## 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

Cut any of the loops of strings below and the whole chain comes apart. You will find many of these kinds of puzzles in my book “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). ## Target 10

Here is a little puzzle of our creation you can make with your kids or in class… ## “Stubborn” Number 33

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″

## Sangaku: Semicircle inscribed in a right triangle

Find the radius r of the semicircle inscribed in the right triangle below: show solution

## Smallest Prime Number Magic Square

American mathematician Harry L. Nelson won the challenge to produce a 3 × 3 magic square containing the smallest consecutive primes: ## Fibonacci Spiral Jigsaw Puzzle

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. 