Report

The Scientific Revolution – Mathematics Ajay Kumar, Lyndon Shi, 9-1 Nicholas Voreas Gerolamo Cardano Father of Complex Numbers 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 An Introduction 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… • No iPod • No modern advancement • No quantum theory Francois Viete 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 • First works – Canon mathematicus, Universalium Inspectionum Liber Singularis, (1579) – Trigonometric tables calculated to 9 decimal places – Collection of trigonometric formulas • In artem analyticam isagoge (1591) – Algebraic notation – Use of letters for unknowns and constants – Vowels are unknowns, letters are constants Trigonometry • Math of triangles • Relationships between sides and angles Symbolic Algebra John Napier 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 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 • Exponential form • How many of one number do we multiply to get another log2(8) = 3 Napiers Bones • Multiplication tables Blaise Pascal Pascal’s Triangle 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) Pascal’s Triangle 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 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 • 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 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 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 • 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 • 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.stand.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.standrews.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>. 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-andleibniz-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-wilhelmleibniz/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>. 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-cardanophysician-extraordinaire.php>. "Pascal's Triangle." Pascal's Triangle. N.p., n.d. Web. 03 Dec. 2012. <http://pages.csam.montclair.edu/~kazimir/applications.html>.