Dividing a circle: the root of every mandala
Six, eight and twelve divisions with a compass. Half an hour, and after it the geometry families stop being mysterious.
Draft copy. This piece was written during the site build and is waiting on an editorial pass — the facts are checked, the prose is not final.
A compass, a sharp pencil and a straight edge. No protractor — you will not need one.
Six, for free
Draw a circle. Without changing the compass setting, put the point anywhere on the circle and strike an arc. Move to where that arc crosses the circle and strike again. Six steps and you are back where you started, exactly.
That is not a coincidence or an approximation: the radius of a circle fits round its circumference exactly six times. Every hexagonal pattern in every culture starts here, and it is why hexagons are so common — they are the division you get for nothing.
Twelve
Bisect each of the six arcs. To bisect: from the two endpoints of an arc, strike two equal arcs that cross, and draw a line from the centre through the crossing.
Eight
Different route. Draw a diameter, bisect it perpendicularly to get four, then bisect each quarter.
Why this matters
Every mandala we draw is built on one of these divisions. Once the construction is on the page, petals and borders do not get placed — they land on the division. That is why constructed symmetry feels settled and freehand symmetry feels nervous.
Next lesson
Building a girih pattern from the five tiles
Draw the tile set, lay it out, then draw the strapwork across it and rub the tiles out. Forty-five minutes.
Keep going
Other lessons
Start here: how to hold the pen
Ten minutes on grip, speed and pressure. Everything else in this section assumes you have done this once.
Straight lines and circles without a ruler
Two drills, twenty minutes, and the reason your circles close badly.
Dot grids: your first kolam
A 3×3 grid, one unbroken line, about fifteen minutes. The oldest drawing lesson there is.