For this program you will need to save c2002.mth, carlson.mth, c1998.mth, and ellipse.mth
in the same folder. Then execute ellipse.mth.
DERIVE program to calculate the perimeter of an ellipse.
RTF version ellipse.rtf
Word version ellipse.doc
Mathtype and Word version ellipsemt.doc

Calculate the perimeter of this ellipse.

, a > 0, b > 0, a > b

Calculate one fourth the perimeter and multiply it by four.

perimeter

The perimeter of an ellipse is an elliptic integral.

Change variables so it will be an elliptic integral in the table.

perimeter

,a>0, b>0, a>b

Before finding the integral in the table, do a numerical approximation. a = 7.5, b = 5

perimeter

perimeter = 39.66344269140738

First set i=1, n=3, and h=3.

The zeros of this rational expression are:

The integral is of the type .

perimeter

Look up this integral in the table and this is the result.

IHAT(ei) = 2·AHAT(ej + ek) + rij·rik·IHAT(-ei)

With i=3,j=1,k=2 this means this:

Calculate .

Substitute .

Substitute

. perimeter

Find the function to evaluate .

Substitute.

perimeter

a = 7.5, b = 5

Calculate the perimeter of this ellipse.

perimeter = 39.66359897322647447832915756945768124182520712081625172416815779