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Q&A #19178


Geometric constructions

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From: Jeanne (for Teacher2Teacher Service)
Date: Dec 23, 2007 at 20:24:13
Subject: Re: Geometric constructions

Hi Randy,

I've not used the safety compasses to teach constructions; however, I assume
most of those in a typical geometry course is possible. My assumption is
based upon the fact that I used to teach geometric constructions using some
pretty rustic tools:  an unlined 3 by 5 inch index card, a pair of pencils
and 1-inch paper clips (usually only 1 is needed, once in a while we needed
more).

Since I can't draw a picture of what we did, I'll describe how we used them.
Draw a dot (point A) on your paper. Place 1 paper clip on your paper so
that "loops" point A.  Place one of your pencils on point A. (If you flick
the paper clip, it will spin around the pencil.  es, a rustic spinner for
probability lessons.)  Place your second pencil inside the paper clip and
pull it taut.  Your pencil points are either ~1 inch apart or ~3/4 inches
apart.  Using the paper clip to hold your radius, construct a circle.  It may
take a few tries but eventually you'll get pretty good at it.

I always had my students work in pairs. One to hold the paper and one to
construct. Also, between the two students, I had a greater likelihood of
them having 2 pencils.

If I needed a longer radius, I linked paper clips.

With these tools, we
1) bisected an angle
2) bisected a segment
3) constructed a perpendicular bisector of a given segment
4) copied an angle  (Mark a 1-paper clip radius distance on each side of the
angle. I'll call the intersection between the sides of the angle and each of
the arcs, point X and Y. I let students mark the distance between X and Y on
their index card. We used this distance to construct the second angle.)
5) constructed inscribed equilateral triangles and hexagons
6) and others...

When we needed to have a radius that could not be accommodated by the 1 inch
paper clips, I had the students use a second index card onto which was marked
two points at the needed distance apart. We used push pins to make holes at
these points. We now had another type of compass to use. This modified
compass was needed for constructions such as constructing an inscribed and
circumscribed circle for a given triangle.

My use of rustic tools was not because I didn't have regular compasses in the
classroom. I actually had a class set of the kinds of compasses students in
a drafting class use. I used the rustic tools because I wanted my students
to do constructions for homework as well as in class. I could easily provide
paper clips, pencils, and index cards to each of my students and I didn't
care if students lost them. I did teach my students how to use the drafting
compasses after they'd mastered the paper clip compass; however, given a
choice, most of them used the paper clips.

Just as my paper clip compass affords benefits and disadvantages, I think the
safety compasses have benefits and disadvantages. It all depends on what
constructions and what mathematics you want your students to learn. My
answer is probably not what you expected to get, but I thought I'd share
anyway.

Good luck.

 -Jeanne, for the T2T service

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