...diagonal is the hypotenuse of an isosceles right triangle. We know from the Pythagorean theorem that the square of the hypotenuse equals the sum of the squares of the other two sides. In this case the sides are equal. To express the diagonal as a function of the...

...complicated. The proof of the theorem is very cumbersome, long and so on. But once the purport of the theorem, "the square of the hypotenuse equals the sum of the squares of the other two sides," is understood, any person who knows how to work it and demonstrate its correctness,...

...500 Bc) Greek philosopher and mathematician who was famous chiefly for his theorem stating that for a right triangle, the square of the hypotenuse equals the sum of the squares of the two sides. His numerical ideas were incorporated into the theory of the four humors (see "The Disease...

...'fits and starts' rather than in a constant, gradual process. Pythagoras' theorem In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Quantum entanglement Phenomenon whereby collections of particles are linked and...

...and proved geometrically step by beautiful logical step that — let me think, it's been a while — the square of the hypotenuse equals the sum of the squares of the other two sides — isn't that it? And then there is the biology teacher whose name I can't remember,...

...these people have found their way into computer animation programs. For example, Pythagoras' law about "the square of the hypotenuse equals the sum of the squares of the other two sides" is centra! to everything that goes on inside a computer animation program. The...

...triangle's being equivalent to the kind of triangle obeying the Pythagorean theorem, the proposition that the square of the hypotenuse equals the sum of the squares of the other two sides. The notion of a right triangle is commonly introduced, and some of its identifying...

...saw a burning house. (Dream world) If wishes were horses, beggars would ride. (Hypothetical world) The square of the hypotenuse equals the sum of the squares of the opposite sides. (Abstract world) Once upon a time is a referring phrase which clearly specifies...

...12 and diagonal of length 13. J Solution: First find h, the length of the altitude of the rectangle. In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. Hence, (leg)8 + (leg)3 - (hypotenuse)3 ha + 12s = 13s h3 + 144 = 169 h2 = 25, h = 5 Since...

...R equals 1 .4 F. The value for R is also found by use of the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the sides. Adapted with permission from Brand, PW (1985). Clinical Mechanics of the Hand (pp. 30-60)....