Magic squares too
Yang Hui gave magic squares of every order from 3 to 10. No record of the larger ones survives in the work of earlier Chinese mathematicians.
34 / ANTIQUITY TO THE RENAISSANCE
Yang Hui
Seven circles overlap on one diagram. In each circle, the centre and the four numbers on its rim add to 65, and many numbers belong to more than one circle.
Explore the mathematics ↓
01 / MAGIC CIRCLES
Follow one circle. Count five numbers.
Add up each circle, then swap numbers to see which totals change.
Finally, use the rule “every circle makes 65” to put four missing numbers back.
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THE IDEAA shared number counts in several totals at once. A swap keeps every total only when both numbers belong to exactly the same circles, and the rule is strong enough to recover missing numbers.
The person behind the ideas
- Wrote mathematical texts for learners.
- Preserved accounts of earlier Chinese methods.
- Collected number squares and circle arrangements.
More of the mathematics
Teaching for understanding
Yang Hui wrote about how to organise mathematical study and explained procedures for beginners, as well as collecting challenging number diagrams.