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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: Reuleaux triangle, Reuleaux drill
Replies: 25   Last Post: May 1, 1995 8:18 AM

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Pao-Ping Lin

Posts: 2
Registered: 12/10/04
Re: Reuleaux triangle
Posted: Apr 29, 1995 3:42 PM
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> In article
> <Pine.OSF.3.91.950410230701.16534A-100000@Kay-

Abernathy.tenet.edu>,
> mkeyton@tenet.edu (Michael Keyton) wrote:
>

> > Drill bits can be made using the triangle to drill
> > "square holes".

>
> Can this triangular drill bit be modelled in Sketchpad or Cabri?
> Anyone here tackled it? Or should I get the book and give it a try?
> -Annie


>>Well, I spent this cold & snowy(!) Saturday trying to model it. The chapter
>>by Rademacher and Toeplitz in "The Enjoyment of Math" gives only minimal
>>information, mostly on the construction of curves of constant breadth and
>>properties thereof.
>>The construction of the bit itself is trivial, it is the rotation of the bit
>>that is the problem - in order for it to rotate inside a square, the centre
>>of rotation itself must move, and not in any standard (i.e. easy to animate)
>>orbit. If you've made or found a sketch please let me know! I'll keep
>>struggling...


I have constructed a sketch to model the "square drill" on the
Geometer's Sketchpad version 2.10 for Mac. You may use button
to animate the "drill" or drag a control point to turn it. The locus of
the center looks like a circle but not. The shape drilled off can be
seen. Its animation is cheating (but what animation is not cheating?). It has
been uploaded to the incoming ftp directory on this Forum.

Pao-Ping Lin unit760@twnmoe10.edu.tw
Department of Mathematics and Science Education
Taipei Municipal Teachers College
Taipei, Taiwan.






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