## CHECK THESE SAMPLES OF Pythagorean Theorem

... or harmony - so is man's capacity for divining or knowing harmony, truth and beauty in his life. The **Pythagoreans** called the universe "kosmos" which meant order or arrangement. They also believed that the whole and the parts are similar in that this similarity can be gleaned by the proportion of the parts to the whole. Thus, the Pythagoras world view influenced not only the scientific fields but the arts as well particularly in music, with his musical notion of octaves.
The **Pythagorean** explanation of the structure of the universe through mathematics should not be viewed simplistically and reduced to the mathematical formulas (i.e. to-date the **Pythagorean** **theorem** is being taught in trigonometry classes). Rather the **Pythagorean** view placed...

4 Pages(1000 words)Case Study

....
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;
1. The 'a' side can take any odd number as its value.
2. The 'b' side is [(a2 - 1) / 2].
3. The 'c' side is equal to (b + 1).
OR
1. The 'a' side can take any even number as its value.
2. The 'b' side is equal to [(a/2)2 - 1].
3. The 'c' side is equal to (b+2).
Proof of above-mentioned rules:
**Pythagorean** **theorem** states a2 + b2 = c2 ------------------------- (Eq-1)
Case-I: Substituting c = b+1, in (Eq-1) we get,
a2 + b2 = (b + 1)2
a2 + b2 = b2 + 1 +...

2 Pages(500 words)Essay

...representation
A
B C
Consider a right angle triangle ABC with right angle at A.
Angle BAC = 90 degree
Then, the square drawn on BC opposite the right angle is equal to the two squares together on BA, AC.
Thus, the sides of a right triangle are related by the squares drawn on them
The **Pythagorean** **Theorem** is a statement about triangles containing a right angle. The **Pythagorean** **Theorem** states that:
"The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."
Illustratation by numbers
A
16
9
B C
Let the sides of the right angle...

14 Pages(3500 words)Essay

...**PYTHAGOREAN** TRIPLES The **Pythagorean** **Theorem** is probably one of the first principles learned in a Trigonometry It is about a property of all right triangles showing a relationship between their sides given by the equation c2 = a2 + b2; that is, the square of the longest side is equal to the sum of the squares of the remaining two sides (Knott 2009). 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 all the three sides, a, b and c, are integers, thus generating a **Pythagorean** Triple (Bogomolny 2009). The most popular example of which is the 3-4-5 triangle, the triple...

2 Pages(500 words)Essay

...= 10000
In all the triples identified, it was verified that a, b, and c are in the exact proportion and relationship in accordance with the **Pythagorean** **Theorem** equation. The two numbers of the lowest value among the three in the triple were represented by a and b and the largest was represented by c.
The **Pythagorean** **Theorem** equation has been successful in providing relationship among the three integers representing the sides of a right triangle through the **Pythagorean** Triples. This equation is truly useful in solving right triangle problems and it is also the foundation in the derivation complex trigonometric equations.
References
Generating **Pythagorean** Triples. (n.d.). Retrieved from ...

1 Pages(250 words)Essay

... Five-Color **Theorem** The five color **theorem**, also referred to as the five color map **theorem**, is a mathematical theoremthat was developed from the graph theory. The **theorem** states that for a given plane divided into adjoining regions, such that it results in a form of a map of countries, no more than five colors are necessary to color the regions of the political map such that no two neighboring areas of the map are colored with the similar color. The five color **theorem** was developed as an extension to the four color **theorem** which was proved to have an error in its proof. To understand the five color theory it is necessary to go to the history behind the development of the color **theorems**. There are three of them, four-color, five-color...

2 Pages(500 words)Essay

...**Pythagorean** Triples A **Pythagorean** triple refer to a set of three positive integers a, b, c such that the sum of the squares of two smaller integers of them equal to the square of the third largest integer i.e. if c > a, b then a2 + b2 = c2, c2 – a2= b2, or, c2 – b2 = a2. **Pythagorean** triples are part of **Pythagorean** **Theorem** which says that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides 1. Each triple set has its many multiples which will be regarded as the same triple set i.e. the set (a, b, c) and its any multiple k, ka, kb, kc, will count as one set.
We are required to build the **Pythagorean** triples and to verify them through the **Pythagorean** **Theorem**. The **Pythagorean** triples (a; b...

