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I deleted some of the material on natural parameterization, specifically the paragraph on dealing with the equations when s is not a closed form expression. First, the material was about simplifying the expression for derivatives in this case and not about evolutes. Second, the expression obtained
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I've added an animated gif showing how the evolute is constructed as the locus of the centers of curvature. The tangent to the astroid is also shown, illustrating simultaneously that the evolute is the envelope of the normals to the curve.Juliusllb 23:32, 10 November 2013 (UTC)
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should, when all the dust has settled, be the same as the expression in the general parameterization case (else there is an error somewhere). Third, I could not find similar material in references. --
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I could not find a reference or a clear definition so I could verify it myself. If someone can clarify or site a source it could probably be re-added.--
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what is the evolute of a sequence of circular arcs, if not disconnected points? And what would be an involute of that?
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involutes are not unique and thus "The original curve is then said to be the involute of its evolute" is wrong
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Continuing the "what to do without a natural parametrisation" stuff: it often happens that
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Also moved statement about parallel curves to the article on parallel curves.--
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381:{\displaystyle q'(t)=2s'(t)s''(t)}
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632:{\displaystyle x=(aC,bS)}
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578:{\displaystyle |r''|^{2}}
214:{\displaystyle s'(t)^{2}}
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30:Start-class
1580:Categories
1300:evolute =
1423:Juliusllb
1431:contribs
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1398:astroid
139:on the
1564:RDBury
1550:RDBury
1467:r=f(s)
1446:RDBury
36:scale.
651:=sin(
643:=cos(
1568:talk
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258:Let
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131:Mid
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285:′
282:s
278:=
275:)
272:t
269:(
266:q
243:)
240:t
237:(
233:′
230:s
207:2
203:)
199:t
196:(
192:′
189:s
143:.
42::
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