A LOOK BACK
HYPATIA: One of Algebra's "Parents"
From "Multiculturalism in Math, Science, and Technology: Readings and Activities" (c) 1993 by Addison Wesley. Used by Permission.
Hypatia (hy PAY sha), an Egyptian woman born in 370, is remembered for her life as a mathematician, scientist, and teacher. She lived in Alexandria and was a professor at the famous university there. Alexandria, located in the Nile River delta on the Mediterranean coast, attracted scholars from all over Africa, Asia, and Europe. Hypatia was considered one of the great lecturers in this center of learning.
Among Hypatias research subjects was the geometry of the conic sections. Conic sections are the figures formed by the intersection of a plane and a cone. Depending on the angle of the plane, the figure formed is either a circle, an ellipse, a parabola, or a hyperbola.
Circle Ellipse Parabola Hyperbola
Neglected for many centuries after Hypatias death, the importance of the conic sections was finally recognized in the seventeenth century. Today, the conic sections are used to describe the orbits of planets, the paths of comets, and the motion of rockets.
In the field of algebra, Hypatia wrote about the work of an earlier Egyptian mathematician named Diophantus. Diophantus, known as the "Father of Algebra," worked with quadratic equations and equations having more than one solution. Historians believe that Hypatias writings provide us with the only surviving copy of his algebra. Some believe that Hypatia deserves to be known as the "Mother of Algebra" because her work preserved and added to that of Diophantus.
Hypatia was also interested in science. In her writings, she described plans for building an instrument called an astrolabe. This device was used to measure the positions of the stars and planets. Hypatia also invented several pieces of apparatus for working with liquids. Among these was a device for distilling water.
Hypatia lived during a time when Egypt was in the process of great social change. When she was still in her prime-in her fortiesa mob of fanatics pulled her from her carriage and murdered her because she was true to the old religion. Some historians believe that Hypatias death in 415 represents the end of ancient mathematics and science. However, her life story continues to inspire students as an example of a woman who excelled in these fields.
1. What factors do you think may have contributed to Alexandria becoming a center of learning?
2. Give some additional applications of the conic sections (circle, ellipse, parabola, hyperbola).
3. Why do you think the importance of the conic sections was not fully recognized until the seventeenth century?
4. Hypatia described an instrument for measuring the positions of the stars and planet How might such measurements have been used during Hypatias time?
5. Hypatias father, Theon, was also a mathematician. Do you think it was common in Hypatias day for a woman to follow in her fathers profession? Why or why not?
Triangular, Square, and Polygonal Numbers
Materials: pencil, circular counters (pennies, bottle caps, beans, or similar objects)
What is the relationship between whole numbers and geometry? Hypatia studied number patterns and their relationship to geometric figures. You can experiment with some of these patterns.
shown. Then add three counters, again forming an equilateral triangle. Continue the process by adding four, and then five, counters
The triangular numbers are the number of counters
in each equilateral triangle. Fill in the next two numbers in -the list below.
List the first five square numbers you have formed: _____, _____, _____, _____, _____
3. By arranging counters into various polygonal shapes, other polygonal numbers can be formed. Use patterns from Steps I and 2 to complete the following table.
Questions for Critical Thinking
A Problem with Many Solutions
Materials: pencil, calculator
One of Hypatias best-known works was her commentary on the mathematics of Diophantus. Diophantus studied problems that led to equations with more than one solution. Such equations are known as indeterminate equations. For example, the problem of changing a one-dollar bill into nickels and dimes leads to an indeterminate equation because there are many different solutions to the problem.
In her paper on Diophantus, Hypatia posed the following problem. Find a number that satisfies these two conditions: (1) it is the sum of two squares, and (2) its square is also the sum of two squares.
Many solutions exist. Hypatia studied a whole class of numbers that could be solutions. These numbers are of the form 4n + 1, where n = 1,2,3, and so on. Many numbers of this form are solutions to the problem. In particular, the formula 4n + 1 generates prime numbers that are always the sum of two squares. Are their squares also the sum of two squares? To find out, use your calculator to help you complete the following table. You do not need to complete rows for which 4n + 1 is not prime.
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This page was last updated on March 25, 2003..