Luckson Matigwa, of Harare and Chipinge, self-educated man and mathematician, showed me the following method as his own invention for ``finding the size of any angle without using a protracter."
You should first make for yourself this simple but useful instrument, which I shall call MATIGWA's MATE: You need three straight strips of wood or plastic, with lengths 60, 60 and 120 (millimetres will do, but the scale can be enlarged without affecting its operation). The three strips must be hinged as shown, so they can move freely in the plane of the piece of paper on which you will perform your measurements and constructions. One of the short strips must be graduated with 1-60, as shown.
Here is Mr Matigwa's method.
To make any angle 0 £ q £ 60o
For example q = 23o.
To make any angle 60o £ q £ 180o
For example q = 94o.
Make an isosceles triangle with base angles
[ 1/2](180-q)=[ 1/2](180-94)=43o.
MATIGWA's MATE is remarkably quick and efficient, and should be very useful as a basic drawing or surveying tool (indeed it is a simple form of sextant). But what about its accuracy?
By the purely intellectual standards of Euclidean geometry, only the
angle 60o is thereby accurately constructed. For the best discussion
of why the method is at best an approximate one, what the accuracy is
over various ranges of angle, and whether much could be gained by a
careful re-calibration of the graduated leg, we
offer a PRIZE.