Talk:Pedal curve
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Hm. Contrary to its pedal curve page, this mathworld page says the epicycloid does not give a rose. But hypo and epicycloids are such close cousins they should both or neither. I'll check carefully. 142.177.20.80 01:08, 2 Aug 2004 (UTC)
- The page is mistaken. Working in the complex plane and starting with P = 0 and z = kcis(t) + cis(kt) (epicycloids have k > 0, hypocycloids k < 0) we get
- and, finally, the pedal curve is
- Noting and letting t = 2θ / (k + 1)
- which is obviously a rose. 142.177.126.230 16:25, 2 Aug 2004 (UTC)
- Mathworld's been corrected =) 142.177.126.230 23:07, 5 Aug 2004 (UTC)
More work needed on contrapedal curve; mainly, what's done in higher spaces? While one could sensibly use the curvature vector, one could also use the perpendicular subspace...and somehow the latter is more appealing. Kwantus 18:53, 2 Aug 2004 (UTC)