Leonardo of Pisa, known since the nineteenth century as Fibonacci, learned Hindu-Arabic numerals as a boy in Bugia on the North African coast where his father was a customs official, and his Liber Abaci of 1202 is the book that carried them into Latin Europe against the entrenched Roman system. The sequence that carries his name appears in it as a puzzle about breeding rabbits and had already been described in Indian prosody centuries earlier by Pingala, Virahanka and Hemachandra, counting the arrangements of long and short syllables. Its later career is largely outside mathematics: the ratio between successive terms approaches the golden section, and that has made the sequence a fixture of sacred geometry, of design mysticism and of a great deal of claiming about ancient architecture that the measurements do not support.
Facts
Disputed
Lifespan or FloruitNo document records Fibonacci's exact birth. Historians of medieval mathematics cite around 1170 in Pisa as the conventional estimate, consistent with his father's known career and with the dedication of his own Liber Abaci, rather than a fixed birth record. Lifespan or FloruitNo document records Fibonacci's exact death. Historians of medieval mathematics cite around 1250 as the conventional estimate, the last period in which he is documented as active in Pisa, rather than a fixed death record. Origins
Place of OriginPisa, Republic of Pisa (Italy) 1 Learn More
The Book That Changed How Europe Counted
Leonardo of Pisa met the Hindu-Arabic numerals as a boy in Bugia, on the North African coast, where his father ran a trading post, and the Liber Abaci of 1202 is his attempt to make Latin Europe use them. It opens by introducing the nine figures and the sign for nothing, then spends most of its length on the arithmetic a merchant actually needs: converting between the currencies and weights of different cities, dividing profits in a partnership, calculating interest, alloying metals, testing whether an answer is right.
The resistance it met is easy to underestimate. Roman numerals were embedded in accounts, in law and in the reckoning board, and the new figures were held to be easy to alter, so several Italian cities forbade their use in official books for a long time afterwards. What carried them in the end was commercial arithmetic taught in the vernacular reckoning schools, not scholarly argument. The religious consequence is indirect and real. Calendar work, and above all the computation that fixes the date of Easter from the moon and the equinox, is arithmetic done at a scale that positional notation makes tractable and Roman numerals do not, and the same is true of the astronomical tables the calendar depends on.
A Sequence He Did Not Discover and a Mysticism He Did Not Teach
The sequence appears in the Liber Abaci as one exercise among hundreds, a puzzle about how many pairs of rabbits there will be after a year if every pair breeds on a fixed schedule. It was not new. Indian writers on prosody had generated the same numbers centuries earlier by counting the ways long and short syllables can fill a line of a given length, and Pingala, Virahanka and Hemachandra are all cited for it in the Sanskrit tradition. The name Fibonacci was not his either; it was applied to him by historians in the nineteenth century, and it is that later naming which attached the sequence to him.
Its career since has mostly been outside mathematics. The ratio between consecutive terms approaches the golden section, and on that thread hangs a large body of claiming about the proportions of the Parthenon, the great pyramid, medieval cathedrals and Renaissance painting. Careful measurement studies of those buildings have repeatedly failed to support the claims, and the arithmetic used to produce them turns out to be flexible enough to find the ratio almost anywhere. That is worth saying plainly, because the sequence does occur genuinely and interestingly in nature, in the spiral arrangement of leaves and seeds, and the real case is obscured rather than helped by the invented ones.
Sources Liber AbaciLeonardo of Pisa (Fibonacci) with Misconceptions about the Golden RatioGeorge Markowsky, The Golden Ratio: A Contrary ViewpointClement Falbo
Cross-Tradition Connections
Associated With
The ratio between successive terms approaches the golden section, which is why the sequence became a fixture of sacred geometry.
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