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

## Magic Topology!

Can you alter this figure-eight-shaped pastry in order to thread the stick into the second loop? Obviously, you cannot unthread the stick from the pastry nor cut the pastry in any way!

The trick is explained in my book: “Impossible Folding Puzzles and Other Mathematical Paradoxes” available on Amazon: https://amazon.com/dp/0486493512/?tag=archimelabpuz-20

## Solving An Impossible Packing Problem

Doesn’t fit? Reconstruct!

## Sprouts Game

## 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

**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).

## Golden Ratio (And Its Inverse) In Yin Yang

The philosophy of the Yin Yang is depicted by the the “taichi symbol” (*taijitu*). In fact, Yin Yang is a concept of dualism, describing how seemingly opposite or contrary forces may actually be complementary,

Curiously enough, in the taichi symbol are hidden the golden ratio and its reverse. As shown in the picture. Continue reading “Golden Ratio (And Its Inverse) In Yin Yang”