A book I’m reading mentioned the process for constructing an equilateral triangle on a given side using only a compass and straight edge. I thought to myself, hey, I never learned to do that in geometry.
So I tried it. Lo and behold, it works. Beautifully.
So go get a compass and straight edge. Follow this:
1. Draw a random line on a blank sheet of paper.
2. Measure that line with the points of your compass.
3. Draw two arcs with the compass, AB and BA, where A and B are the endpoints of your line.
4. The intersection point of the two arcs is the third point of an equilateral triangle.
5. Use the straight edge to complete the figure.
I swear, I think I learned more geometry in that one lesson than in years of mathematics. Geometry, once upon a time, wasn’t looking at mysterious diagrams in a book and guessing at mysterious answers — it was building shapes with real tools.
And yet we wonder why national-average math scores drop year after year.
Hmmm. Did any of my readers get this sort of “practical” geometry instruction? Or was I sick that day?
You’re in good company. The Greek mathematician Euclid made the construction of an equilateral triangle Proposition 1 of Book I of The Elements.
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI1.html
Be sure to read the criticism of the proof. That gives you a real (and somewhat bewildering and frustrating) sense that there’s a lot going on beyond the shapes and tools.
Dear Raymond,
Thanks for the information about Euclid’s first proposition. I notice in the critique and in the proof that most problems are labeled Q.E.D., (or originally the Greek equivalent), to show that the solution is demonstrated thus; but that this proof is demonstrated and then the Greek/Latin QEF is listed — quod erat faciendum… “Thus it is done/thus is it made.” It may be the case that Euclid’s proposition isn’t good enough for people who never pick up a straightedge and compass, but I’ve now done this proof at a number of different sizes with the actual tools, and I’m convinced. 🙂
Actually, yes. I don’t remember even having a textbook. Los Angeles public school!