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mLine 50:
Line 50: − Now let's divide the second one through both sides of the equation:+ − :(''l''<sub>1</sub><sup>2</sup> / ''h''<sup>2</sup>) + (''l''<sub>2</sub><sup>2</sup> / ''h''<sup>2</sup>) = 1+ − − And separate out one leg-length factor from each leg-length-square fraction: − − :''l''<sub>1</sub> (''l''<sub>1</sub> / ''h''<sup>2</sup>) + ''l''<sub>2</sub> (''l''<sub>2</sub> / ''h''<sup>2</sup>) = 1
Pythagorean theorem (view source)
Revision as of 08:37, February 15, 2021
, 08:37, February 15, 2021→Reasoning: correct passage in wrong direction
:(''l''<sub>1</sub><sup>2</sup> / ''h'') + (''l''<sub>2</sub><sup>2</sup> / ''h'') = ''h''
:(''l''<sub>1</sub><sup>2</sup> / ''h'') + (''l''<sub>2</sub><sup>2</sup> / ''h'') = ''h''
And since ''l''<sub>1</sub> and ''l''<sub>2</sub> are whole numbers, what results when they are multiplied by themselves, namely ''l''<sub>1</sub><sup>2</sup> and ''l''<sub>2</sub><sup>2</sup>, certainly are as well.
So let's relabel ''l''<sub>1</sub><sup>2</sup> and ''l''<sub>2</sub><sup>2</sup>, ''o''<sub>1</sub> and ''o''<sub>2</sub>, to show they are natural numbers like the ''n''s
===Conceptualization (cont'd)===
===Conceptualization (cont'd)===