Beyond whole-number coefficients
His algebra could use irrational quantities within equations, not just as answers.
21 / ANTIQUITY TO THE RENAISSANCE
Abu Kamil Shuja
A carpet covering 18 floor tiles has a side of √18: not a whole number of tiles. Yet √18 and √8 add as neatly as 3 and 2.
Explore the mathematics ↓
01 / SQUARE-ROOT ARITHMETIC
Different roots. The same rod.
Two square carpets lie on a tiled floor. Count the tiles each one covers: its side is the square root of that number.
Measure both sides with one rod, the diagonal of a tile. Then lay the edges end to end.
Carpets:
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THE IDEA√18 + √8 = 3√2 + 2√2 = 5√2. Count both roots in the same unit, then add the counts. Adding under the root sign (√26) gives a shorter, wrong length.
The person behind the ideas
- Worked after al-Khwarizmi and before al-Karaji.
- Combined algebra with geometric problems.
- His writings later influenced Fibonacci.
More of the mathematics
Geometry and algebra
He applied algebra to regular pentagons and decagons and worked with powers above the square.