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
The three blue points always lie on a straight line. The blue points are the closest points to the moving red point on the lines. In other words the blue points are the projections of the moving red point to the lines.
Summation of Alternating Inverse Powers of Phi…
List of sums of reciprocals.
A “Kepler triangle” is a right triangle having edge lengths in a geometric progression, in which the common ratio is √ϕ, where ϕ represents the golden ratio.
Well, let’s construct a square with side length √ϕ that inscribes a Kepler triangle, that is, a right triangle with edges 1 : √ϕ : ϕ (or approximately 1 : 1.272 : 1.618), as shown in the picture. Draw then the circumcircle of the Kepler triangle (highlighted in orange in the picture) whose diameter is the hypotenuse of the triangle.
Then, the perimeters of the square (4√ϕ≈5.0884) and the circle (πϕ≈5.083) coincide up to an error less than 0.1%. From this, we can get the approximation coincidence π≈4/√ϕ
The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number.