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- #1

- Feb 14, 2012

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This is a dimensionless number. Show that the smartest triangles are equilateral triangles.

- Thread starter anemone
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- Thread starter
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- #1

- Feb 14, 2012

- 3,931

This is a dimensionless number. Show that the smartest triangles are equilateral triangles.

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- #2

The objective function \(\displaystyle A(x,y,z)=\frac{\sqrt{s(s-x)(s-y)(s-z)}}{4s^2}\) where \(\displaystyle s=\frac{x+y+z}{2}\)

Subject to the constraint \(\displaystyle g(x,y,z)=x+y+z-p=0\)

will necessarily lead to the implication:

\(\displaystyle x=y=z=\frac{p}{3}\)

Thus, the triangle having the greatest IQ is equilateral.

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- #3

- Feb 14, 2012

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- #4

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- #5

- Feb 14, 2012

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Looks to me these copy/paste/edit things are signs of you're on the verge of cheating...

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- #6

It's only cheating if I copy/paste the work of someone else...which I would never do of course.Looks to me these copy/paste/edit things are signs of you're on the verge of cheating...