Lesson 5 gambling, betrayal & murder algebra

Mathematics of the Italian Renaissance MAT 112-16 Summer 2011 Prof. Douglas Furman – Mathematics Dept. SUNY Ulster – International Programs Gambling, Betrayal & Murder: Cardano & The Italian Algebraists

The Italian algebraists of the Renaissance were able to accomplish what had eluded humanity for over three millenia!

Let’s go back 3000 years before the Renaissance! BM 13901

Babylonian Sexagesimal Numerals

QUIZ! ,[object Object],[object Object]

Let’s Look at a Babylonian Quadratic Equation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

How did the Babylonians do it? ,[object Object],[object Object],[object Object],[object Object]

What did the Greeks contribute to Algebra? Geometric/mechanical solutions to certain particular cubic equations

Along comes the Islamic Age ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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The Arabs solve the cubic equation by geometrical means. ,[object Object],[object Object],[object Object],[object Object]

The Arabs solve the cubic equation by geometrical means. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Europe Slowly Awakens Mathematically ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Luca Pacioli ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Scipione del Ferro (1465-1526) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Niccolo Fontana “Tartaglia” ( 1500 – 1557) ,[object Object],[object Object],[object Object],[object Object]

Fior challenges Tartaglia to a Debate ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Girolamo Cardano (1501-1576) ,[object Object],[object Object]

Girolamo Cardano (1501-1576) ,[object Object],[object Object],[object Object],[object Object]

Girolamo Cardano (1501-1576) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Girolamo Cardano (1501-1576) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Girolamo Cardano (1501-1576) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Tartaglia and Cardano ,[object Object],[object Object],[object Object],[object Object],[object Object]

Lodovico Ferrari (1522 – 1565) ,[object Object],[object Object],[object Object],[object Object]

Cardano & Ferrari ,[object Object],[object Object],[object Object],[object Object]

Hannibal della Nave (Del Ferro’s Son-in-Law) ,[object Object],[object Object],[object Object]

Artis Magnae, Sive de Regulis Algebraicis Liber Unus (1954) ( Book number one about The Great Art, or The Rules of Algebra )

Epilogue… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Lesson 5 gambling, betrayal & murder algebra

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Lesson 5 gambling, betrayal & murder algebra