The Blockhead. The History of Mathematics, Part 15. Chuck Garner, Ph.D. Department of Mathematics Rockdale Magnet School for Science and Technology

Transcription

1 The History of Mathematics, Part 15 Chuck, Ph.D. Department of Mathematics Rockdale Magnet School for Science and Technology March 4, 2014

2 Outline

3 Outline

4 Abu Ja far Muhammad ibn Musa That fondness for science, that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating.

5 Wrote Al-Kitāb al-mukhtasar fī hisāb al-jabr wa-l-muqābala in 830 (The Compendious Book on Calculation by Completion and Balancing) Words algebra and algorithm derived from him and his work Considered the father of algebra

6 Outline

7 Fibonacci Leonardo Pisano Bigollo (Fibonacci)

8 Liber Abaci Rare 15th century manuscript of the Liber abaci, auctioned for $180,000 in Modern edition is cheaper

9 Frederick II Math Competition Problem 1 Find a rational number such that the sum of its square and five and the difference of its square and five are both squares of rational numbers.

10 Frederick II Math Competition Problem 1 Find a rational number such that the sum of its square and five and the difference of its square and five are both squares of rational numbers. Answer: 41/12

11 Frederick II Math Competition Problem 1 Find a rational number such that the sum of its square and five and the difference of its square and five are both squares of rational numbers. Answer: 41/12 Problem 2 Find a number so that the square of its cube, twice its square, and ten roots measures 20.

12 Frederick II Math Competition Problem 1 Find a rational number such that the sum of its square and five and the difference of its square and five are both squares of rational numbers. Answer: 41/12 Problem 2 Find a number so that the square of its cube, twice its square, and ten roots measures 20. Answer:

13 Frederick II Math Competition Problem 3 Three men posses a pile of money, thier chares being 1, 1, and 1. Each man takes some money from the pile until nothing is left. The first man then returns 1 of what 2 he took, the second 1, and the third When the total so returned is divided equally among the men, it is found that each possesses what he is entitled to. How much money was in the original pile, and how much did each man take from the original pile?

14 Frederick II Math Competition Problem 3 Three men posses a pile of money, thier chares being 1, 1, and 1. Each man takes some money from the pile until nothing is left. The first man then returns 1 of what 2 he took, the second 1, and the third When the total so returned is divided equally among the men, it is found that each possesses what he is entitled to. How much money was in the original pile, and how much did each man take from the original pile? Answer: 47 in the pile; the men took 33, 13, and 1

15 Outline

16 Reminder: Weekender #7 due March 12 An excerpt from the Treviso Arithmetic Article on the Italian abacists Next: The First Controversy