Why half the size?
Only then are the two arms the same length and turning equally fast. A wheel a third of the ring’s size draws a curve with three points; a quarter-size wheel draws four.
32 / ANTIQUITY TO THE RENAISSANCE
Nasir al-Din al-Tusi
Roll a wheel around inside a ring twice its size. A pen on the wheel’s rim does not draw a loop: it slides back and forth along a straight line.
Explore the mathematics ↓
01 / THE TUSI COUPLE
Can circles draw a straight line?
Roll a toothed wheel inside a toothed ring and watch what a pen on its rim draws.
Compare smaller wheels, then split the motion into two turning arms.
Wheel:
=
=
THE IDEAWhen the wheel is half the ring’s size, the pen’s position is the sum of two equal arms turning at the same rate in opposite directions. Their up-and-down parts cancel, so two circular motions add up to motion along a straight line.
The person behind the ideas
- Directed the observatory at Maragheh.
- Developed mathematical models for astronomy.
- Wrote extensively on plane and spherical trigonometry.
More of the mathematics
Astronomy and trigonometry
Al-Tusi directed a major observatory at Maragheh, and his Treatise on the Quadrilateral set out plane and spherical trigonometry as a subject in its own right.