MEDIEVAL AND RENAISSANCE MATHEMATICS BY: Tajana Novak, Andrea Gudelj, Sr đ ana Obradović, Mirna Marković April, 2013.

MEDIEVAL MATHEMATICS  From the 4th to the 15th centuries  the early Middle Ages or Dark Ages (from 4 00AD to AD)  period of stagnation  the late Middle Ages (just before the Renaissance)  spreading the knowledge from the East

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

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.

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

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

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

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

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, decimal notation