Algebra I

Mr. HelselAssignment # 1Period 4

Math Masters

This assignment requires you to do a brief written paper on a historical mathematician. It is expected that your paper will be 2/3 to 1 page in length (typed - single spaced). Your paper may be hand-written, as long as it is legible.

At a minimum, your paper should include the following:

  • The name of the mathematician
  • Dates of his/her life
  • Country/region where the mathematician was born/lived and/or worked
  • Contribution to the field of mathematics
  • A bibliography with a minimum of three sources
  • One or more sources must not be from the internet
  • Two of the three sources must not be Wikipedia (If you have three sources, you may only use Wikipedia once.)

It is expected that you will not just cut and paste information from the internet.

Your grade will be your beginning homework grade for the 1st Marking Period.

If you complete all of the above requirements, you will receive a grade of 100. For each item missing, 10 points will be subtracted.

If the mathematician you select is not selected by anyone else in the twoAlgebra I classes, you will receive 15 extra points.

On your assignment, please be sure to include your name and period at the top of the page. Papers submitted with your class period missing will lose 2 points!

A sample assignment is on the reverse.

Due Date: September 16, 2010
Mr. HelselAlgebra IPeriod #

Diophantus

Diophantus (circa 200/214 - circa 284/298) was an ancient Greek mathematician who lived around 250 A.D. Little is known about Diophantus' life, and it is believed that he was a Hellenized Babylonian. He lived in Alexandria (Egypt) and died when he was 84 years old. The years of his life have been estimated based upon both references in his writings and references to his works by other mathematicians.

Diophantus was known for his study of equations with variables which take on rational values and these Diophantine equations are named after him. Diophantus, sometimes known as the "father of Algebra," is best known for his Arithmetica (The Arithmetic), a work on the solution of algebraic equations and the theory of numbers.

The Arithmetica is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. The method for solving the indeterminate equations is known as Diophantine analysis. Only six of Diopantus' original thirteen books are known to have survived and it is thought that the others must have been lost quite soon after they were written.

This work considered the solution of many problems concerning linear and quadratic equations, but only considered positive rational solutions. Equations which led to negative solutions or irrational square roots were considered as useless. As a specific example, Diophantus calls the equation 4 = 4x + 20 'absurd' because it would lead to a meaningless answer. There is no evidence to suggest that Diophantus realized that a quadratic equation could have two solutions. However, the fact that he was always satisfied with a rational solution and did not require a whole number is more sophisticated than we might realize today.

It was in the margin of a French translation of Diophantus' work Arithmetica that Pierre de Fermat wrote his famous comment that is known as Fermat's last theorem.

Diophantus also wrote about polygonal numbers.

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Larson, Ron and Robert P. Hostetler. Trigonometry. 6th ed. Boston: Houghton Mifflin, 2004.

www-groups.dcs.st-andrews.ac.uk/~history/mathematicians/diophantus.html