Ellipse Area and CircumferenceDate: 04/19/2001 at 20:34:07 From: Sonja Farthing Subject: Ellipses Hi, I need to find out how to find the area and circumference of an ellipse, as well as how to draw one for a school project. I have looked at some of the ones in the archives but do not understand the answers or the symbols. Please help me. Thank you. Date: 04/19/2001 at 21:26:20 From: Doctor Jaffee Subject: Re: Ellipses Hi Sonja, You can draw two line segments through an ellipse, each of which will split the ellipse into two pieces that are reflections of each other. In other words, an ellipse has two axes of symmetry, one horizontal and the other vertical. Now, if we call the distance from the center of the ellipse to an end of the horizontal axis of symmetry a, and we let b equal the distance from the center to the end of the vertical axis of symmetry, then the area of the ellipse will be pi*a*b, where pi is approximately 3.14. We can find the circumference using calculus, but an easier method (although it only results in an approximate answer) is the formula circumference = 2*pi*sqrt[(1/2)(a^2 + b^2)]. Here is one way you can draw an ellipse. Get a piece of corkboard and attach a piece of paper (the longer side oriented left to right) to the corkboard using two thumbtacks, the first thumbtack approximately 4 inches from the left of the center of the paper and the other thumbtack about 4 inches to the right of center. Attach a piece of string, one end to each thumbtack. The length of string should be about 10 inches. Pull the string taut with a pencil and, keeping the string taut, move your pencil along the paper. The result should be an ellipse. I hope this explanation is helpful. If it needs clarification, write back, or if you are having difficulties, let me know. - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ |
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