- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,888

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

- Thread starter anemone
- Start date

- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,888

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

- Admin
- #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.

- Thread starter
- Admin
- #3

- Feb 14, 2012

- 3,888

- Admin
- #4

- Thread starter
- Admin
- #5

- Feb 14, 2012

- 3,888

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

- Admin
- #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...