1 Pages(250 words)Speech or Presentation

Divorce is a lawful procedure in which an adjudicator or any other power dissolves the bonds of marriage offered between two people, hence restoring them to the position of being on there own and permitting them to wed other persons. Most states in America have their own laws when it comes to divorce. Most of them allow no-fault divorce. This is where termination of matrimony does not need an assertion or evidence of mistake of whichever party. . With introduction of no-faulty divorce, it motivated a countrywide discussion over dissociate change. Followers of no-fault divorce renowned that there were various troubles with alternative arrangement divorce

I would not advocate for a change in the current law. This is for the ratio...

1 Pages(250 words)Essay

...Coase **Theorem** Coase **Theorem** Coase **theorem** targets economic efficiency that is attributed to economic allocation and outcome when externalities are present. The theory stipulates that if trade is possible in the presence of an externality when transaction costs are significantly low, the end result will be an efficient outcome when initial allocation of property is not considered. The major obstacles to Coasian bargaining emerge when property rights have been defined poorly (Buchanan, 2005). This paper will discuss Coase **theorem** as an alternative to government regulation in terms of facilitating for the provision of goods and services.
Ronald Coase stipulated that transaction costs that are found in the real world are not sufficiently low...

2 Pages(500 words)Essay

..., 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, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is ‘x’?
Solution:
By **Pythagorean** **Theorem**, x2 + (2x + 4)2 = (2x + 6)2
--- x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36
Combining similar terms,
--- x2 + 16x - 24x + 16 - 36 = 0
Reduces to Quadratic Equation: x2 - 8x - 20 = 0
where the left side can be factored into (x - 10) * (x + 2) = 0
Then by Zero-Factor Rule: x - 10 = 0...

1 Pages(250 words)Speech or Presentation

...Bayesian **Theorem** Introduction Reverend Thomas Bayes developed Bayes’ **theorem** of probability. The **theorem** provides understanding about the how the probability of a **theorem** is affected by a new set of evidence. It is applied to in a variety of context to explore a relationship between theory and evidence. Contemporary, the **theorem’s** application is broad, ranging from mathematics to the field of science. It explains the relations between two theories and evidences. It allows the researcher to determine the relation between current beliefs with respect to previous beliefs and evidences.
Simon Jackman (2009) defines Bayes’ **theorem** as ‘a **theorem** that illustrates conditional probability of the set on the given observed outcome, that is obtained...

15 Pages(3750 words)Essay

... **Theorem** is used to determine the size of a television or a computer monitor. Through determining the length and breadth of the screen and using the formula of **Pythagorean** **Theorem** [c= √(a2+b2)], the diagonal size of the screen is determined (Maor, 2007). **Pythagorean** **Theorem** is highly effective and is comparatively easy than any other mathematical tool hence, it is extensively used. There is no other geometrical concept required to determine the size of the screen. Moreover, there are no other available tools in the modern day that determines the same (Lorenz Educational Press, 2014).
**Pythagorean** **Theorem** is also effective in determining the size of a ladder for painting a building of specific height and maintaining a specific distance...

1 Pages(250 words)Essay

...Maximum Power Transfer **Theorem** and Kirchhoff’s law Experiment The maximum Power transfer Introduction The **theorem** of maximum power transfer posits that for a maximum power to be obtained from a source having a finite internal resistance, the load resistance should be equated to the source observed from the terminal output. It leads to the production of maximum transfer of power. When the load resistance is greater than the source resistance, the efficiency would be higher because a high percentage of the source would be moved to the load. The magnitude of load power would be low due to the resistance in the circuit that increases. Whenever the resistance of the load reduces, most of the power will be dissipated within the source...

4 Pages(1000 words)Lab Report

... No: The Central Limit **Theorem** The Central Limit **Theorem** The main aim of this paperis to give you brief introduction about an important topic of the Statistics, which is used in the analysis of Descriptive Statistics with the help of SPSS and also useful in conducting the statistical inference. Before solving your problems with the help of Central Limit **Theorem**, you should make sure that you have read all the necessary instructions and notes to understand this topic completely as it is not as easy as it seems to be. Since another basic purpose of this paper is to get you familiar with the Central Limit **Theorem** and tell you its importance in statistical inference. No doubt, statistics is an important subject, which helps us in all of our...

7 Pages(1750 words)Term Paper