The Scientific Revolution – Mathematics Ajay Kumar, Lyndon Shi, Nicholas Voreas 9-1.
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Transcript of The Scientific Revolution – Mathematics Ajay Kumar, Lyndon Shi, Nicholas Voreas 9-1.
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
• 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
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
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
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)
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.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>.
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>.
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>.