Doesn’t fit? Reconstruct!

### Sprouts Game

### Equi-extended and isoperimetric non-congruent triangles

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.

### Icosahedron with golden ratio cross-sections

3 intersecting golden rectangles (1 : φ) will create the vertices of an icosahedron.

### Autokinetic Wireframe Cubes

Curiously enough, the cubes don’t move, only the background color changes…

Here is **our tutorial** to create an amazing autokinetic animation.

### Original Proof of the Pythagorean Theorem

Clever visual proof by Mike Hirschhorn.

### Repunit Primes

Write the digit “1” exactly 317 times, and you get a palindromic prime number. Moreover, 317 itself is a prime number!

### Visual Proof (sum of cubes)

The sum of the sequence of the first *n* cubes equals [*n*(*n*+1)/2]² as shown below:

1³+2³+3³+…+*n*³ = (1+2+3+…+*n*)² = [*n*(*n*+1)/2]²

### Topology & Ethology

### 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.