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Line 46: − #Let's divide one of the two prime number "''h''" factors contained in the "''h''<sup>2</sup>" by both sides of the equation:+ − #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+
Pythagorean theorem (view source)
Revision as of 08:49, February 15, 2021
, 08:49, February 15, 2021→Reasoning: ditto
===Reasoning===
===Reasoning===
1. Let's divide one of the two prime number "''h''" factors contained in the "''h''<sup>2</sup>" by both sides of the equation:
:(''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''
2. 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.
3. 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)===