The Scientific Revolution – Mathematics

1. The Scientific Revolution – Mathematics Ajay Kumar, Lyndon Shi, Nicholas Voreas 9-1

2. Gerolamo Cardano Father of Complex Numbers

3. Gerolamo Cardano- Biography • Born 1501 • Unhappy childhood – illegitimate son • Inventor, astrologer, philosopher, algebraist, physician • Known as the “Gambling Scholar” for his gambling skills • Wrote more than 200 books on subjects that interested him • Committed suicide (September 21, 1576)

4. Complex Numbers An Introduction

5. Complex Numbers • Also known as imaginary numbers • A variable (i) stands for the square root of a negative number • Always do the i part first when solving

6. Without Complex Numbers… • No iPod • No modern advancement • No quantum theory

7. Francois Viete

8. Life • French Mathematician • Lived 1540 to 1603 • Father of modern symbolic algebra • Career as a lawyer, worked on mathematics in spare time • Involved in politics, worked for Kings Henry III & IV • Decoded messages sent to Philip II of Spain

9. Books • First works –Canon mathematicus, Universalium Inspectionum Liber Singularis, (1579) • Trigonometric tables calculated to 9 decimal places • Collection of trigonometric formulas • In artemanalyticamisagoge(1591) • Algebraic notation • Use of letters for unknowns and constants • Vowels are unknowns, letters are constants

10. Trigonometry • Math of triangles • Relationships between sides and angles

11. Symbolic Algebra

12. John Napier

13. Life • Scottish noble/landowner • Lives 1550 to 1617 • Protestant • Attention to land (inventions) • Theologian/astronomer, worked on mathematics in spare time • Invented logarithms, Napier’s Bones, decimal point

14. Books • The Plaine Discovery of the Whole Revelation of St. John (1593) • Against Papacy • A Description of the Wonderful Canon of Logarithms (1614) • Explained inventions • Logarithmic tables • Led to base 10

15. Logarithms • Exponential form • How many of one number do we multiply to get another log2(8) = 3

16. Napiers Bones • Multiplication tables

17. Blaise Pascal Pascal’s Triangle

18. Blaise Pascal • Born: June 19, 1623 (Clermont) • Was kept away from mathematics at an early age – led to curiosity on the subject • Easily mastered properties of geometry by experimenting himself • Invented “arithmetic machine” – could add/subtract • Spent some time studying religion • Died: August 19, 1662 (Paris)

19. Pascal’s Triangle

21. Isaac Newton • Born Dec. 25, 1642 in Woolsthorpe, England • Father died before he was born, mother moved away • Grew up with his uncle • Attended Trinity College at the University of Cambridge in 1661, received bachelor of arts in 1665 • In 1669, appointed professor of mathematics at Trinity College, and elected to the Royal Society in 1672 • Elected to Parliament in 1691, warden of the mint in 1696 • Died March 20, 1727

22. Newton’s Development of Modern Calculus • First version of Newton’s calculus published in 1665-6 • Seemed to be derived from ideas of motion • Considered variables changing with time • His calculus was geometrical, as opposed to analytical • Used “infinitesimals”, infinitely small but not zero • Later replaced by notions

23. Applied his version of calculus to general physics • Included the laws of differentiation and integration, second and higher derivatives, and the notion of an approximating polynomial series • Calculus today is used in many ways, some including physical sciences, engineering, computer science and statistics

24. Gottfried Wilhelm Leibniz • Born in 1646 • Early years influenced by moral and religious views of mother • Attended University of Leipzig at age 14 in 1661 • Studied philosophy, mathematics, rhetoric, Latin, Greek and Hebrew • Graduated with bachelor’s in 1663, got master’s degree in philosophy the same year • Death on November 14, 1716

25. Development of the Binary System • Developed by Gottfried Wilhelm Leibniz • Belief that all logic can be translated from a verbal representation to an absolute mathematical condition • Ideas were repelled, Leibniz dropped the idea for about 10 years • Hope revived when the Book of Change was published, and he found confirmations of his ideas within this book

26. If such things as yes/no, on/off and male/female could be reduced to straightforward propositions, why couldn’t logic and thought? • Went out to define his binary system • Transposed numbers into seemingly infinite rows of ones and zeroes • At the end of his life he began to believe that his binary number were quasi-religious mysticisms • Claimed that it portrayed creation, with one being God, and zero being void

27. Bibliography • Hartshorne, Robin. "François Viète - Life." Mathematicians. 1998. University of California Berkeley Math Department. 02 Dec. 2012 <http://math.berkeley.edu/~robin/Viete/index.html>. • Hartshorne, Robin. "Work." Mathematicians. 1998. University of California Berkeley Math Department. 02 Dec. 2012 <http://math.berkeley.edu/~robin/Viete/work.html>. • O'Conner, J. J., and E. F. Robertson. "François Viète." Viete biography. Jan. 2000. School of Mathematics and Statistics University of St Andrews, Scotland. 02 Dec. 2012 <http://www-history.mcs.st-and.ac.uk/Biographies/Viete.html>. • O'Conner, J. J., and E. F. Robertson. "John Napier." Napier Biography. School of Mathematics and Statistics University of St Andrews, Scotland, Apr. 1998. Web. 02 Dec. 2012. <http://www-history.mcs.st-andrews.ac.uk/Biographies/Napier.html>. • Russel, Deb. "John Napier Biography." John Napier Biography. About.com, 2012. Web. 02 Dec. 2012. <http://math.about.com/library/weekly/blbionapier.htm>.

28. Bibliography •  "1660-1670 Newton and Leibniz, Founders of Modern Calculus." IT Support from MSP Provider in New Jersey RSS. N.p., n.d. Web. 04 Dec. 2012. <http://www.powersolution.com/1660-1670-newton-and-leibniz-founders-of-modern-calculus/>. • "Gottfried Wilhelm Leibniz - Biography." Gottfried Wilhelm Leibniz. N.p., n.d. Web. 04 Dec. 2012. <http://www.egs.edu/library/gottfried-wilhelm-leibniz/biography/>. • "Gottfried Wilhelm Leibniz (1646 - 1716)." Gottfried Wilhelm Leibniz (1646 - 1716). N.p., n.d. Web. 04 Dec. 2012. <http://www.kerryr.net/pioneers/leibniz.htm>. • "The History of Calculus." The History of Calculus. N.p., n.d. Web. 04 Dec. 2012. <http://www.uiowa.edu/~c22m025c/history.html>.

29. Bibliography •  "Google Images." Google Images. N.p., n.d. Web. 03 Dec. 2012. <http://www.google.com/imgres?um=1>. • "Articles with Keyword Pascal. - Answers in Genesis." Articles with Keyword PascalEnter Website Address or Keywords to Cite. - Answers in Genesis. N.p., n.d. Web. 03 Dec. 2012. <http://www.answersingenesis.org/articles/cm/v20/n1/pascalEnter website address or keywords to cite.>. • "Blaise Pascal (1623 - 1662)." Blaise Pascal (1623 - 1662). N.p., n.d. Web. 03 Dec. 2012. <http://www.maths.tcd.ie/pub/HistMath/People/Pascal/RouseBall/RB_Pascal.html>. • "Gerolamo Cardano, Physician Extraordinaire." World Research Foundation RSS. N.p., n.d. Web. 03 Dec. 2012. <http://www.wrf.org/men-women-medicine/gerolamo-cardano-physician-extraordinaire.php>. • "Pascal's Triangle." Pascal's Triangle. N.p., n.d. Web. 03 Dec. 2012. <http://pages.csam.montclair.edu/~kazimir/applications.html>.