# History to Enrich Mathematics Learning!

Although the NCTM Standards do not have student expectations for learning mathematics history, exposure to this history can help students see real-world connections in mathematics.

Approximating Pi
Mathematics and science owe a great deal to Archimedes, including a way to approximate pi. Here is historical information along with an applet to approximate pi using the perimeter lengths of polygons inscribed within and circumscribed around a circle.

The Beginnings of Probability
Teachers can share some of this mathematics history as they work with students to compute probabilities for simple compound events, an NCTM expectation for students in grades 6-8.

The Golden Ratio
This rich site connects linear measurement, ratio and proportion, art, and mathematics history.

Measuring the Circumference of the Earth
This Internet project is hands-on, real-world, and historical. Students join with classes around the world to repeat the experiment of Eratosthenes — measuring the shadow of a meter stick and making calculations to approximate the circumference of Earth.

Pythagorean Puzzle
The Pythagorean theorem is at the intersection of algebra and geometry. At this site, learn about the life of Pythagoras and the development of the Pythagorean theorem. And use an applet to explore the meaning of the most famous equation in algebra.

Manipula Math with Java: Pythagorean Theorem
Here is another applet offering a more sophisticated approach to affirm in a visual way the validity of the Pythagorean theorem.

Tortoise and Hare Race
Uing an applet, students can vary parameters for the race. There is information about Zeno’s paradox along with exploration questions for students that can lead to a discussion about infinity.

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# Pythagoras and His Theorem

A topic once reserved for high school geometry, the Pythagorean theorem is now part and parcel of the middle school curriculum. These resources offer visual demonstrations that can make the abstract theorem more concrete for students and lead them in analyzing the mathematical relationships involved, as recommended by the Principles and Standards for School Mathematics. The last resource offers background information on Pythagoras himself.

Pythagorean Theorem (Grades 6-8)
Using this virtual manipulative, students move squares and triangles to demonstrate the validity of the Pythagorean theorem. This manipulative is not a proof, but a good introduction to the topic, nevertheless.

Pythagorean Theorem (Manipula Math)
These 19 applets deal with various aspects of the theorem and its uses. The first nine involve visual, informal proofs of the Pythagorean theorem; they allow students to define any right triangle, then move pieces to show that the two squares on the legs really do have the same area as the square on the hypotenuse. Other applets show a “Pythagoras tree” and problems (interactive, of course) that can be solved using the theorem.

Pythagoras of Samos
This online biography of the famous mathematician is from the MacTutor History of Mathematics Archive. What is known, or guessed, of his life and his work is noted here. Referring to the famous geometric theorem, the biographer states, “Although the theorem, now known as Pythagoras’s theorem, was known to the Babylonians 1,000 years earlier, he may have been the first to prove it.” This is a professional rather than a student resource.

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