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The Scientific Revolution – Mathematics. Ajay Kumar, Lyndon Shi , Nicholas Voreas 9-1. Gerolamo Cardano. Father of Complex Numbers. Gerolamo Cardano - Biography. Born 1501 Unhappy childhood – illegitimate son Inventor, astrologer, philosopher, algebraist, physician

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the scientific revolution mathematics

The Scientific Revolution – Mathematics

Ajay Kumar, Lyndon Shi, Nicholas Voreas

9-1

gerolamo cardano
Gerolamo Cardano

Father of Complex Numbers

gerolamo cardano biography
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)
complex numbers

Complex Numbers

An Introduction

complex numbers1
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
without complex numbers
Without Complex Numbers…
  • No iPod
  • No modern advancement
  • No quantum theory
slide8
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
books
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
trigonometry
Trigonometry
  • Math of triangles
  • Relationships between sides and angles
slide13
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
books1
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
logarithms
Logarithms
  • Exponential form
  • How many of one number do we multiply to get another

log2(8) = 3

napiers bones
Napiers Bones
  • Multiplication tables
blaise pascal

Blaise Pascal

Pascal’s Triangle

blaise pascal1
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)
slide21

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
slide22

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
slide23

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
slide24

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
slide25

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
slide26

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
bibliography
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>.
bibliography1
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>.
bibliography2
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>.