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:
Continue like this, keeping the tightened knots exactly 1˝ apart, until you’ve tied the 11th knot (at the maroon arrow).
Bring the remaining cords beyond the 11th knot together with the original 10-12˝ tail you left in front of the 1st knot and tie an overhand 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 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˝ version is nifty, because when you fold it in half, it can also measure 36˝ — one yard — in 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 ever so much better than a massive metal T-square, a modern tool that serves the same purpose.
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 orange arrow below). I like a double-overhand knot — two loops around instead of just one — as it gives a larger and straighter-lying knot.
Now, add another knot (at the purple arrow), being careful as you tighten it to position it exactly 1˝ away from your first knot.
Now, add another knot (at the purple arrow), being careful as you tighten it to position it exactly 1˝ away from your first knot.
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