Amusez-vous à résoudre les énigmes
*96% des meilleurs étudiants en mathématiques des États-Unis ont buté devant cette énigme
Il s’agit d’un test créé en 1995 par l’Association Internationale pour l’Evaluation du rendement scolaire. Il a servi à comparer les niveaux d’aptitude des étudiants de seize pays différents.
Voici l’énoncé: « Un fil est attaché de manière symétrique autour d’une tige circulaire (d’un cylindre). Le fil fait très exactement quatre fois le tour du cylindre. La circonférence du cylindre est de 4 cm et sa longueur est de 12 cm. Trouvez la longueur du fil et montrez tout votre raisonnement. »
Dans le livre « Assessing Mathematical Proficiency », Jan De Lange a dévoilé la solution. Si vous ne voulez pas (encore) la connaître, ne lisez pas la suite de l’article…
*Voici la solution. Le fil se déroule en une ligne droite et touche le bas du rectangle à un quart de la longueur du cylindre, soit 3 cm. La deuxième partie du fil commence en haut du cylindre et en touche le bas 3 cm plus loin, jusqu’à ce que le rectangle soit découpé en quatre triangles à angles droits. Il suffit ensuite d’appliquer le théorème de Pythagore, soit a2+b2=c2, ce qui donne 32+42=25, la racine carrée de 25 est 5 et le fil fait 4 fois le tour du cylindre, donc le fil fait 4 x 5cm, c’est à dire 20cm. *Lundi 17/08/2015 – 7sur7
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*FINALE du 24éme Championnat des jeux mathématiques et logiques.
–25 août 2010
**cliquer ici: http://www.lefigaro.fr/assets/pdf/FI2010jour1.pdf
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