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From: 2.7182818284590... on 14 Apr 2010 21:39
What is the shape whose path is a semicircle of radius R traced from a
point on the edge of this strange wheel as it rolls along a straight
line?

I realize that by tracing the edge of a normal circle as it rolls down
a flat plane yields a cycloid. However, what if the shape that is
drawn is a semi-circle?

Thanks in advance.
From: Virgil on 14 Apr 2010 22:59
In article
<5d694be8-4eb8-4307-9777-c8c304beebfe(a)l37g2000vbd.googlegroups.com>,
"2.7182818284590..." <tangent1.57(a)gmail.com> wrote:

> What is the shape whose path is a semicircle of radius R traced from a
> point on the edge of this strange wheel as it rolls along a straight
> line?
>
> I realize that by tracing the edge of a normal circle as it rolls down
> a flat plane yields a cycloid. However, what if the shape that is
> drawn is a semi-circle?
>
> Thanks in advance.

A cycloid is generated by a point on the circumference of a circle as
the circle rolls along a line. Since all points on such a circle
generate congruent cycloids, it does not matter which point is chosen.

But for your problem, the choice of different points on the boundary of
that semicircle will generate differing non-congruent paths.

So you problem is not well formed.
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