Talk:Cissoid of Diocles

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Proof the cissoid is the described roulette, in case someone's interested.

f(t) = − t2 + ibt   f'(t) = − 2t + ib
r(t) = t2 + ibt   r'(t) = 2t + ib
f(t)-r(t){f'(t)\over r'(t)}=2bt^2(b+2it)/(b^2+4t^2)

thus

y = 4bt3 / (b2 + 4t2)
x = 2b2t2 / (b2 + 4t2)
y2 = 16b2t6 / (b2 + 4t2)2
x^3/(2a-x)={8b^6t^6\over(2a(b^2+4t^2)-2b^2t^2)(b^2+4t^2)^2}

if b2 = 4a then

y^2={4at^6\over(a+t^2)^2}={x^3\over2a-x}

142.177.124.178 06:26, 21 Jul 2004 (UTC)

Well, it's nice to know that some anonymous user read an article which I started. I'll take your word that your proof is correct. Maybe I will get around to adding something similar to it in the article. --AugPi 14:27, 27 Jul 2004 (UTC)
Holy...I thought I was putting too much math in articles like roulette and evolute. I knew it was so from Mathworld but rather than just copy (esp since Mathworld is occasionally wrong) I like to have done a proof first. 142.177.126.230 22:34, 2 Aug 2004 (UTC)
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