Cool Proof of Heron's Formula

by rrusczyk, Dec 14, 2007, 5:06 PM

Check this out. This slick proof by AoPS Community member Miles Edwards was just published in American Mathematical Monthly.

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7 Comments

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:D I can't wait to show this to my geometry class. Last week, my teacher took up two boards writing up the proof for Heron's formula.

by n0vad3m0n, Dec 14, 2007, 7:37 PM

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there was a cool geometric proof that was shown to us at AwesomeMath, I forget the details though.

But the above proof is also cool.

by CatalystOfNostalgia, Dec 14, 2007, 7:45 PM

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awesome!

...

now lets do the same thing with the orthocenter...

by Altheman, Dec 14, 2007, 10:12 PM

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complex number bash for the win!

by diophantient, Dec 15, 2007, 1:35 AM

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Elegant proof, Miles! Congratulations.

As an alternative to complex numbers, we can use the trig identity
\[ \tan \alpha + \tan \beta + \tan \gamma 
    = (\tan \alpha)(\tan \beta)(\tan \gamma)
\]
because $ \alpha$, $ \beta$, and $ \gamma$ add up to 180 degrees.

by Ravi B, Dec 15, 2007, 1:59 AM

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Nice! I thoughts that name sounded familiar...I think he was a Red MOPper two years ago.

by JSteinhardt, Dec 16, 2007, 3:51 AM

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thanks a lot i have been geting to this point thanks for the completion though.......

by 21 7 15, Dec 24, 2007, 5:01 PM

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