All of the information below was found on Wikipedia.
In mathematics, the Pythagorean theorem or Pythagoras’ theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
proof can be found at the following link:
One can see the use of triangles in many everyday items such as this tile:
There are also many "pop references" to the Pythagorean Theorem:
Pop references to the Pythagorean theorem
The Pythagorean theorem has arisen in popular culture in a variety of ways.
A verse of the Major-General's Song in the Gilbert and Sullivan musical The Pirates of Penzance, "About binomial theorem I'm teeming with a lot o' news, With many cheerful facts about the square of the hypotenuse", with oblique reference to the theorem.
The Scarecrow of The Wizard of Oz makes a more specific reference to the theorem when he receives his diploma from the Wizard. He immediately exhibits his "knowledge" by reciting a mangled and incorrect version of the theorem: "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. Oh, joy! Oh, rapture! I've got a brain!" The "knowledge" exhibited by the Scarecrow is incorrect. The accurate statement would have been "The sum of the squares of the legs of a right triangle is equal to the square of the remaining side."
In an episode of The Simpsons, after finding a pair of Henry Kissinger's glasses in a toilet at the Springfield Nuclear Power Plant, Homer puts them on and quotes Oz Scarecrow's mangled version of the formula. A man in a nearby toilet stall then yells out "That's a right triangle, you idiot!" (The comment about square roots remained uncorrected.)
The Text to Speech software in Mac OS X has a voice called Ralph that recites the theorem as its example speech.
In Freemasonry, one symbol for a Past Master is the diagram from the 47th Proposition of Euclid, used in Euclid's proof of the Pythagorean theorem.
In 2000, Uganda released a coin with the shape of an isosceles right triangle. The coin's tail has an image of Pythagoras and the equation α2 + β2 = γ2, accompanied with the mention "Pythagoras Millennium". Greece, Japan, San Marino, Sierra Leone, and Suriname have issued postage stamps depicting Pythagoras and the Pythagorean theorem.
In Neal Stephenson's speculative fiction Anathem, the Pythagorean theorem is referred to as 'the Adrakhonic theorem'. A geometric proof of the theorem is displayed on the side of an alien ship to demonstrate their understanding of mathematics.
A project or an exploration:
The students will explore who Pythagoras was, and complete a 3 to 5 page research paper, with diagrams. The students will also complete four real-life problems involving the Pythagorean Theorem.
If the two legs of a right triangle are 3 and 4, what is the length of the hypotenuse?
There should be a fancy link or picture here somewhere. "I am a winner, I can do anything, I am a winner, I can do anything!!!!!"