How to Construct Rational Numbers

In this video, Chris Tisdell explores how we can create special numbers called rational numbers using just a circle arc template and a straightedge. This exercise is not only a classic puzzle but also a fascinating way to see how numbers and geometry can come together.

Chris starts with this number line, and our goal is to find two specific rational numbers: one-third (1/3) and two-thirds (2/3). Chris draws a ray that starts at our zero point.

Next, Chris uses a tool called a circle arc template. Chris uses the circle arc template to create three points where the ray meets the arcs.  On our number line, remember we marked zero at the beginning? Well, Chris finds another point there. This point represents the number "1" on our number line, this is the radius of our circle arc template.

Now, let's connect the dots, or in this case, the points. From the third marker on our ray, Chris draws a straight line to the point on the number line that represents "1."

But what about those other two points on the ray? Here's where it gets really interesting. Chris draws two more straight lines, just like the first one, but these lines are parallel to the previous line, and to each other.

These parallel lines meet our number line at two special spots. These spots represent our desired numbers: one-third (1/3) and two-thirds (2/3).

So, there you have it! Using a circle arc template and some clever straight lines, Chris shows us how to construct the rational numbers 1/3 and 2/3 on a number line. It's like a mathematical adventure, exploring how geometry and numbers work together.

This exercise not only helps us understand rational numbers but also shows how mathematics can be like a puzzle waiting to be solved. So, the next time you hear about rational numbers, you'll know that you can create them on a number line, thanks to the magic of circles, lines, and a little bit of mathematical know-how.