A visual intuitive proof that √ab cannot be larger than (a+b)/2, where a, b ∈ R*+
A cross-section of the dodecahedron can be an equilateral triangle, a square, a regular pentagon, a regular hexagon (two ways), or a regular decagon.
Here is a little puzzle of our creation you can make with your kids or in class…
Mathematics is sometimes weird… Read more: The hole truth of topology.
It is conjectured that n is a sum of 3 cubes if n is a number that is not congruent to 4 or 5 mod 9. The number 33 enters this category, but for 64 years no solutions emerged — that is, whether the equation 33 = x³ + y³ + z³ has an integer solution. Continue reading ““Stubborn” Number 33″
Find the radius r of the semicircle inscribed in the right triangle below:
show solutionhide solution
h = 6 · 8/10 = 4.8
4.8/r = 8/(8-r)
r = 3
American mathematician Harry L. Nelson won the challenge to produce a 3 × 3 magic square containing the smallest consecutive primes:
Each piece of this puzzle is similar (the same shape at a different size). The placement of the pieces is based on the golden angle (≈137.5º), and results in a pattern frequently found in nature (phyllotaxis), for instance on sunflowers. The puzzle features 8 spirals in one direction, and 13 in the other. You can build your own Fibonacci spiral puzzle by following John Edmark’s tutorial.