Finding the Circumference of a Circle Using Its Shadow
Date: 1/26/96 at 5:23:17 From: Anonymous Subject: Formula for circumference of circle I am attempting to find the circumference of a large sphere hanging 25 feet in the air. It occurred to me that I could measure the shadow diameter and calculate from there, but I have long forgotten the formula and I'm not sure if that's the right approach anyway. I'd sure appreciate some help. Thank you. Paul Oldenburg
Date: 1/27/96 at 21:17:13 From: Doctor Ken Subject: Re: Formula for circumference of circle Hello! Sure, that approach will work fine, as long as I understand your question correctly. You're looking for the length that a belt would have to be to go around the big sphere in the air, right? If you measure the diameter of the shadow, then the circumference of the circle (and the length of the belt) will be Pi times the diameter, and Pi is about 3.14159. One thing to keep in mind: make sure that the light you're using to cast the shadow is pretty far away from the sphere, or else the shadow is going to be a lot bigger than the actual sphere in the air (consider what happens when the light is REALLY close to the sphere - the shadow is really big!). -Doctor Ken, The Math Forum
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