The infamous problem of representing numbers with four 4’s appeared for the first time in 1881 in a London science journal. In 2001, a team of mathematicians from Harvey Mudd College found that we can even get four 4’s to approximate four notable constants: the number e, π, acceleration of gravity, and Avogadro’s number.
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”
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
Doesn’t fit? Reconstruct!
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.
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.
3 intersecting golden rectangles (1 : φ) will create the vertices of an icosahedron.
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.
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).