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. ...Show more

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
Save Your Time for More Important Things
Let us write or edit the essay on your topic
"The Pythagorean Theorem"
with a personal 20% discount.
Grab the best paper

Related Essays

Pythagorean triplets
2 pages (500 words) Essay
History of Mathematics Essay
The number seven had been thought of as a special number for perfection in many early cultures. The idea may be from the seven stars or planets that name the days of the week: Sun, Moon, Mars, Mercury, Jupiter, Venus, and Saturn (What is the Origin of the Seven Day Week).
2 pages (500 words) Essay
Education Testing Assessment Selection and Development
In a multiple-paragraph composition, explain the advantages and disadvantages of America's two-party system. Include an introduction, supporting body paragraphs with good details and examples, and a conclusion. Use a thesis statement in your introduction and topic sentences in your supporting paragraphs.
2 pages (500 words) Essay
Math Standards
Once students are able to commit these to memory, their ability to solve longer problems with ease becomes apparent, and students can easily undertake multiple step problems using all of these skills. As a student progress through their elementary, middle school, and high school educational lives they should acquire and reach a certain number of these skill benchmarks.
2 pages (500 words) Essay
Pythagorean triples
Hence, given any two sides of a right triangle (triangle with a 90-degree angle) the unknown side can always be solved by algebraically manipulating the equation presented above. A special case of such triangles is when
2 pages (500 words) Essay
Comment
The responsibility of protecting our environment from degradative activities is bestowed upon the human beings to enable them live this life as we have always known it. It is therefore a major
1 pages (250 words) Essay
The Pythagorean Theorem
For measuring the length of each road, the odometer tool of car or other motor are used. For determining the distance, no other geometrical tool is required. Moreover, for resolving such kind of issues Global
1 pages (250 words) Coursework
Find out how much would it cost
to get a custom paper written by a pro under your requirements!
Win a special DISCOUNT!
Put in your e-mail and click the button with your lucky finger
Your email
YOUR PRIZE:
Apply my DISCOUNT