Math History

Arabic number system.

See Where_did_the_Australian_number_system_come_fromand What_is_the_name_of_the_English_number_systemfor related information.

John Venn is most famous for his development of diagrams, later named after him, that depict relationships between sets. Although Gottfried Wilhelm von Liebniz and Leonhard Eulerhad used similar diagrams, Venn's were considered more descriptive and easier to understand. He also helped to develop George Boole's system of mathematical logic.

Venn was born in Hull, England on August 4, 1834, a descendant of a long line of Church of England evangelicals. He received his early education at two schools in London, at Highgate and Islington, but historical records indicate that either he was so poor a student or the schools were so incompetent that he was ill prepared for college. Nevertheless, he entered Gonville and Caius College at Cambridge in 1853 and earned a degree in mathematics there in 1857. The school made him a fellow upon graduation--he would retain that status for the rest of his life.

Becoming a priest in 1859, Venn went to work as a curate in the town of Mortlake. However, by 1862 he was back in the world of academia with a job at Cambridge University as a lecturer in moral science. His courses' main topics were probability theoryand logic. It was at this point that Venn began developing Boole's mathematical logic, using what would become known as Venn diagrams to do so.

A Venn diagram is a pictorial representation of the relationships among sets. There is an outer rectangle that stands for the universal set, within which are circles or ellipses representing subsets of the universal set. For instance, Venn called three circles (R, S, and T) subsets of set U. The intersections of these circles and their complements split set U into eight nonoverlapping areas, the unions of which produced 256 distinct Boolean combinations of sets R, S, and T.

In 1866 Venn wrote The Logic of Chance, which had major influence on the evolution of the theory of statistics and developed an aspect of probability theory called frequency theory. Meanwhile, he was becoming dissatisfied with the Anglican Church, which he decided to leave in 1870. Afterward, although Venn continued to be a devout church-goer, he dedicated himself mainly to his academic career.

Venn published Symbolic Logic, an attempt to correct and interpret Boole's work, in 1881. His Principles of Empirical Logic came out in 1889, but critics largely agreed that the first work was Venn's most original. Meanwhile, Venn had become enamored of history and had written one for his alma mater in 1897. More impressive, however, was his compilation (with his son) of a history of Cambridge University. An enormous undertaking, the first of two volumes appeared in 1922.

Aside from his academic endeavors, Venn also enjoyed building machines. His talent for such extended to a device that bowled balls for cricket; the machine was so effective that the top players of an Australian team could not even make contact with the balls during a trial run in 1909. Venn died in Cambridge, England in 1923

If the two numbers are the same then the GCF is the common value. Otherwise:

1. find the difference between the larger number and the smaller number.
2. replace the larger of the two numbers by this difference.
3. if the two numbers are the same then that is the GCF, but if not go back to step 1.

Euclidean Algorithm

It is not necessary to actually list the factors of all numbers to get the GCF for only two numbers. You can use the Euclidean algorithm.

(1) Divide the larger number by the smaller one.

(2) If there is no remainder, the GCF is the same as the smaller number.

(3) Repeat step 1 with the smaller number and the remainder.

Example:

GCF of 51 and 85.

85/51 = 1 R 34

51/34 = 1 R 17

34/17 = 2 R 0<== By step 2, we are done. Our answer is 17.

Lets try one that doesn't reduce -- GCF(17,39)

39/17 = 2 R 5

17/5 = 3 R 2

5/2 = 2 R 1

2/1 = 2 R 0, so our answer, the GCF, is 1.