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Cardano’s Solution to the Cubic. Daniel Blanchette , Christian Landry. 1300 BC. Babylonians Solved quadratics of the form . x 2 + p = qx. 200 BC. Chinese are solving quadratic by completing the square. 628 AD. Brahmagupta solves quadratic for positive roots only. 1261.

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cardano s solution to the cubic

Cardano’s Solution to the Cubic

Daniel Blanchette, Christian Landry

slide2

1300

BC

Babylonians Solved quadratics of the form

x2 + p = qx

slide3

200 BC

Chinese are solving quadratic by completing the square

slide4

628

AD

Brahmagupta solves quadratic for positive roots only

slide5

1261

Yang Hui solves quadratic with negative roots using Pascal’s Triangle

slide8

1450

Johannes Guttenberg invents the printing press

slide9

1453

  • - Ottoman empire captures Constantinople
  • Fall of Byzantine empire
  • End of 100 year war
slide11

1466

- End of Thirteen year war.

- Royal Prussia annexed to Poland.

slide12

1469

  • Unification of Spain
  • Wedding of Isabela 1 of Castile to Ferdinand Aragon
slide14

1481

  • Spanish Inquisition begins
slide15

1489

  • John Widmann uses the + and – signs for the first time in a printed book
slide16

1492

  • Christopher Columbus discovers the Americas
slide17

1494

  • Lucia Pacioli writes summa de Arithmetica
slide18

1501

  • Michealangelo begins work on the Statue of David
slide19

1501

  • NilakanthaSomayaji writes Tantrasangraha
slide20

1503

  • Da Vinci begins to paint the Mona Lisa
slide21

1512

  • Coppernicius says the earth resolves around the sun
slide23

1521

  • Aztec Empire falls
  • Montezuma II is killed
slide26

1527

  • Rome is sacked
  • End of Italian Renaissance
slide28

1531

  • England renounces the papacy
  • King Henry VIII head of Church of England
slide29

1534

  • Jacques Cartier claims Quebec for France
scipiones del ferro
Scipiones Del Ferro
  • Feburary 6th 1465 – November 5th1526
  • First to solve depressed cubic
  • Not much known about mathematics
niccolo fontana tartaglia
Niccolo Fontana Tartaglia
  • ? 1499 – December 13th 1557
  • Engineer, Mathematician
  • Translated Euclid, Archimedes
  • Studied path of Cannonball
  • Devised a method to obtain
  • binomial Coefficients
  • Volume of tetrahedron given lengths
  • Solved cubic, did not publish.
gerolamo cardano
GerolamoCardano
  • September 24th 1501 - September 21st 1576
  • Mathematician, Inventor, Physician, Lawyer
  • First to describe Typhoid Fever
  • First to acknowledge imaginary numbers
  • First to write systematically about Probability
  • First to publish solution to cubic, quartic
  • Introduced Binomial Coefficients and theorem
questions comments
Questions/ Comments?
  • A polynomial with an odd order must have at least one solution that is real. Why?
slide42

Gauss wrote “Oh..Great Archimedes, How come you did not make this discovery? If you had done that, the world would have been thousand of years more advanced”

  • Do you agree with Gauss?, If yes, why is it that the author of this book did not cover more about Brahmagupta?