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Hi, you don't have to split a triangle into integers. For example, you could have 50^2 = 25^2 + 43.3^2 Strictly speaking, if you have a circle of radius 50, y
by kalid 19y ago
Hi, you don't have to split a triangle into integers. For example, you could have
50^2 = 25^2 + 43.3^2
Strictly speaking, if you have a circle of radius 50, you can take the sine and cosine of any angle and get a possible way to split the length.
- pixcavator 19y agoFair enough. Still, what is the point of the article? Some additive quantities are squares of other quantities, you add them, and it looks like the Pythagorean Theorem, without triangles... Is that it?
- kalid 19y agoTwo 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?