James Bernoulli

James Bernoulli (Jacob I)
Born	December 25, 1654 Basel, Switzerland
Died	August 16, 1705 Basel, Switzerland
Residence	Switzerland
Nationality	Swiss
Field	Mathematician
Institution	University of Basel
Alma mater	University of Basel
Academic advisor	Gottfried Leibniz
Notable students	Johann Bernoulli
Known for	Bernoulli trial Bernoulli numbers
Religion	Calvinist
Brother of Johann Bernoulli.

James Bernoulli (also known as Jacob I) was born in Basel, Switzerland on December 27, 1654 and lived until August 16, 1705. He is one of the eight prominent mathematicians in the Bernoulli family. This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... December 25 is the 359th day of the year (360th in leap years) in the Gregorian Calendar, with 6 days remaining in the year. ... Events April 5 - Signing of the Treaty of Westminster, ending the First Anglo-Dutch War. ... Basel (British English traditionally: Basle and more recently Basel , German: Basel , French: Bâle , Italian: Basilea ) is Switzerlands third most populous city (166,563 inhabitants (2004); 690,000 inhabitants in the metropolitan area stretching across the immediate cantonal and national boundaries made Basel Switzerlands second-largest urban area... August 16 is the 228th day of the year (229th in leap years) in the Gregorian Calendar. ... // Events Construction begins on Blenheim Palace, in Oxfordshire, England. ... Basel (British English traditionally: Basle and more recently Basel , German: Basel , French: Bâle , Italian: Basilea ) is Switzerlands third most populous city (166,563 inhabitants (2004); 690,000 inhabitants in the metropolitan area stretching across the immediate cantonal and national boundaries made Basel Switzerlands second-largest urban area... Image File history File links Flag_of_Switzerland. ... Image File history File links Flag_of_Switzerland. ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... The University of Basel (German: Universität Basel) is located at Basel, Switzerland. ... The University of Basel (German: Universität Basel) is located at Basel, Switzerland. ... It has been suggested that this article be split into multiple articles. ... Johann Bernoulli (Basel, July 27, 1667 - January 1, 1748) was a Swiss mathematician. ... In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, called success and failure. ... In mathematics, the Bernoulli numbers Bn were first discovered in connection with the closed forms of the sums for various fixed values of n. ... In an unadorned church, the 17th century congregation stands to hear the sermon. ... Johann Bernoulli (Basel, July 27, 1667 - January 1, 1748) was a Swiss mathematician. ... Basel (English traditionally: Basle [ba:l], German: Basel [ba:z@l], French Bâle [ba:l], Italian Basilea [bazilE:a]) is Switzerlands third most populous city (188,000 inhabitants in the canton of Basel-City as of 2004; the 690,000 inhabitants in the conurbation stretching across the... December 27 is the 361st day of the year in the Gregorian Calendar (362nd in leap years). ... Events April 5 - Signing of the Treaty of Westminster, ending the First Anglo-Dutch War. ... August 16 is the 228th day of the year (229th in leap years) in the Gregorian Calendar. ... // Events Construction begins on Blenheim Palace, in Oxfordshire, England. ...

Following his mommies wish, James studies theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences. This included the work of Robert Boyle and Robert Hooke. Events January 29 - Feodor III becomes Tsar of Russia First measurement of the speed of light, by Ole Rømer Bacons Rebellion Russo-Turkish Wars commence. ... Events March 11 – Chelsea hospital for soldiers is founded in England May 6 - Louis XIV of France moves his court to Versailles. ... Robert Boyle Robert Boyle (January 25, 1627 – December 30, 1691) was an Irish natural philosopher, chemist, physicist, inventor, and early gentleman scientist, noted for his work in physics and chemistry. ... Robert Hooke, FRS (July 18, 1635 – March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. ...

He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers on transcendental curves (1696) and isoperimetry (1700, 1701). In 1690, James became the first person to develop the technique for solving separable differential equations. Calculus is the name given to a group of systematic methods of calculation, computation, and analysis in mathematics which use a common and specialized algebraic notation. ... It has been suggested that this article be split into multiple articles. ... Johann Bernoulli (Basel, July 27, 1667 - January 1, 1748) was a Swiss mathematician. ... In mathematics, a transcendental curve is a curve that is not an algebraic curve. ... The year 1696 had the earliest equinoxes and solstices for 400 years in the Gregorian calendar, because this year is a leap year and the Gregorian calendar would have behaved like the Julian calendar since March 1500 had it have been in use that long. ... Isoperimetry literally means having an equal perimeter. In mathematics, isoperimetry is the general study of geometric figures having equal boundaries. ... Events January 1 - Russia accepts Julian calendar. ... Events January 18 - Frederick I becomes King of Prussia. ... Events Giovanni Domenico Cassini observes differential rotation within Jupiters atmosphere. ... // A separable first order ordinary differential equation A separable ordinary differential equation of the first order has the general form: where f(t) is some known function. ...

Upon returning to Basel in 1682, he founded a school for mathematics and the sciences. He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life. Basel (British English traditionally: Basle and more recently Basel , German: Basel , French: Bâle , Italian: Basilea ) is Switzerlands third most populous city (166,563 inhabitants (2004); 690,000 inhabitants in the metropolitan area stretching across the immediate cantonal and national boundaries made Basel Switzerlands second-largest urban area... Events March 11 – Chelsea hospital for soldiers is founded in England May 6 - Louis XIV of France moves his court to Versailles. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... The University of Basel (German: Universität Basel) is located at Basel, Switzerland. ... Events March 19 - The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. ...

James is best known for the work Ars Conjectandi (The Art of Conjecture), published eight years after his death in 1713 by his nephew Nicholas. In this work, he described the known results in probability theory and in enumeration, often proving alternative proofs of known results. This work also includes the application of probability theory to games of chance and his introduction of the theorem known as the law of large numbers. The terms Bernoulli trial and Bernoulli numbers result from this work. Bernoulli crater, on the Moon, is also named after him jointly with his brother Johann. // Events April 11 - War of the Spanish Succession: Treaty of Utrecht June 23 - French residents of Acadia given one year to declare allegiance to Britain or leave Nova Scotia Canada first Orrery built by George Graham Ongoing events Great Northern War (1700-1721) War of the Spanish Succession (1702-1713... The law of large numbers is a fundamental concept in statistics and probability that describes how the average of a randomly selected sample from a large population is likely to be close to the average of the whole population. ... In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, called success and failure. ... In mathematics, the Bernoulli numbers Bn were first discovered in connection with the closed forms of the sums for various fixed values of n. ... Bernoulli is a lunar impact crater that is located in the northeast part of the Moon. ... Apparent magnitude: up to -12. ...

Bernoulli chose a figure of a logarithmic spiral and the motto "Eadem mutata resurgo" ("Changed and yet the same, I rise again") for his gravestone; the spiral executed by the stonemasons was, however, an Archimedean spiral.[1] A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. ... An Archimedean spiral is a curve which in polar coordinates (r, θ) can be described by the equation with real numbers a and b. ...

External links

• James Bernoulli at the Mathematics Genealogy Project
• O'Connor, John J., and Edmund F. Robertson. "James Bernoulli". MacTutor History of Mathematics archive.
• Jakob Bernoulli: Tractatus de Seriebus Infinitis (pdf)
• Eric W. Weisstein, Bernoulli, Jakob (1654-1705) at ScienceWorld.