Fibonacci & Medieval Europe
How Hindu-Arabic numerals transformed European computation
8.1 Leonardo of Pisa
Leonardo of Pisa (c. 1170–1250), known as Fibonacci, published Liber Abaci in 1202, introducing Hindu-Arabic numerals and positional notation to a European audience. The book demonstrated the system's power through hundreds of practical problems in commerce, measurement, and number theory.
8.2 The Fibonacci Sequence
The famous sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ... appeared in Liber Abaci as the solution to a problem about rabbit populations. The ratio of consecutive Fibonacci numbers converges to the golden ratio φ = (1 + √5)/2 ≈ 1.618..., which appears throughout nature and art.
8.3 Medieval European Mathematics
Key developments include the growth of scholastic logic at medieval universities and the work of Nicole Oresme (c. 1320–1382) on graphing velocities and summing geometric series. Oresme's graphical representation of varying quantities anticipated Cartesian coordinates by nearly three centuries.