Check out the attachment

Printable View

- April 9th 2005, 03:51 PMArtristeTriangle Paradox
Check out the attachment

- April 9th 2005, 05:39 PMpaultwang
The title "

**Triangle**Paradox" gives a hint: They are**not**triangles with or without the hole! ;)

Hint:

In order for red and green triangles to line up perfectly, they must be similar triangles having the same slope. Yet they aren't. - April 12th 2005, 10:42 AMCoolerOptical illusion
In fact the two "triangles" are not the same size.

The one with the hole in it is bigger. - August 13th 2005, 02:20 AMCold
The triangle makes use of the properties of the Fibonacci numbers. Notice that the triangle is of has sides 13 and 5 (Fibonacci). In particular it is possible to show that (Fn)^2 (the nth Fibonacci number squared) differs from F(n-1) x F(n+1) by 1 always. Sometimes + 1 sometimes - 1. The triangle you show just plays on this. Have a look at a 21 x 21 square and a 34 x 13 rectangle.