## Puzzle Creation for Associations

For 20 years, Archimedes Lab has created visual puzzles for the association RMT (Rallye Mathématique Transalpin). You can use them for your personal projects or for your math class. Enjoy!
Depuis plus de 20 ans, Archimedes Lab crée des puzzles – qui sont utilisés comme des attestations – pour l’association RMT (Rallye Mathématique Transalpin). Merci de respecter les copyrights. Amusez-vous bien!
Association RMT: http://www.armtint.org Continue reading “Puzzle Creation for Associations”

## Sprouts Game

All possible ways a game of “Sprouts” with two initial dots can evolve. Sprouts is a paper-and-pencil game that can be enjoyed simply by both adults and children. ## Equi-extended and isoperimetric non-congruent triangles

The picture below shows the ONLY one pair of triangles with the following properties:
· One triangle is a right triangle and one is isosceles,
· All side lengths of both triangles are rational numbers, and
· The perimeters and areas of both triangles are equal. ## Icosahedron with golden ratio cross-sections

3 intersecting golden rectangles (1 : φ) will create the vertices of an icosahedron. ## Equable Triangles

There are only five integer-sided triangles whose area is numerically equal to its perimeter:
(5, 12, 13), (6, 8, 10), (6, 25, 29), (7, 15, 20), and (9, 10, 17)
As you can see from the picture, only 2 of them are right triangles. ## Elementary 4-manifold topology

Cut any of the loops of strings below and the whole chain comes apart. You will find many of these kinds of puzzles in my book “Impossible Folding Puzzles and Other Mathematical Paradoxes” .

## Infinite Pythagorean Triplets

Consider the following simple progression of whole and fractional numbers (with odd denominators):
1 1/3, 2 2/5, 3 3/7, 4 4/9, 5 5/11, 6 6/13, 7 7/15, 8 8/17, 9 9/19, …
Any term of this progression can produce a Pythagorean triplet, for instance:
4 4/9 = 40/9; the numbers 40 and 9 are the sides of a right triangle, and the hypotenuse is one greater than the largest side (40 + 1 = 41). 