The Pythagorean Theorem - Essay Example

Only on StudentShare

Extract of sample
The Pythagorean Theorem

Therefore the four triangles together are equal to two such rectangles. Their area is 2ab.
At the same time, an equal square with side a + b (Fig. 2) is made up of a square whose side is a, a square whose side is b, and two rectangles whose sides are a, b. Therefore the area of that square is
Let ABC represent a right triangle, with the right angle located at C, as shown on the figure. We draw the altitude from point C, and call H its intersection with the side AB. The new triangle ACH is similar to our triangle ABC, because they both have a right angle (by definition of the altitude), and they share the angle at A, meaning that the third angle will be the same in both triangles as well. By a similar reasoning, the triangle CBH is also similar to ABC. The similarities lead to the two ratios..: As
Another proof by dissection is due to Perigal (left figure; Pergial 1873; Dudeney 1970; Madachy 1979; Steinhaus 1999, pp. 4-5; Ball and Coxeter 1987). A related proof is accomplished using the above figure at right, in which the area of the large square is four times the area of one of the triangles plus the area of the interior square. From the figure d=b-a, so
Perhaps the most famous proof of all times is Euclid's geometric proof , although it is neither the simplest nor the most obvious. ...
Download paper

Summary

In mathematics, the Pythagorean Theorem is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras who lived in the 6th century B.C.
"In any right angle triangle, the area of the square of the side opposite the right angle i.e…
Author : jaidakoss

Related Essays

Pythagorean triplets
For a right triangle, the 'c' side (the side opposite the right angle) is the hypotenuse. In general the 'a' side is the shorter of the two sides. There are some simple rules for determining a subset of Pythagorean triplets;
2 pages (502 words) Essay
History of Mathematics Essay
The Pythagorean idea of the world was that natural numbers were the answer to the different secrets of humans and matter. They thought that everything was made up of numbers, the reason for what anything was could only be figured out in numbers (Early Concepts of Number and Number Mysticism).
...
2 pages (502 words) Essay
Education Testing Assessment Selection and Development
Students will create a multiple-paragraph response that focuses on the costs and benefits of America's two-party system. They will include a thesis statement at the end of an introductory paragraph, use topic sentences at the beginning of each body paragraph, and offer strong supporting examples and details.
...
2 pages (502 words) Essay
Math Standards
They should have the ability to find correct answers to addition,
...
2 pages (502 words) Essay
Write a brief summary of historical orientation of mathematics combining Political events, Cultural events and Mathematical Ideas. Please click on the following link that gives us a timeline of events.
In 500 BCE, cubes were being used immensely well within Europe. 400 BCE saw Plato, Theaeteus, Eudoxus and Aristotle doing their significant works within Europe. 300 BCE was known for the Archimedes Principle in Europe, and Euclid and Apollonius in Asia and Africa. Trigonometry began in 200 BCE in African and Asian regions.
...
1 pages (251 words) Essay
pythagorean triples
The most popular example of which is the 3-4-5 triangle, the triple which, according to Knott (2009), was known to the Babylonians since way back 5,000 years and was possibly used as a basis in making true right angles in ancient building construction.
...
2 pages (502 words) Essay
The Pythagorean Theorem
This GPS navigation also requires the application of Pythagorean Theorem (Maor, 2007).
...
1 pages (251 words) Coursework
Got a tricky question? Receive an answer from students like you! Try us!