Date: 04/11/2002 at 12:03:14 From: Allison Milam Subject: Circle/Ellipse Diameter If you initially have a circle and it gets smushed into an ellipse, how do you determine what the diameter of the initial circle was, knowing the major and minor diameter of the ellipse?
Date: 04/11/2002 at 12:54:44 From: Doctor Peterson Subject: Re: Circle/Ellipse Diameter Hi, Allison. That depends on how it was "smushed"! What was preserved - does it still have the same area (as if it is made of clay or some uncompressible material), or the same perimeter (as if it is contained in an unstretchable membrane, but the inside can compress), or what? Answering that question will probably make it clear how to answer your question. You may need to use our Geometric Formulas page to see how to carry out the plan: Ellipse http://mathforum.org/dr.math/faq/formulas/faq.ellipse.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 04/11/2002 at 13:25:07 From: Allison Milam Subject: Circle/Ellipse Diameter I am a forensic scientist in the field of firearm and toolmark examination. We use the diameter of the base of a bullet as a way of figuring out caliber. Therefore, when we get a damaged bullet where the base has changed from a circle to an ellipse we would like to be able to determine what the initial diameter was.
Date: 04/11/2002 at 13:33:54 From: Doctor Peterson Subject: Re: Circle/Ellipse Diameter Hi, Allison. You can probably assume that the area remains the same, although I could easily imagine metal deforming in such a way that the area might change. With that assumption, you just have to find the area of the ellipse K = pi A/2 B/2 where A and B are the major and minor axes (diameters), as opposed to the usual a and b, the semi-axes (radii). Since a circle of diameter D with the same area would require K = pi (D/2)^2 we have pi D^2/4 = pi AB/4 D^2 = AB D = sqrt(AB) So just take the square root of the product of A and B (called the geometric mean) as your presumed original diameter. I would recommend testing this on some deformed bullets whose caliber you know, in order to check our assumptions. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 04/11/2002 at 13:49:04 From: Allison Milam Subject: Circle/Ellipse Diameter Thank you very much for your time. We are going to manually deform some known caliber bullets with a hammer and try out these formulas. If it works I will write an article to share the information with others in the field. Again, thank you for your help.
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