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Cardano and Lagrange: Mathematicians who Transformed the Field

Learn about the lives and contributions of mathematicians Girolamo Cardano and Joseph Louis Lagrange, who made significant advancements in the field of mathematics. Explore Cardano's work on cubic equations and his struggles in his personal life, as well as Lagrange's contributions to calculus and number theory.

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Cardano and Lagrange: Mathematicians who Transformed the Field

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  1. Technology Based By: Tiffany Cox

  2. GirolamoCardano Born: September 24, 1501 at Pavia, Italy Died: September 21, 1576 at Rome, Italy Causes of death: Unspecified Religion: Roman Catholic Occupation: Doctor, Mathematician

  3. cubic equations had to deal with ax3 - bx + c = 0 and ax3 - bx = c as two different cases Cardano introduced binomial coefficients and the Binomial Theorem, and introduced and solved the geometric hypocyloid problem, as well as other geometric theorems

  4. Threw his life he was tormented that his father (a friend of Leonardo da Vinci) married his mother only after Cardano was born. His mother tried several times to abort him. Cardano's reputation for gambling and aggression interfered with his career. He practiced astrology and was imprisoned for heresy when he cast a horoscope for Jesus.

  5. This and other problems were due in part to revenge by Tartaglia for Cardano's revealing his secret algebra formulae. His son apparently murdered his own wife. Leibniz wrote "Cardano was a great man with all his faults; without them, he would have been incomparable.”

  6. Father: Facio Cardano (jurist, b. 1444, d. 1524) Mother: Chiara Micheria (d. 26-Jul-1537) Wife: Lucia Bandarini (m. 1531, d. 1546) Son: Giovanni Battista Cardano (physician) Son: Giambatista Cardano (b. 14-May-1534, d. 13-Apr-1560, execution) Son: Aldo Urbano Cardano (b. 25-May-1543) Daughter: Clara (b. 1536)

  7. Joseph Louis Lagrange • French mathematician • He was born in Italy from 1736-1813. • Joseph studied at the College of Turin • At first he didn't have great enthusiasm for mathematics. • He started becoming interested in mathematics when he read the copy of Halley's 1693 work on algebra.

  8. Joseph didn't like studying with the other leading mathematics he was more of a self taught. He published his first mathematics work in 1754. It was an analogy between binomial theorem and he successive derivatives of the product of functions. He made important discoveries that could contribute substantially to the new subject of calculus of variations. He sent it to Euler and after impressing him with his work, he then was appointed professor of mathematics at Royal Artillery School in Turin in the 1755.

  9. Then shortly after he was elected to Berlin Academy in 1756. A year after he became a member of the Royal Academy of Science of Turin. He was a major contributor the three volumes. He then published calculus of variations and calculus of probabilities. Also he made a major study on the propagation of sound, and the theory of vibrating strings. He took consist of n masses then joined by weightless strings. He solved the resulting system of n+1 differential equations, and then let n get large to obtain a functional solution.

  10. And also worked on number theory. In 1770 that every positive integer is the sum of four squares. In 1770, he also presented an important work which made a fundamental investigation of why equations of degrees up to 4 could be solved by radicals. The paper is the first to consider the roots of a equation as abstract quantities rather than having numerical values. A year after in 1771, he proved Wilson's theorem, and that n is prime if and only if (n-1)! + 1 is divisible by n. Then in 1770, he presented an important work that made fundamental investigation of why the equations of the degrees up to 4 could be solved by radicals. It was the first to be consider of the roots of a equation as abstract quantities rather than having the numerical values.

  11. In 1787 his wife and Frederick 11 passed away. His position in Berlin has become a less happy one. He left his position to become a member of the Academie des Science in Paris. He contuniued there for the rest of his career. He published 2 volumes of calculus lectures. Then in 1797, he published the first theory of functions of the real variable with Theorie des fonctions analytique, but he failed because he didn’t give enough attention to matters of the convergence. Napoleon then named the Legion of Honor and Count of the Empire in 1808 to Lagrange.

  12. Ada Lovelace NAME: Ada Lovelace OCCUPATION: Mathematician BIRTH DATE: December 10, 1815 DEATH DATE: November 27, 1852 Died from: Uterine Cancer in London PLACE OF BIRTH: London, United Kingdom PLACE OF DEATH: London, United Kingdom MAIDEN NAME: AugustaAdaByron

  13. Ada is considered to have written the instructions for the first computer program in the mid-1800’s. She also is considered to be the first computer programmer. Lovelace showed talent for numbers and language. At the age 17 she began studying advanced mathematical calculations.

  14. She described how codes could be created from the device and to handle letters and symbols along with numbers. She had a method for the engine to repeat a series of the instructions. It is also known as looping that computer programs use today. In the latwer years she has developed mathematics schemes for winning at gambling.

  15. But then unfortunately her schemes failed When she died she was buried next to her father at Church of St. Mary Magdalene in Nottingham, England in the graveyard. In 1835 she meet her husband William King. They had 3 children together and shared a love for horses. They also socialized with many of the interesting minds of the times.

  16. Later in her life she became to have health problems with asthma and her digestive system. The doctors tried giving her painkillers but it didn’t help. Her personality began to change Then she reportedly starting experiencing mood swings and hallucinations.

  17. Work Cited "Greatest Mathematicians Born between 400 and 1580 A.D." Greatest Mathematicians Born between 400 and 1580 A.D. N.p., n.d. Web. 30 Apr. 2013. "Girolamo Cardano." Girolamo Cardano. N.p., n.d. Web. 30 Apr. 2013. "Joseph-Louis Lagrange." Joseph-Louis Lagrange. N.p., n.d. Web. 23 Apr. 2013.  "Mathematicians." Famous. N.p., n.d. Web. 24 Apr. 2013. "Smithsonian.com." Surprising Science Five Historic Female Mathematicians You Should Know Comments. N.p., n.d. Web. 30 Apr. 2013. "Ada Lovelace Biography." Bio.com. A&E Networks Television, n.d. Web. 30 Apr. 2013.

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