Talk:Cissoid of Diocles
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Proof the cissoid is the described roulette, in case someone's interested.
- <math>f(t)=-t^2+ibt<math> <math>f'(t)=-2t+ib<math>
- <math>r(t)=t^2+ibt<math> <math>r'(t)=2t+ib<math>
- <math>f(t)-r(t){f'(t)\over r'(t)}=2bt^2(b+2it)/(b^2+4t^2)<math>
thus
- <math>y=4bt^3/(b^2+4t^2)<math>
- <math>x=2b^2t^2/(b^2+4t^2)<math>
- <math>y^2=16b^2t^6/(b^2+4t^2)^2<math>
- <math>x^3/(2a-x)={8b^6t^6\over(2a(b^2+4t^2)-2b^2t^2)(b^2+4t^2)^2}<math>
if <math>b^2=4a<math> then
- <math>y^2={4at^6\over(a+t^2)^2}={x^3\over2a-x}<math>
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 (http://mathworld.wolfram.com/CissoidofDiocles.html) 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)
- 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)