Mathematics at your fingertips – Armelle L'Hermite (Scientific instruments workshop) =====================================================================================================================================================================
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** HP is partnering in Tangente's 30th-anniversary celebrations. The HP team will be in the conference room at 12:30 for the teachers' meeting and at the scientific instruments workshop at various times throughout the day. They invite you to explore mathematics in the touchscreen era with HP Prime, the first graphing calculator with a color multitouch screen. The workshops give all visitors a chance to try the HP Prime calculator for themselves: draw with a fingertip, play your favorite games, program in a simple language… Discover its unique environment, designed to meet the challenges of digital technology in education: a mobile app for phones and tablets, a virtual calculator for PC or Mac, and wireless connectivity… And ask for the free mobile app!
Building giant polyhedra together – François Gaudel (Madame de Genlis room) =======================================================================================================================================================
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Having already taken part in previous Tangente anniversary celebrations, the Science ouverte association invites the public to help create a temporary collaborative structure. The aim is to build one or more giant polyhedra, depending on the space available. They are assembled from wooden dowels fitted with a circular eye bolt at one end, together with cable ties, and dismantled at the end of the day. Explanations of the polyhedra accompany their construction. Such structures have already been built many times in numerous venues: Palais de la Découverte, Cité des Sciences et de l'Industrie, Palais des Congrès du Futuroscope, the town hall of Paris's fifth arrondissement, Château de Ladoucette in Drancy, Université Paris 13 in Bobigny, as well as in high schools and middle schools. Depending on the ceiling height and the space available, it is possible to build
• A truncated icosahedron (soccer ball), either 5 m in diameter—and therefore 5 m high—or 3 m. A clear area measuring 7 m by 7 m is required.
• A Sierpiński tetrahedron 6.5 m high (allow a construction area at least as large as for the preceding structure). It can also be built at half scale, approximately 3.25 m high.
• Various stellated polyhedra ranging from 3 m to 4.5 m in size.
The Möbius strip – François Lavallou (Current affairs room) =============================================================================================================================
A long rectangular strip of paper whose shorter edges are glued together forms a right circular cylinder. It is well known that giving the strip an odd number of half-twists—usually just one—before gluing produces what is known as a Möbius strip, named after Möbius (1790–1868); it was also described by Johann Listing (1808–1882). The recyclable-materials logo is an example with three half-twists. This surface, long known, has the distinctive property of having only one side. During the industrial expansion of the 19th century, this property was widely used in belt-driven machinery. Crossing the belts at the join caused wear on "both sides" of the belt, thereby extending its working life.
Cutting it into n strips is well understood for n=2 and n=3, but very few people can give the answer for n=17. Everything becomes clear once the twist is viewed as a permutation of order two: two half-twists return you to the starting point. The conclusion is left to your ingenuity.