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.
Take 6 points on a circle such that every second edge (green chords) has length equal to the radius of the circle. Then the midpoints of the other three sides of the cyclic hexagon form an equilateral triangle.
Read more: https://www.archimedes-lab.org/2-Sunday_puzzle_43.html
A 3D regular hexahedron solid (cube) passing through a 2D plane:
In geometry, the isogonic center (aka Fermat–Torricelli point) of a triangle, is a point such that the total distance from the three vertices of the triangle to the point is the minimum possible.
For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1 to 100. This theory is true in all cases except for an unproven exception: 42.
By 2016 and over a million hours of computation later, researchers of the UK’s Advanced Computing Research Center had its solution for 42.
More intriguing number facts here.
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
3,139,971,973,786,634,711,391,448,651,577,269,485,891,759,419,122,938,744,591,877,656,925,789,747,974,914,319,422,889,611,373,939,731 produces reversible primes in each row, column and diagonal when distributed in a 10×10 square.
Diagram by HT Jens Kruse Andersen.
Two moving tangent circles can trace ellipses