Restoring and balancing
His methods systematically transformed equations into forms with known solutions.
18 / ANTIQUITY TO THE RENAISSANCE
Muhammad ibn Musa al-Khwarizmi
A square garden and ten strips as long as its side cover 39 square units. Fill in four corners, and the garden’s side appears.
Explore the mathematics ↓
01 / COMPLETING THE SQUARE
Complete the square. Find the side.
A “root” is the side of the square. Share the 10 roots around the garden as four strips, then fill the four empty corners.
The completed square has a side you can find. The garden’s side is that length minus the two strips.
Problem:
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THE IDEAAdding the missing corners turns x² + 10x into a whole square, (x + 5)². Its area is 39 + 25 = 64, its side 8, so x = 8 − 5 = 3.
The person behind the ideas
- Worked in Baghdad under Abbasid patronage.
- His algebra treatise treated linear and quadratic equations.
- His name is the source of the word “algorithm.”
More of the mathematics
Numerals and astronomy
He also wrote on Indian arithmetic, astronomical tables and geography.