What is a Ruler and Compass Construction?

I’d never heard of this thing until grad school. And even then, I never asked what it was. Over the course of time I eventually figured it out, but never really got an opportunity to do much with it. Nor have I had a chance to teach it.

A teacher interview question from Oleg Gleizer’s book inspired me to think about, and learn, this nifty skill.

So what is it?

Here’s the definition (mostly from Wikipedia):

A ruler-and-compass construction is the construction of lengths, angles, and geometric figures using only a ruler and compass.

This means that you can take one of those “pointer and pencil circle making things” and anything really straight (the side of your new iPhone, the edge of a file folder, etc.) and make pretty much create anything in geometry.

Pretty cool, huh?

I gave it a shot!

I used Oleg’s teacher interview question:

Given a straight line and a point away from it, how would you draw another straight line passing through the point and perpendicular to the original line, using a compass and straightedge as tools?

Can I do it? Of course!

Well… I thought about it and it seemed like I could. So I went out and got a compass, and used a fingernail file as a straight edge. Here’s how I did it:

Here’s the line and the point. Easy peasy.

I made an arc from the point through the line, so I would have two spots on the line (where the circle piece went through):

From those two places, I made two more arcs through the point above and long enough to run into each other below:

I connected the point with the intersection of the arcs at the bottom and VOILA: perpendicular line to the other line!

Join me in the journey!

This is the first in my ruler and compass journey. They’re kind of fun, and I want to do more. So I will house them here, for future reference.

Here are the first 10 on my list. I grabbed them off this website.

  1. Line perpendicular to given line through given point not on given line. (this one)
  2. Perpendicular bisector of given segment.
  3. Right angle at given point on given line.
  4. Square with given segment as side.
  5. Equilateral triangle with given segment as side.
  6. Hexagon with given segment as side.
  7. Copy a given angle to a given segment.
  8. Line parallel to given line through point not on given line.
  9. Dividing given segment into N equal parts.
  10. Bisecting a given angle.

Grab a straightedge and compass for each member of your family and join me – let me know you’re on board in the comments or via email.

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2 Responses to What is a Ruler and Compass Construction?

  1. That looks really cool! Although…. I have no idea why I would want to do that. I think I’m really going to have to get my brain in to a math mindset to get on the same wavelength as you when I read here! lol (Word nerd<math nerd…lol)

    • That book I ordered is one groovy reason why you might want to dig out a compass. I just got it in the mail and I’m so excited about making some pretty designs!

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