Cardano’s Solution to the Cubic

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# Cardano’s Solution to the Cubic - PowerPoint PPT Presentation

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

Daniel Blanchette, Christian Landry

1300

BC

Babylonians Solved quadratics of the form

x2 + p = qx

200 BC

Chinese are solving quadratic by completing the square

628

Brahmagupta solves quadratic for positive roots only

1261

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

1450

Johannes Guttenberg invents the printing press

1453

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

1466

- End of Thirteen year war.

- Royal Prussia annexed to Poland.

1469

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

1481

• Spanish Inquisition begins

1489

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

1492

• Christopher Columbus discovers the Americas

1494

• Lucia Pacioli writes summa de Arithmetica

1501

• Michealangelo begins work on the Statue of David

1501

• NilakanthaSomayaji writes Tantrasangraha

1503

• Da Vinci begins to paint the Mona Lisa

1512

• Coppernicius says the earth resolves around the sun

1521

• Aztec Empire falls
• Montezuma II is killed

1527

• Rome is sacked
• End of Italian Renaissance

1531

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

1534

• Jacques Cartier claims Quebec for France
Scipiones Del Ferro
• Feburary 6th 1465 – November 5th1526
• 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.
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