The Pythagorean Triangle:

Make a Measuring Device


What you see in this illustration is a simple string version of the 3-4-5 Pythagorean triangle — easier to see if we add some grid lines to mark off the precise measurements along its 3- and 4-square edges, and the 5 knot-defined sections along its diagonal side:


Continue like this, keeping the tightened knots exactly 1˝ apart, until you’ve tied the 11th knot (at the red arrow).

Bring the remaining cord beyond the 11th knot together with the original 10-12˝ tail you left in front of the 1st knot and tie an overhand knot with these combined strands (at the green arrow), again being careful to keep the tightened 12th knot 1˝ away from both knot #1 and knot #11.  Trim the ends to a tassel or attach a charm here if you like.

So, what’s this thing good for?  You can use it as ancient carpenters are purported to have used a larger version of this: to find and check right angles.

For example, the large final knot (at the purple arrow here) can be placed at a corner. 

Stretch the cord leading out to knot #8 (blue arrow) straight out taut along the floor. 

If the wall is set properly, knot #3 (at the red knot) will meet the wall and there will be no droopy slack in the cord between knots #3 and #8 (the area indicated by the turquoise arrow). 

If there’s slack in the cord between #3 and 8, the wall is slanting inward. 

If knot #3 can’t meet the wall, the wall is slanting outward.

To do accurate measuring for building purposes (anything larger than a sand box,

I think), you’d want a larger version of this device, created with 6˝ of cord (or even 12˝) between each knot. 

The 6-foot version is nifty, because when you fold it in half, it can also measure 36˝ — one yard or three-feet — with knots at 6˝ increments. 

This certainly isn’t high-tech, but it’s a good, graphic way to play with measurements and angles, kids think it’s fun (so do grown-ups), and it fits in the pocket so much better than a massive metal T-square, a modern tool that serves some of the same purposes.

To make a string Pythagorean triangle for yourself, use a heavy-ish string that isn’t stretchy, something that handles easily and holds a knot without slipping loose.

Knots take up quite a bit of cord, so I like to start with about 54˝ — about one-and1/2 yards — just to avoid running short.

Leaving a tail of 10-12˝ inches, tie the first knot (at the yellow arrow below).  I like a double-overhand knot — two loops around instead of just one — as it gives a larger and straighter-laying knot.

Now, add another knot (at the purple arrow), being careful as you tighten it down to position it exactly 1˝ away from your first knot.