Draw exact figures with an unmarked straightedge and compass
Mathematicians of old worked out how to draw exact figures with just two tools: an unmarked straightedge for drawing lines, and a compass for drawing circles and carrying lengths. Walk through the classic constructions step by step first, then take on the challenges yourself.
The ancient Greeks set a strict rule: figures had to be drawn with an unmarked straightedge and a compass, nothing else. Remarkably, those two tools are enough to produce exact results like perpendicular bisectors and angle bisectors without measuring a single angle — the secret is the symmetry of "equal distances, equal radii".
How to use it — in "Watch an example", step through a construction one move at a time with the buttons. In "Construct it yourself", pick the straightedge or the compass, then click two points in turn. The straightedge draws the line through both points; the compass draws a circle centred on the first point with its radius reaching the second. Wherever lines and circles cross, a new point appears automatically and is yours to build on.
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Pick two points
Constructions solved: 0
There are only two moves these tools allow — drawing the line through two points that already exist, and drawing a circle centred on an existing point, with the distance between two other points as its radius. Repeating just those two is enough to produce perpendicular bisectors, angle bisectors and regular triangles, pentagons, hexagons and octagons, exactly.
🤔 So why is there no regular heptagon (7 sides) example? Unlike the triangle, pentagon, hexagon and octagon, the regular heptagon has been mathematically proven impossible to construct with straightedge and compass alone! Which regular polygons are constructible depends on whether the number of sides is a power of 2 times distinct "Fermat primes" (special primes like 3, 5, 17, 257, 65537) — and 7 does not fit. Isn't it striking that mathematics can prove something cannot be done?