The Legend and Origins of Lo Shu

The Lo Shu Square is one of the oldest mathematical diagrams in human history, dating back over 4,000 years to ancient China.

The Mythical Origin

According to Chinese legend, around 2800 BCE, Emperor Yu was working to control the floodwaters of the Yellow River when a divine turtle emerged from the Lo River. On its shell was a pattern of dots:

```

4 9 2

3 5 7

8 1 6

```

This pattern, where every row, column, and diagonal sums to 15, became known as the Lo Shu (洛書).

Mathematical Significance

The Lo Shu is a perfect magic square:

• All rows sum to 15
• All columns sum to 15
• Both diagonals sum to 15
• The center number (5) is the average of all numbers 1-9

This mathematical perfection was seen as evidence of cosmic order and divine wisdom.