Doesn’t fit? Reconstruct!
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.
3 intersecting golden rectangles (1 : φ) will create the vertices of an icosahedron.
Curiously enough, the cubes don’t move, only the background color changes…
Here is our tutorial to create an amazing autokinetic animation.
Clever visual proof by Mike Hirschhorn.
Write the digit “1” exactly 317 times, and you get a palindromic prime number. Moreover, 317 itself is a prime number!
The sum of the sequence of the first n cubes equals [n(n+1)/2]² as shown below:
1³+2³+3³+…+n³ = (1+2+3+…+n)² = [n(n+1)/2]²
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.