1 / 15

Guillaume De l'Hôpital By: Alex Asay

Guillaume De l'Hôpital By: Alex Asay. http://www.gap-system.org/~history/Posters2/De_L%27Hopital.html. Background Information. Born in Paris in 1661 Parents were Anne-Alexandre de l'Hospital and Elizabeth Gobelin Became the nobleman of St. Mesme Great at math while growing up

chenoa
Download Presentation

Guillaume De l'Hôpital By: Alex Asay

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Guillaume De l'Hôpital By: Alex Asay http://www.gap-system.org/~history/Posters2/De_L%27Hopital.html

  2. Background Information • Born in Paris in 1661 • Parents were Anne-Alexandre de l'Hospital and Elizabeth Gobelin • Became the nobleman of St. Mesme • Great at math while growing up • Stunned math geniuses by the time he was 15 • Solving an “impossible” problem

  3. Other Background Information • Served as a cavalry officer in the French Army • Had to resign because of his near-sightedness • He hired Bernoulli in 1691 to teach him more about math, which he devoted himself

  4. Spark of Fame • l'Hôpital became famous for writing a book Analyse des infiniment petits pour l'intelligence des lignes courbes (Analysis of the Infinitely Small to Learn about Curved Lines) • Sparked controversy after five years • Bernoulli claimed the ideas behind • This book contained “l'Hôpital’s Rule”

  5. The Beginning • The first chapter jumps right into two definitions: • Definition 1: “Variable quantities are those that increase or decrease continuously while a constant quantity remains the same while other vary.” • Definition 2: “The infinitely small part by which a variable quantity increases or decreases continuously is called the differential of that quantity.”

  6. The Beginning • After this, it moves onto two axioms (commonly accepted principles and rules): • Axiom 1: “Grant that two quantities whose difference is an infinitely small quantity may be taken (or used) indifferently for each other; or (what is the same thing) that a quantity which is increased or decreased only by an infinitesimally small quantity may be considered as remaining the same.” • Axiom 2: “Grant that a curved line may be considered as the assemblage of an infinite number of infinitely small straight lines; or (what is the same thing) as a polygon with an infinite number of sides, each of infinitely small length such that the angle between adjacent lines determines the curvature of the curve.”

  7. “l'Hôpital’s Rule” • It states a method for finding the limit of a rational function that has both a denominator and numerator of zero at a point. • If the limit of f(x) as x approaches c which equals the limit of g(x) as x approaches c which equals 0 or the limit of g(x) equals plus or minus infinity and the limit of f’(x) divided by g’(x) as x approaches c exists, then the limit of f(x)/g(x) as x approaches c equals the limit of f’(x)/g’(x) as x approaches c.

  8. Requirements of the Limit • In order for “l'Hôpital’s Rule” to exist, the limit of f’(x)/g’(x) as x approaches c must exist

  9. The Rule in Numerical Form http://www.camotruck.net/rollins/math/lhopital-h.gif

  10. Results of the Controversy • l'Hôpital was wrong! • In 1921, an early Bernoulli manuscript was discovered revealing very similar traits to the items discussed in l'Hôpital’s book • On March 17, 1694, he sent a letter to Bernoulli asking him if he would stay quiet about the dilemma if he would get paid. • Basically, l'Hôpital bribed Bernoulli to shut up!!! • Bernoulli accepted

  11. Additional Fame • Found the solution to the brachystochrone (the curve of the fastest decent in a gravitational field of a weighted particle that is moving between two points) • The problem was solved by others including Newton, Leibnitz, and Jacob Bernoulli

  12. Additional Fame • He also published a rule on analytical conics in 1707 that was considered to be the standard reference for that topic for about 100 years.

  13. The l'Hôpital Legacy • l'Hôpital died in Paris on February 2, 1704. • It is believed that he was a generous, modest, and charismatic man • He had three kids with his wife Marie-Charlotte de Romilley de La Chesnelaye.

  14. Cited Sources • World of Mathematics. World of Mathematics on Guillaume Francois Antoine L'Hospital. Guillaume Francois Antoine L'HospitalBiography. http://www.bookrags.com/biography/guillaume-francois-antoine-lhospital-wom/ • l'Hôpital's rule. May 15, 2009. <http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule> • Kensington Intermediate Senior High. <http://www.edu.pe.ca/kish/Grassroots/math/guillaum.htm>

  15. Additional Cited Sources • JOC/EFR. 2008. < http://www-history.mcs.standrews.ac.uk/Biographies/De_L'Hopital.html> • Dictionary.com, LLC. <http://dictionary.reference.com/browse/axioms>

More Related