This document provides an overview of mathematics during the Medieval and Renaissance periods. During the Medieval period from the 4th to 15th centuries, knowledge spread from the East and mathematicians like Fibonacci introduced the Hindu-Arabic numeral system and recursive sequences. In the late Middle Ages, Oresme developed rectangular coordinates and Regiomontanus wrote on trigonometry. The Renaissance began in Italy from the 14th to 16th centuries and marked a new way of thinking including the concept of zero and advances in algebra by figures like Pacioli, Tartaglia, Ferrari, Cardano, Bombelli, and Stevin.

1. MEDIEVALAND
RENAISSANCE
MATHEMATICS
BY: Tajana Novak, Andrea Gudelj, Srđana Obradović, Mirna Marković
April, 2013.

2. MEDIEVAL MATHEMATICS
 From the 4th to the 15th centuries
 the early Middle Ages or Dark Ages (from
400AD to 1400AD)
 period of stagnation
 the late Middle Ages (just before the
Renaissance)
 spreading the knowledge from the East

4. MEDIEVAL MATHEMATICIANS
 Adelard of Bath, Herman of Carinthia, Gerard of
Cermona –translated Euclid’s “Elements”
 Robert of Chester –translated Al- Khwarizmi’s book
into Latin
 Leonardo of Pisa (Fibonacci)- Europe’s first great
medieval mathematician
-Hindu-Arabic numeral system (Liber Abaci, 1202 AD)
-horizontal bar notation for fractions
-first recursive number sequence
-Liber Quadratorum, 1225 AD

5. Woman teaching geometry
 The frontispiece of an
Adelard of Bath Latin
translation of
Euclid's Elements, the
oldest surviving Latin
translation of the
Elements is a 12th-
century translation by
Adelard from an Arabic
version.

7. MEDIEVAL MATHEMATICIANS
 Nicole Oresme – used a system of rectangular
coordinates
-harmonical series is a divergent infinite series
 Johann Müller (Regiomontatus)- trigonometry
-De Triagulis, in 1450’s, first great book of
trigonometry

8. RENAISSANCE MATHEMATICS
 began in Italy
 From 14th to 16th century
 new way of thinking
 concept of ‘zero’
 many advancements in algebra

9. RENAISSANCE MATHEMATICIANS
 Leonardo da Vinci
- exploration of the world of
proportionality and spatial
mechanics
- preferred drawing as his primary
tool to execute his studies
-eg: rhombicuboctahedron,
Leonardo's Vitruvian man's
perfect mathematical proportions

10. RENAISSANCE MATHEMATICIANS
 Albercht Durer- supermagic square
 Luca Pacioli- late 15th and early 16th centuries
- Summa de Arithmetica, Geometria, Proportioni et
Propotiionalita , 1494. – a book of arithmetic,
geometry and book-keeping
- symbols for plus and minus – standard notation
-The Divine Proportion

11. RENAISSANCE MATHEMATICIANS
 Niccolo Fontana Tartaglia- formula for solving
cubic equations, complex numbers
 Ludovico Ferrari- quadratic equations
 Gerolamo Cardano- Ars Magna,1545
-first systematic treatment of probability
 Rafael Bombelli –L’Algebra,1572 –imaginary numbers
 Simon Stevin- De Thiende, 1585- decimal notation