Bounds and approximations
An approximation gives a nearby value. Bounds give two values with the true answer between them.
14 / ANTIQUITY TO THE RENAISSANCE
Zu Chongzhi
Roll a wheel exactly one unit across. After 113 turns it lands almost exactly on the 355 mark of a ruler. That is what 355/113 means.
Explore the mathematics ↓
01 / APPROXIMATION & ERROR
How close is close enough?
Each turn moves the wheel π units: a little more than 3. After a whole number of turns, the paint mark on its rim touches the ruler again.
Hunt for the number of turns that lands closest to a ruler mark. The magnifiers show how close each landing really is.
Where does the wheel land?
A wheel exactly 1 unit across rolls along a ruler marked in whole units. After some turns, how close does its paint mark land to a ruler mark?
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THE IDEA355/113 = 3.14159292… A fraction approximates π well when some number of turns lands almost exactly on a whole mark. After 113 turns, nothing lands closer until 33,102 turns.
The person behind the ideas
- Worked in fifth-century China on mathematics and astronomy.
- Gave 355/113 as a close approximation to π.
- Also worked on calendar calculations; his mathematical treatise is lost.
More of the mathematics
Calendars
Accurate periods for the Sun and Moon helped Zu propose improvements to the calendar.