Dear sir,
I am investigating into isoperimetric shapes and got stuck at proving that an isosceles triangal has a larger area with a given perimeter and that the equilateral has the largest of all trianals. I think that it has something to do with making the base of the triangle the diameter of a cirle and joining the points with a semi-circle. I have already prooved that the circle is most efficient with an isoperimetric quotient of 1. Please could you help.
Thank you, Best Wishes, Chris

>Dear sir,
> I am
>investigating into isoperimetric shapes and
>got stuck at proving that
>an isosceles triangal has a
>larger area with a given
>perimeter

than what? Unless you specify some constraints,
this formulation is incorrect. There are scalene
triangles with areas greater than that of
some isosceles triangles of equal perimeter.

For the statement to be true you have to fix
the base. After you do, think of how you draw
an ellipse with two given foci.

>I have
>already prooved that the circle
>is most efficient with an
>isoperimetric quotient of 1.

Well, congratulations.

> Please
>could you help.

Hope the above helps.