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Two main points, mostly to look at this old theorem in new ways. 1) The sides of a triangle (3-4-5) can represent portions of any shape. For example, circle ar
by kalid 19y ago
Two main points, mostly to look at this old theorem in new ways.
1) The sides of a triangle (3-4-5) can represent portions of any shape. For example, circle area (radius 3) + circle area (radius 4) = circle area (radius 5).
Instead of radius, you could pick diameter, circumference, or any line segment and the relationship would hold.
2) You can use the Pythagorean Theorem to split any squared quantity into two smaller ones. This can yield surprising insights; is it immediately clear that a list of 50 takes as long to bubble sort as a list of 30 and 40? =)
- pixcavator 19y agoThere may be a point here, but I am still uncomfortable with the use of the Pythagorean theorem here. Even if applied to areas only, it seems like a stretch. In fact with this approach one can suggest other identities. For example, if you replace squares with cubes (or circles with spheres), you will have a^3+b^3=c^3. And this clearly has nothing to do with the Pythagorean theorem.
- testapplication 19y agoYou might want to try that math again; it doesn't work for spheres.
- pixcavator 19y agoWhat math?