Associated Topics || Dr. Math Home || Search Dr. Math

### Collapsible Compass

```Date: 11/21/2003 at 00:05:12
From: HEF
Subject: Collapsible Compass

I need to know what a collapsible compass is and what it is used for.
All I know is that when you pick it up from the paper, you lose your
place.
```

```
Date: 11/21/2003 at 08:43:34
From: Doctor Peterson
Subject: Re: Collapsible Compass

Hi, HEF.

The collapsible is not something that is "used"; rather, it represents
the fact that Euclid wanted to make as few assumptions (postulates, or
axioms) at the base of his proofs as possible. So rather than assume
that it was possible to move a line around, keeping the same length
(as you could do with a real, fixed compass), or equivalently that you
can draw a circle with a given center and length, he assumed only that
you can draw a circle with a given center and through a given point.
Then he went on to prove that if you could do that, you COULD then
construct a circle with a given radius, or move a line to a given
place:

Collapsible Compass
http://mathforum.org/library/drmath/view/52601.html

Once that was proved, you didn't have to use a collapsible compass,
but could use a regular one, knowing that any construction you could
do this way, you could do with a collapsible compass. The link in the
page above explains this a little more fully.

Note that a real "collapsible compass" would not work, because the
radius would change as you drew the supposed circle! The idea is that
it holds together and keeps its radius as long as the center point is
in place, but loses it when you pick it up. I don't know of any
design for a real-world compass that would work that way; this is a
tool that exists only in the mind of a geometer, as a description of
Euclid's postulate 3.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Constructions
High School Euclidean/Plane Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search