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.

The Pythagorean Theorem
This site invites learners to discover for themselves “an important relationship between the three sides of a right triangle.” Five interactive, visual exercises require students to delve deeper into the mystery; each exercise is a hint that motivates and entices. The tutorial ends with information on Pythagoras of Samos and problems that rely on the theorem for their solutions.

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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