Drawing Regular Polygons

Many years ago when I was at school (about 1975) I was shown how to draw regular polygons in Technical Drawing Class

I'm not sure if this is still taught in these days of computers so here goes

The drawing equipment I was using was a bit ancient and infirm (a little like myself) plus I was doing the drawing on my lap with a dog nuzzling me, so the accuracy is a little off

Using a decent compass and a table would probably make this much more accurate :-)

Compass

Pencil

Ruler

Draw a baseline the length of one side of your desired polygon (I have used 40mm here)

Subdivide the line either by measuring or, as I have, using the arcs drawn with a compass from each end

Draw a line perpendicular to the first (this is where the subdivide using a compass comes in handy) by drawing through the 2 compass arc crossover points for a perpendicular

Place the compass point at one end of the baseline, draw an arc the length of the side of the polygon (in this case 40mm) from other end to intersect the perpendicular

Place the compass point in the centre of the baseline, draw a second arc half the length of the side of the polygon (in this case 20mm) from the centre of the base to intersect the perpendicular

These will give you the centres for circles to draw a 6 sided (hexagon) or 4 sided (square) polygon

Label these 2 points as 6 and 4, (you don't have to do this, I have for clarity)

Again I subdivided using drawn compass arcs, but easy enough to just measure the distance between points 4 and 6 with a ruler and mark halfway, mark this as point 5

I set the compass to a distance between points 4 and 6 and then stepped off along the perpendicular line to give points 8,10,12 etc, then using the same distance stepped off from point 5 to give points 3,7,9,11 etc. Again you can just use a ruler for this.

I then numbered all the points, just for clarification on this 'ible

Place the point of your compass on the number corresponding to the number of sides of the polygon you want to draw, in the first picture I have it on the 3 to draw a triangle

Open up the compass so that pencil is at one end of the baseline, draw a circle

Open up the compass to the length of the baseline (in this case 40mm) and with the compass on one end of the baseline, strike an arc to intersect the circle (in this case it will be at point 6 on the perpendicular)

Draw a line from each end of the baseline to this point and you have an equilateral triangle.

In this case put the compass point at Point 4

Open up the compass so that pencil is at one end of the baseline, draw another circle

Open up the compass to the length of the baseline (in this case 40mm) and with the compass on one end of the baseline, strike an arc to intersect the circle

Step out the 40mm baseline around the circle and "join the dots" for a square

Carry on in the same manner for subsequent points, first picture shows 5 sided (Pentagon),6 sided (Hexagon),7 sided (Heptagon) - I've called it a Septagon because that's what they were called when I went to school!!!

Second picture is a continuation with Hexagon, Nonagon and Decagon, in theory you can go as high as you want.