While trying to sleep last night I discovered a new triangle. I call it the Piangle.
What's a Piangle? Maybe this will make it clear.
The Piangle is an unraveled circle. Imagine cutting a radius, then draw some inner circles.
Next unroll each outline to the right.
This is a right triangle, so by the Pythagorean theorem the length of the hypotenuse is , which is or .
The Piangle is not distorted, it's just an unrolled circle. It even has the same area as its corresponding circle. Its area is 1/2*b*h = = .
Proof that I discovered this: the hypotenuse = ≈ 6.3622651. Googling that doesn't return anything about the triangle.