Chapter Six

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Chapter Six
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The First Awakening

• Fibonacci

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6.1 The Decline and Revival of Learning
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The Dark Ages

• A time of complete intellectual stagnation
• Marked a very low point in mathematics
• Christian church became the center of
  intellectual life
• System of monastery schools was started

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Frankish King Charlemagne (742814)

• Carolingian Renaissance originated in his courts
• Developed a new curriculum and a new educational
  system
• Invited the most popular scholar of the time to
  help, Alcuin of York

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Englishman Alcuin of York

• Educational Advisor to Charlemagne
• Ruled that every monastery should have its own
  school with the seven liberal arts divided into
  the quadrivium and the trivium
• Propositions for Sharpening a Youthful Mind
• Retired from the court in 796

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New Schools

• Foremost teachers and students were attracted to
  the cathedral schools Cologne, Tours, Liege,
  Chatres, Reims, and Paris
• Early associations of groups of students around
  one teacher paved the way for universities
• Logic and mathematics became the prominent theme
  of study

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Translations to Arabic

• By the tenth century, almost all texts of Greek
  science were available in Arabic.
• By translation many classic Greek works were
  preserved Euclids Elements and Ptolemys
  Almagest are two examples.

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Toledo

• Western students flocked to this center of
  learning.
• School of translation began here.
• Gerard of Cremona (1114 1187)
• Made known in the second half of the twelfth
  century
• Learned Arabic from a Christian translator

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Aldebard of Bath(1090-1150)

• Disguised himself as a Mohammedan student
• Gained a copy of Euclids Elements, which he
  later translated

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6.2 The Liber Abaci and Liber Quadtratorum
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Background on Fibonacci

• Leonardo of Pisa
• Labeled the greatest mathematician of the Middle
  Ages
• Born in Pisa about 1175
• Educated in North Africa
• Traveled all over the Mediterranean as a young
  man analyzing arithmetic of different countries
• Returned to Pisa in 1202 and wrote his famous
  Liber Abaci

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Liber Abaci

• Explains the virtues of the number system
• Second edition in 1228 explains the Arabic
  numerals
• Composed of almost all the arithmetical
  knowledge of his time

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Liber Quadratorum

• Devoted to Diophantine equations of second degree
• Given a problem from Emperor Frederick II to test
  his
• mathematical skill, he gave a correct answer
• Also given another problem as a challenge
• Find a cube that with two squares and ten roots
  should be equal to 20.

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Jordanus de Nemore

• A contemporary of Fibonacci
• Known only by few works that have been found
• De Triangulus and De Numeris Datis

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Other Followers

• Thomas Bradwardine (1290 1349)
• Nicole Oresme (1323 1349)
• Nicholas Cusa (1401 1465)

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Nicole Oresme
Nicholas Cusa
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Homework problems from 6.2
s 3, 4, 8, 15