A hexagon from a circle
Honeycomb cells have six sides. Can a compass draw one?
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- A circle about O, and a point S on it.
- Keep the span at the radius. Step round.
- Six steps come back to S.
- Join the six points. Six triangles meet at O.
The rule
Yes. A compass can draw a hexagon, a shape with six sides. To step is to mark the same span again and again.
Draw a circle. Keep the compass at the radius. Step it round the circle. Six steps come back to the start. Join the six points. That is a regular hexagon.
A regular hexagon has six equal sides and six equal corners. Each step makes a triangle with the centre. All three sides of that triangle equal the radius. So it is equilateral, and its corner at the centre is 60°. Six corners of 60° fill 360°: 6 × 60 = 360.
Each side of the hexagon equals the radius. Two of the triangles meet at each corner of the hexagon. Each corner of the hexagon is 60° + 60° = 120°.
Example: a 30 mm radius gives sides of 30 mm.