Chief Delphi - Math Quiz: Parabola Path

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- - Math Quiz: Parabola Path (http://www.chiefdelphi.com/forums/showthread.php?t=126639)

Ether

16-03-2014 23:44

Re: Math Quiz: Parabola Path

Quote:

Originally Posted by faust1706 (Post 1360056)

Are the curves closed?

That's not the answer I was looking for.

faust1706

16-03-2014 23:47

Re: Math Quiz: Parabola Path

I was asking whether curves E and C are closed, that wasn't may answer. I am still trying to wrap my head around what the question is asking

Ether

16-03-2014 23:48

Re: Math Quiz: Parabola Path

Quote:

Originally Posted by faust1706 (Post 1360071)

I was asking whether curves E and C are closed,

Not necessarily.

faust1706

17-03-2014 11:07

Re: Math Quiz: Parabola Path

Curve E is the evolute of the osculating circle, so curve E is the evolute of the involute of curve C.

I do not have a lot of faith in this answer. This really stretched by brain. If it's wrong please correct me and thank you for supplying me with these awesome questions!

Ether

17-03-2014 13:04

Re: Math Quiz: Parabola Path

Quote:

Originally Posted by faust1706 (Post 1360224)

curve E is the evolute of the involute of curve C.

So far so good. Now take that one step further...

faust1706

17-03-2014 14:18

Re: Math Quiz: Parabola Path

The involute of an evolute is the original curve itself, and I believe the evolute of an involute is the original curve too, so that means that Curve E and Curve C are the same.

Ether

17-03-2014 16:39

Re: Math Quiz: Parabola Path

Quote:

Originally Posted by faust1706 (Post 1360369)

I believe the evolute of an involute is the original curve too, so that means that Curve E and Curve C are the same.

The evolute of an involute is the original curve, less portions of zero or undefined curvature.

the original curve is the evolute of its involute

Ether

20-03-2014 10:48

Re: Math Quiz: Parabola Path

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Quote:

Originally Posted by faust1706 (Post 1360071)

Quoth the Kamen

Poe enthusiasts might enjoy the raven's version of what happened:

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