Pythagorean theorem essay paper

He visited Italy with his father. Combining the smaller square with these rectangles produces two squares of areas a2 and b2, which must have the same area as the initial large square. He was one of the most important Hindu mathematicians of the second century. The area of a rectangle is equal to the product of two adjacent sides.

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Essay, Research Paper: Pythagorean Theorem

It used to 2 2 2 find the unknown side of a right triangle. In words, the Pythagorean Theorem states that the square on the hypotenuse of a right triangle has an area equal to the combined areas of the squares on the other two sides.

The angle opposite the side of the legs was the right angle, it had a length of 5. The group believed in many things had to do with numbers.

I say this because the theorem was studied by so many great thinkers. The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret. This Pythagorean triple, 3: In the problem Euclid studied he would always use 3, 4, and 5 as the sides of the right triangle.

Putting the two rectangles together to reform the square on the hypotenuse, its area is the same as the sum of the area of the other two squares. There is evidence to suggest that Pythagoras and Polycrates were friends at first but when Polycrates abandoned his alliance with Egypt and attacked it, their friendship abruptly ended.

The later discovery that square root of 2 is irrational and, therefore cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers. Like this term paper? Another geometrical discovery made by Pythagoras is that the diagonal of a square is not a rational multiple of its side.

Pythagoras also invented the five regular solids. This belief by the Pythagoreans led to many discoveries including the Pythagorean Theorem. It is said Pythagoras was a man that spent his life traveling the world in search of wisdom.

Sometimes the Pythagorean Theorem is also referred to as the 47th Problem of Euclid. This theorem may also be summed up by saying that the area of the square on the hypotenuse, or opposite side of the right angle, of a right triangle is equal to sum of the areas of the squared on the legs.

But using it as a platform for other geometries sparked an entire cosmology in mathematics and philosophy, demonstrating that the Theorem is fairly universal in its ability to be the springboard to other dimensions of mathematical expressions and mechanics.

The group, as led by Pythagoras, could be described as almost cult-like because that it had symbols, rituals, and prayers. Pythagoreans also thought that numbers had characteristics: Next, we will cross-multiply the ratios obtained above to get: His most important being the Pythagorean Theorem.

The latter discovery proved the existence of irrational numbers and therefore changed the entire Greek mathematical belief that whole numbers and their ratios could account for geometrical properties.

Essay: Pythagoras

The group was almost cult-like in that it had symbols, rituals and prayers.The Pythagorean theorem states that: "The area of the square built on the hypotenuse of a right triangle is equal to the sum of the squares on the remaining two sides.". According to the Pythagorean Theorem, the sum of the areas of the red and yellow squares is equal to the area of the purple square.

Pythagorean theorem

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The free Research Papers research paper (Pythagoras, a Man of Math essay) presented on this page should not be viewed as a sample of our on-line writing service. Pythagorean Theorem Make sure you build or generate at least five more Pythagorean Triples using one of the many formulas available online for doing this.

Research Papers/Pythagoras, a Man of Math research paper 2511

After building your triples, verify each of them in the Pythagorean Theorem equation. The Pythagorean Theorem Essay Sample. Introduction a 2 + b 2 = c 2 where a and b are the sides of a right triangle and c is the hypotenuse is the answer most students will give when asked to define the Pythagorean Theorem.

Ask them to prove it and most can’t. In this paper I will attempt to use the Pythagorean Theorem to solve the problem which reads Ahmed has half of a treasure map which indicates that the treasure is buried in the desert 2x+6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure.

The thing that Pythagoras is probably the most famous for is the Pythagorean Theorem. The Pythagorean Theorem is used in the field of mathematics and it states the following: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides.

Pythagorean theorem essay paper
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