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Fractions lead to Pythagoreans (Posted on 2016-06-28)

Write down two fractions whose product is 2.

Add 2 to each. Keep them improper.

Cross multiply to get two whole numbers.

These numbers are the legs of a Pythagorean triangle!

Prove this always works.

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Negative thinking

| Comment 2 of 4 |

This does not work if one of the fractions is less than or equal to -2.

If equal to -2, then one of the cross-products is 0.

If less than -2, then one (but not both) of the cross-products is negative.

This does appear to work with two negative fractions, both of which are greater than -2.

For instance, -4/3 and -3/2 lead to cross products of 3 and 4.

Posted by Steve Herman on 2016-06-28 18:26:51

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