Pythagorean Thereom Numbers
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I've been trying to find numbers that apply for the PT (Pythagorean Thereom) but I can't find many unique ones. Anybody have a formula for this?
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Well, the Pythagorean Theorem itself is a^2 + b^2 = c^2. Any numbers that apply to this formula applies to the Pythagorean Theorem itself, however, some commonly used ones are 3, 4, 5 / 5, 12, 13 / 7, 24, 25 / and 8, 15, 17. All multiples of these three numbers are also applicable, for instance 6, 8, 10. However, all the numbers must be multiplied by the same amount, i.e 32 for 6, 42 for 8, and 5*2 for 10, so 6, 8, 10 is also follows the Pythagorean Theorem.
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If you mean cool ways to generate Pythagorean triples, then look at wikipedia.
$$\text{1. Find a (any) fraction } \frac{a}{b}, \text{ where }a \text{ and } b \text{ are relatively prime (a.k.a. coprime, mutually prime).} \newline \text{2. Find numbers (most likely fractions) }x \text{ and }y \text{ that satisfy the system} \newline System= \left\{ \begin{array}{l} x+y=\dfrac{a}{b} \\ x-y=\dfrac{b}{a} \end{array} \right. \newline -------------------------------- \newline \text{Let's say your }x \text{ is the fraction } \frac{c}{d} \text{, and your }y \text{ is the fraction } \frac{e}{f}. \newline \text{Then your triple is } \newline d^2+e^2=c^2. \newline \text{You can use a calculator to check.} \newline -------------------------------- \newline \footnotesize{\LaTeX} \text{is } 100 \% \text{ by me.} $$
My teacher once taught me a way using fractions. It is complicated, but it's cool: -
@JoyfulSapling That's actually really cool
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