The Pythagorean Theorem (Essay Sample)
IT is basically about the proof and application of THE Pythagorean Theoremsource..
The Theorem of Pythagorean
A right-angled triangle has the relationship of its sides usually shown by the theorem of Pythagoras’s. This theorem is also called the theorem of Pythagorean where the squares of the shorter lengths of the triangle when summed is equal to the squared hypotenuse (Weisstein, 2006). This relationship is shown by use of an equation which is shown below. The two short sides length of the triangle and the hypotenuse are denoted by the letters a, b, and c respectively. Below is the drawing of the triangle and its equation for lengths.
Proofs of the Pythagorean Theorem
There are several proofs that show this theorem which are explained below;
* Rearrangement and dissection proof
This proof is usually the opposite of Einstein’s proof which is described. Inside a square, four triangles that are right-angled are moved forming two squares. When they are moved again, they form one square as it drawn below. In forming of the two squares first, the areas of the squares are a2and b2 whereas the other one is c2.
* Algebraic Theorem
Four right-angle triangles are used in this proof where the four triangles are arranged inside a square. The small square dimension is (b-a) by (b-a) whereas the bigger one is c by c as drawn in the figure below;
* Einstein’s proof
This proof shows a right-angled triangle being dissected without moving any side of the right-angled triangle.
* Similar triangles proof
Here two similar triangles no matter the size of the triangles are used in this proof. This proof indicates that the ratio of any two triangles that are similar and are right-angled is usually same.
Applications of Pythagoras Theorem
The Pythagoras theorem is used in various activities in the real life. Applications of this theorem in real life are given below:
This theorem is applied in finding the shortest distance in navigation that is two-dimensional. The two triangle’s legs are the two distances where
- Macro and Micro Economic FactorsDescription: The financial performance of an international organization is determined by both Micro and Microeconomic factors are factors such as forces of demand and supply that are linked to several markets and segments of the economy. Other examples of microeconomic factors include competition and the price of goodsz...5 pages/≈1375 words| 8 Sources | APA | Mathematics & Economics | Essay |
- The Role of John Tukey in the Development of StatisticsDescription: John Wilder Tukey, a famous statistician, was born in 1915 in New Bedford, Massachusetts. His early education was school-based up until college. Then, he joined Brown University and obtained a Bachelor’s and Master’s degrees in chemistry and proceeded to Princeton University for his Ph.D. in pure mathematic...1 page/≈275 words| 2 Sources | APA | Mathematics & Economics | Essay |
- Foreign Capital Inflows in Australia Description: Australia has been a recipient of net capital inflows from various countries like the US, United Kingdom, Belgium, and Japan for decades. Consequently, the receipt has enabled the country to attain significant economic growth, technology adoption n, and improved living standards....3 pages/≈825 words| 6 Sources | APA | Mathematics & Economics | Essay |