Early Middle Ages


Lecture 2. Culture and Math in 14



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Lecture 2. Culture and Math in 14th-15th centuries




Late Middle Ages 1300-1450: many disasters, population of France dropped 50% in 1300-1350, recovered till 1450

Climate change: Medieval Warm Period (950-1250) transformed into the Little Ice Age (1350-1850)

1315-1317 Great Famine: heavy rains and cool at summer, no crops, no bread (available “only for kings”)

1337-1453 100 Years’ War in France; popular revolts in Flanders (1323-28), France (1356-58), England (1381)



1347-1350 Plague Black Death killed 35 million (1/3 of population) in Europe, epidemy repeated every 10 years

Religious Wars: Reformation, Great Papal Schism 1378-1418 (three rival Popes, each supported by some states)



Giotto

Petrarca


Italian Renaissance started as a cultural movement in Florence in 14th century
Dante Alighieri (1265–1321) poet, the author of Divine Comedy, "the Father of the Italian language".

Francesco Petrarca (1304–1374) scholar and poet, a model for lyrical poetry and “Italian style”, “Father of Humanism”

Giovanni Boccaccio (1313–1375) writer, poet, humanist, the author of The Decameron and On Famous Women

Giotto di Bondone (1267–1337) painter and architect, broke with “Byzantine style” and initiated “Renaissance style”


Dante

Math Ideas in 14th century


1321 Levi ben Gerson (Gersonides): Book of Numbers on arithmetical operations, permutations and combinations, 1342 De sinibus, chordis et arcubus (On Sines, Chords and Arcs): proves the sine theorem

1364 Nicole Oresme Latitudes of Forms an early version of coordinate system that may be influences Descartes







Nicole Oresme (1320-1382) most original thinker of XIV: philosopher, economist, astronomer, mechanic and math

Introduced an idea of graph of function, named coordinates lattitudo and longitude; for the graph of speed as function of time realized that the distance is the area; introduced an average speed.

Proved divergence of a harmonic series; used fractional powers of numbers.

Discussed possibility of rotation of Earth; incommensurability of lengths of day/month/year in a book of 1382 Le Livre du ciel et du monde (The Book of Heaven and Earth) he translated it from Latin to French by request of king Charles V




Leonardo

Botticelli



Quattrocento: Italian Renaissance of 15th cent. under patronage of Lorenzo de Medici 1449–1492, Lord of Florence

Leonardo da Vinci 1452–1519 polymath, a greatest painter, "Universal Genius", "Renaissance Man"

Sandro Botticelli, 1445–1510 painter

Lorenzo de‘ Medici





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