent a
mathematical challenge.
Stomachion was an ancient game widespread in Greece and Rome (Napolitani 2001), and basically consists on a 14-piece
dissection puzzle where the pieces are polygons that can be reassembled to form different shapes (geometrical shapes but
also animals, trees, etc.). But the biggest challenge is to arrange them in different ways to form a square. The game is
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attributed to Archimedes, as one of its most complete descriptions was found in the Archimedes’ Palimpsest . A research
published by Dr. Reviel Netz of Stanford University and his co-workers (Netz et al. 2004) argued that actually Archimedes
was attempting to determine in how many ways the pieces could be assembled into the shape of a square. Therefore the
puzzle could represent an early problem in combinatory, even if the ancient authors exclude the use of combinatorial
analysis in the Archimedes’ treatise (Napolitani 2001). An interesting point is that Archimedes was able to calculate the area
of each polygon of the Stomachion.
The exhibit
In the Arkimedeion Museum, Stomachion is proposed both as interactive computer game and as interactive exhibit; this last
is a big 14-piece dissection puzzle made of wood. Visitors can manipulate pieces and place them on a table to form classical
The foremost document containing the work of Archimedes is the Archimedes Palimpsest, discovered in 1906 in Constantinople
(Istanbul) by the Danish professor Johan LudvigHeiberg . The palimpsest is now stored at the Walters Art Museum in Baltimore,
Maryland, where it has been subjected to a range of modern tests including the use of ultraviolet and x-ray light to read the overwritten.
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shapes. These represent the first and simple level of the game, and it is particularly useful for young students. In fact, here
children can test their ability to solve puzzles, and understand some important geometrical properties of polygons. For
mathematics enthusiasts and more expert in mathematics, it is possible to go a little more in deep, analyzing the case of the
square and trying to form it with different arrangements 2. In any case, to help visitors not familiar with the game, a touchscreen monitor installed on the exhibit shows instructions and suggestions on request, as a “tutorial”.
Figure 9.The Stomachion exhibit. This wood game is especially studied to result appealing for children and young students. The first
level approach is easy and, at the same time, instructive, and can be used to discover some important geometrical properties of polygons.
Figure 10. The “tutorial” assists visitors in the use of the wood exhibit “Stomachion”. On the right, one of the different shapes that can be
realized using the all pieces. On the left, one of the 536 dispositions of pieces to form a square.
The computer game
In Stomachion brain-teaser there are 536 possible independent ways to arrange polygons to form a square, and it could be
interesting to see all of them, or better to give the possibility to find them interactively. For this purpose an interactive
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Actually, the most interesting aspect of the Stomachion – the real “mathematical challenge” - is to determine in how many ways the pieces can be
assembled to form a square. This brainteaser was solved first on 2003 by Bill Cutler. He demonstrated, with the aid of a computer, that there are 536
possible independent arrangements. It means that solutions obtained by rotation and/or reflection of another given solution are not considered in this
number. computer game has been developed. It can identify and enumerate each solution of the puzzle, and, when a solution is
found, a counter shows the number of the remaining arrangements. Another important feature of the game is the capability
to check partial arrangements and to show which polygon is in the right place and which is not and, on request, to provide
suggestions on the following piece and its correct position.
A scoring system is under development. We consider it a very important part of the game, as it pushes users to avoid asking
for help and suggestions, therefore to think better and faster, and finally to improve the understanding of many mathematical
and geometrical issues.
The game is developed with Adobe Flash technology. This fact ensures compatibility with many platforms and devices and
allows its distribution online to entertain and engage gamers all over the world, increasing the Archimedes’ worldwide
reputation.
Archimedes is, undoubtedly, one of the greatest mathematical geniuses ever. It must be realized, however, that the
distinction between the different categories of scientists, based on the current classification of scientific disciplines, is not
applicable to ancient scientists like Archimedes. Thus, when we say that Archimedes was a great mathematician, this is
because today we include in mathematics much of his work. But such precinct is actually too limiting as Archimedes
applied his formal and logical deductive methodologies both to quite abstract mathematical issues and to problems we today
consider belonging to the field of physics, such as the laws of the lever, the buoyancy, the study of the equilibrium of the
bodies (statics). The countless contributions he gave to the development of what we now call the physical sciences are based
on mathematical considerations, often geometric (algebra had not been formalized yet). The original opera of Archimedes is
hard to understand for modern readers because of formalism, language, key “primitive” assumptions and the logical
construction used to expose its results. They are objectively a tremendous obstacle for reading and understanding the work
of this great genius. That's why we believe that our work of "adaptation", using a modern formalism and a multimedia
interactive presentation, can be really effective in introducing the user (museum visitor or student) to Archimedes and in
disseminating the results of the work of this great scientist, unfortunately well known most of the time for the famous
Archimedes' principle of buoyancy, and not for the many other contributions he gave to the modern science.
Figure 11.Screenshots from the Stomachion computer game.
Acknowledgment
Infmedia Company, the Italian software house that developed multimedia software in cooperation with the Informando team of CNR;
Luca Busi Video recording studio “Zero-frame” for the introductory video. Weisstein, Eric W. "Stomachion." From MathWorld--A
Wolfram Web Resource. http://mathworld.wolfram.com/Stomachion.html
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Affiliation and address information
Silvia Merlino
ISMAR-CNR, U.O.S. La Spezia,
Forte Santa Teresa,
Pozzuolo di Lerici,
19038 La Spezia.SP
Italy
e-mail: [email protected]