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Geometry - Bisecting a Line

by Andy Slater

So you have a line, and you want to spilt it in two. Maybe you want to go on to split it into four, but that's simply a case of splitting the halves in half again, the first thing you need to do is split it into two.

At this point you reach for a ruler, but what if the line turns out to be 5 7/16 of an inch long and you don't want to do the maths? Or the line is about 3 feet long and you only have a 6 inch ruler?

You can split a line in two, without measuring, using a pair of compasses. Aris Kafantaris provided the following image to illustrate the process:

Geometry - Bisecting a Line

All you do is to set the compasses to a measurement which is greater than half the length of the line (just guess) and drawing a couple of arcs with the point of the compass on one end and then the other. The diagram shows full circles but you only need to draw the bits where you anticipate that they will cross. A line drawn between the points where the arcs cross will cut across the centre of the original line at 90 degrees.

What's that you say? Your compasses are not big enough? No problem. Take a length of thread, tie one end around a pencil and tie the other end around a pin. Note that it needs to be tied loosely so that the thread 'slips' as opposed to wrapping itself around the pin or pencil as you draw the arcs. I've actually done this in gardens to mark out an area for paving using a couple of wooden stakes (one hammered into the ground and the other used to scribe a line in the dirt) joined together with a 20' length of washing line cord.

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