[alogo] Maximal Ellipse inscribed in a square

The maximal Ellipse inscribed in a square is the incircle of the square.

This follows immediately from the relation between the square side x and the axes of the ellipse inscribed in the square. They satisfy the relation (prove it) a + b = x/2. Under this condition, for constant x, the area of the ellipse E(a,b) = pi*a*b, becomes a maximum when a = b = x/2.

[0_0] [0_1] [0_2]

For an application of this fact to the problem of finding the maximal ellipse, inscribed in an arbitrary parallelogram, look at the file ParaCircumscribed.html .

For a similar discussion concerning the minimal in area ellipse, circumscribed on a square , look at the file MinimalEllipse.html .

Produced with EucliDraw©