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Cardano’s Solution to the Cubic

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

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  1. Cardano’s Solution to the Cubic Daniel Blanchette, Christian Landry

  2. 1300 BC Babylonians Solved quadratics of the form x2 + p = qx

  3. 200 BC Chinese are solving quadratic by completing the square

  4. 628 AD Brahmagupta solves quadratic for positive roots only

  5. 1261 Yang Hui solves quadratic with negative roots using Pascal’s Triangle

  6. 1450 Johannes Guttenberg invents the printing press

  7. 1453 • - Ottoman empire captures Constantinople • Fall of Byzantine empire • End of 100 year war

  8. 1466 - End of Thirteen year war. - Royal Prussia annexed to Poland.

  9. 1469 • Unification of Spain • Wedding of Isabela 1 of Castile to Ferdinand Aragon

  10. 1481 • Spanish Inquisition begins

  11. 1489 • John Widmann uses the + and – signs for the first time in a printed book

  12. 1492 • Christopher Columbus discovers the Americas

  13. 1494 • Lucia Pacioli writes summa de Arithmetica

  14. 1501 • Michealangelo begins work on the Statue of David

  15. 1501 • NilakanthaSomayaji writes Tantrasangraha

  16. 1503 • Da Vinci begins to paint the Mona Lisa

  17. 1512 • Coppernicius says the earth resolves around the sun

  18. 1521 • Aztec Empire falls • Montezuma II is killed

  19. 1527 • Rome is sacked • End of Italian Renaissance

  20. 1531 • England renounces the papacy • King Henry VIII head of Church of England

  21. 1534 • Jacques Cartier claims Quebec for France

  22. Scipiones Del Ferro • Feburary 6th 1465 – November 5th1526 • First to solve depressed cubic • Not much known about mathematics

  23. 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.

  24. 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

  25. Cardan Grille

  26. Gimbals

  27. Cardan Shaft (Drive Shaft)

  28. Combination Locks

  29. Questions/ Comments? • A polynomial with an odd order must have at least one solution that is real. Why?

  30. Where have you seen the use of auxiliary equations before?

  31. How did Yang Hui obtain negative roots?

  32. 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?

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