MEDIEVAL AND RENAISSANCE MATHEMATICS BY Tajana Novak Andrea

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

MEDIEVAL MATHEMATICS From the 4 th to the 15 th centuries the early Middle Ages or Dark Ages (from 400 AD to 1400 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 12 thcentury 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 trigonometry (Regiomontatus)- -De Triagulis, in 1450’s, first great book of trigonometry

RENAISSANCE MATHEMATICS began in Italy From 14 th to 16 th 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 Luca Durer- supermagic square Pacioli- late 15 th and early 16 th 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

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