How does the Pythagorean theorem describe a circle?The Pythagorean theorem states, for a right triangle with legs a,b and hypotenuse c, a 2 + b 2 = c 2 By replacing c with r, radius this equation becomes the equation of circle at centre (0,0).How does Pythagoras' equation end up describing the circle?

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How does the Pythagorean theorem describe a circle?The Pythagorean theorem states, for a right triangle with legs a,b and hypotenuse c,      a    2    +      b    2    =      c    2  By replacing c with r, radius this equation becomes the equation of circle at centre (0,0).How does Pythagoras&#039; equation end up describing the circle?

Dayana Zuniga · Accepted Answer

It is ultimately tied to the notion of distance and how we calculate it in the xy-plane that we&#039;re familiar with. Imagine placing a right triangle, with sides a,b,c, with one vertex at the origin, like below:

icedagecs · Accepted Answer

This circle has the origin as it centre, so the four Cartesian quadrants each contain a quarter of it. In the first quadrant, a,b are both positive. Consider the right-angled triangle whose vertices are (0,0),(a,0),(a,b) with       a    2    +      b    2    =      c    2   by Pythagoras; the third vertex lies on the circle, so smoothly rotating the length-c hypotenuse from (c,0) to (0,c) traces out the quarter-circumference in the first quadrant. As we continue through other quadrants, the right-angled triangle ends up flipped horizontally and/or vertically, but the above formulae for its vertices remain correct. In short, we make a circle by rotating a radius, and each location it has along the way lets us construct such a triangle.

How does the Pythagorean theorem describe a circle? The Pythagorean theorem states, for a right tri

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