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The Piangle

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  1. Apparently this has been defined before: https://betterexplained.com/guides/calculus/ I don't know if he realized that each slice of the triangle corresponds to consecutive rings of the circle. Also we only need one triangle if we just measure it in radians
  2. 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.
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