REQUIRED READING Rudolf Wittkower Architectural Principles in the Age of Humanism, 1998 Pythagoras RECOMMENDED READING Peter Kingsley, Ancient Philosophy, Mystery, and Magic: Empedocles and Pythagorean Tradition, 1997 The 6th-century BCE Greek philosopher and mathematician Pythagoras lived most of life in southern Italy. There he founded the Pythagorean brotherhood that, although religious in nature, contributed to the development of mathematics and European rational philosophy. None of Pythagoras's writings survive. His doctrines are known mostly through his disciples. He is generally credited with the theory of the functional significance of numbers in the objective world and in music. Pythagoras of Samos Pythagoras and the Pythagoreans UNDER CONSTRUCTION Plato RECOMMENDED READING Francis M. Comford, Plato Cosmology: The Timaeus of Plato, [1956] 1997 SWEET BRIAR LIBRARY: B387.A5 C6 1956 The ancient Greek philosopher Plato (c. 428/427 - 348/347 BCE) discusses number in the Republic and the Timaeus An Excerpt from Plato's Timaeus UNDER CONSTRUCTION Leonardo Fibonacci RECOMMENDED READING Trudi H. Garland, Fascinating Fibonaccis: Mystery and Magic in Numbers, 1987 RECOMMENDED READING Richard A. Dunlap, The Golden Ratio and Fibonacci Numbers, 2000 Leonardo Fibonacci (c. 1170 - after 1240; also known as Leonardo of Pisa) was an Italian mathematician. He wrote the Liber abaci (1202; "Book of the Abacus"), which was the first European work to include Indian and Arabian mathematics. He produced another work in 1220 called Practica geometriae ("Practice of Geometry"). In the 1220s Leonardo was invited to appear before the emperor Frederick II at Pisa. For the next several years, he corresponded with Frederick II and his scholar. In 1225, he dedicated his Liber quadratorum ("Book of Square Numbers") to Frederick. Besides his role in introducing Hindu-Arabic numerals to Europeans, Leonardo is best known today for the so-called Fibonacci sequence, which is derived from a problem in the Liber abaci: A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive? The resulting number sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, in which each number is the sum of the two preceding numbers. It is the first recursive number sequence (in which the relation between two or more successive terms can be expressed by a formula) known in Europe. In 1753, the mathematician Robert Simson at the University of Glasgow in Scotland noted that, as the numbers increased in magnitude, the ratio between succeeding numbers approached the number of the golden ratio, whose value is 1.6180 . . . In the 19th century the term Fibonacci sequence was coined by the French mathematician Edouard Lucas. Scientists began to discover examples of the Fibonacci sequence in nature. For example: in the spirals of sunflower heads in pine cones in the regular descent (genealogy) of the male bee in the related logarithmic (equiangular) spiral in snail shells in the arrangement of leaf buds on a stem in animal horns UNDER CONSTRUCTION Magic Numbers and Squares RECOMMENDED READING Annemarie Schimmel, The Mystery of Numbers Numbers, 1994 SWEET BRIAR LIBRARY: BF 1623 .P9 E55 A magic square consists of the distinct positive integers 1, 2, ..., such that the sum of the n numbers in any horizontal, vertical, or main diagonal line is always the same number, known as the magic constant. Numbers Magic Squares Magic Square UNDER CONSTRUCTION Numerology RECOMMENDED READING Dudley Underwood, Numerology: Or, What Pythagoras Wrought, 1997 Numerology UNDER CONSTRUCTION

Further Reading Lionel March Architectonics of Humanism: Essays on Numbers in Architecture, 1998 SWEET BRIAR LIBRARY: NA 2760 .M35 1998 Anthony Grafton and Nancy Siraisi (eds.) Natural Particular: Nature and the Disciplines in Renaissance Europe, 1999 SWEET BRIAR LIBRARY QH 81 .N3 1999 Clifford A. Pickover The Zen of Magic Squares, Circles, and Stars 2002 ***

---

CONTENTS & SCHEDULE RESOURCES