## Geometry et Trigonometry

it was math so a lot of people didn’t pay much attention. and there was a lot of “I’m never going to need this” nonsense going on at my school…

But now you need it: well a little of it. you can do a lot with a little.

squares and circles: the geometric relationship between squares and circles is neglected in geometry class. Sure they point out that blah blah blah circle center of square etc. and most people didn’t listen.

look: it really is simple: and it really is useful!

a circle and a square look like they have nothing to do with one another, look again:

if you bisect the angle your line (dotted) is the centerline of the circle. you can use this knowledge to make a center finder for turning on the lathe. or find the center on anything roundish. Or you can use this to make a center finder for your lathe stock.

the same basic principles apply to these also:

the center for this rough piece is somewhere in the middle of the triangle scratched on the end.

Also if your round is larger: on any right triangle if you center a circle on the center of the hypotenuse who’s diameter is the length of the hypotenuse the circle will touch the point of the right angle, so:

rotate the square a bit and do it again:

then the 2 lines cross right at the centerpoint.

jumping back to that first geometry: chairmakers (like Curtis Buchanan) uses it every time he drill his legs for his stretchers. See if the center of the circle is always in line with the center of the square…

if we make a 90 degree v cut in two blocks of wood exactly equidistant from the ends. and stand those blocks up. we get this sort of set up:

where, no matter what the different diameters are or how lumpy/fancy the turning is, straight rod or windsor leg, the centerline of the turning will be parallel to the bench top. so we can set an angle guide to help us aim our drill into the legs at the correct angle.

Here’s another one, you want a nice arc that is a part of a circle but you don’t know where the center of the circle is. or you don’t have a compass around…

put 2 nails at the ends and use your square…

if you slide the square, keeping contact with the 2 nails and a pencil in the peak, it will draw a circle.

Most of the trigonometry that you will need is just what Pythagoras knew. if you haven’t got a square or your object is really big enough that a square isn’t big enough. remember the pythagorean theorem. 345. as in 3″, 4″, 5″. or any measure. a triangle with legs of 3 units and 4 units and a hypotenuse of 5 units has a right angle between the 3 and 4 sides. See you don’t even need the squares or square roots or sines and cosines etc.

3 feet by 4 feet then 5 feet across the diagonal will make a right angle.

So you see: a little understanding of Geometry and even Trigonometry can help you with every project!

be well

K