Date post: | 29-Jun-2015 |
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Education |
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Evolute and Involute
Let 𝐶 and 𝐶1 are two one-one correspondence space curves such that tangent at any point on 𝐶 is a normal to the corresponding point on 𝐶1 then C is called evolute of 𝐶1 and 𝐶1 is called involute of 𝐶. i.e. if C is evolute of 𝐶1 then
a. 𝐶1 lies in the tangent surface of C b. tangent vectors to 𝐶 and 𝐶1 are perpendicular
Blue curve- Evolute
Red curve- Involute
Blue curve- Evolute
Red curve- Involute
Circle- Evolute
Dotted curve- Involute