Any star on a circle
Each point of the star is an angle at the rim, worth half the arc of circle it looks across. The five points of a pentagram look across five arcs that make up the whole circle, so together they make half of 360°.
36 / ANTIQUITY TO THE RENAISSANCE
Thomas Bradwardine
Join pins round a circle, skipping one pin each time, and a star appears. However lopsided the pins, its points add up to the same angle.
Explore the mathematics ↓
01 / STAR POLYGONS
How big are a star’s points, all together?
Thread a star on a round board: from every pin, skip one pin and go to the next.
Measure its points and lay them side by side. Make the star lopsided: the total stays put.
Walk the needle round the thread and count its turns, to see why every extra pin adds two right angles.
Pins:
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THE IDEAA star made by skipping one pin of n has points that add up to (n − 4) × 180°: two right angles for five pins, and two more for every extra pin. Walking the thread you turn round exactly twice, so the points make up the rest of n straight angles.
The person behind the ideas
- A Fellow of Merton College, Oxford, by 1321.
- Wrote Speculative Geometry (Geometria speculativa), which treats star polygons, and a treatise on the ratios of speeds in motions (1328).
- Became Archbishop of Canterbury in 1349 and died of the plague a few weeks later.
More of the mathematics
Ratios of speeds
In 1328 Bradwardine proposed that speed increases arithmetically as the ratio of force to resistance increases geometrically: to double a speed, square the ratio. It was influential medieval mathematics, not a correct law of motion.