Daniel Blanchette, Christian Landry. 1300BC1300BC Babylonians Solved quadratics of the form x 2 + p...
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Transcript of Daniel Blanchette, Christian Landry. 1300BC1300BC Babylonians Solved quadratics of the form x 2 + p...
Cardano’s Solution to the Cubic
Daniel Blanchette, Christian Landry
1300
BC
Babylonians Solved quadratics of the form
x2 + p = qx
Chinese are solving quadratic by completing the square
200 BC
Brahmagupta solves quadratic for positive roots only
628
AD
Yang Hui solves quadratic with negative roots using Pascal’s Triangle
1261
Johannes Guttenberg invents the printing press
1450
- Ottoman empire captures Constantinople - Fall of Byzantine empire- End of 100 year war
1453
- End of Thirteen year war. - Royal Prussia annexed to Poland.
1466
- Unification of Spain- Wedding of Isabela 1 of Castile to Ferdinand Aragon
1469
- Spanish Inquisition begins
1481
- John Widmann uses the + and – signs for the first time in a printed book
1489
- Christopher Columbus discovers the Americas
1492
- Lucia Pacioli writes summa de Arithmetica
1494
- Michealangelo begins work on the Statue of David
1501
-Nilakantha Somayaji writes Tantra sangraha
1501
- Da Vinci begins to paint the Mona Lisa
1503
- Coppernicius says the earth resolves around the sun
1512
- Aztec Empire falls- Montezuma II is killed
1521
- Rome is sacked- End of Italian Renaissance
1527
- England renounces the papacy- King Henry VIII head of Church of England
1531
- Jacques Cartier claims Quebec for France
1534
Scipiones Del Ferro
-Feburary 6th 1465 – November 5th 1526- First to solve depressed cubic- Not much known about mathematics
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
-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
Cardan Grille
Gimbals
Cardan Shaft (Drive Shaft)
Combination Locks
A polynomial with an odd order must have at least one solution that is real. Why?
Questions/ Comments?
Where have you seen the use of auxiliary equations before?
How did Yang Hui obtain negative roots?
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?