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The equation holds good for sets of three integers known as triples. Since the equation is based on Pythagorean Theorem, hence the name Pythagorean triples. A well known example of such a triple is (3, 4, 5). This implies that 32+42=52
Other such examples are (5, 12, 13), (7, 24, 25), (8, 15, 17) etc. Euclid's formula proves quite helpful in generating a series of such triples. As per this formula for an arbitrary pair of positive integers m and n such that m > n, the three numbers are;
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Prestressing is normally accomplished in 3 ways which are: pre-tensioned concrete, followed by bonded and the unbonded and post-tensioned concrete.Pre-tensioned concrete is then cast all around the already tensioned tendons. The pickled concrete sticks to and also ties itself with the bars.
Initially, it dealt with areas, volumes, and lengths but in the 3 BC, geometry took a new path as a result of efforts from Mathematicians such as Euclid with his Euclidean geometry. He laid down the foundation of today's geometry; absolute geometry is type of geometry that has developed in the recent years by designing some of the theories and axioms of Euclidean geometry by Mathematician Janos Bolyai in 1892.
These latter problems may be tricky and hard to conceptualize but with a clear basis and knowledge of different types of problems and techniques to apply, they can be solved easily.
According to Chapter 2, task 2.2.1 on similarities and ratio, so many mathematical tasks can be developed and solved.
Let us start investigating this problem by looking back in time and history of this problem. It not only makes our study more interesting, it also throws light on the path that we should follow. It is a well-known fact that for an arbitrary closed curve in the plane of a fixed perimeter, it is the circle that encloses the largest area.
The word "fractal" was created by Benoit Mandelbrot and it means "to break", whereas the form of adjective "fractus" means "fragmentated". (Brandt 24)
It is a matter of fact that the word "fractal" has two definite meanings: the first meaning refer to colloquial use and the second is connected with geometry.
If we read the history of Pythagoras we would come to know his influence upon other philosophers like Plato's whole theory is very much affected by his thinking about geometry. He develops it in books VI and VII of the Republic, and says that "what we are talking about in geometry and mathematics, which are generally abstract entities of timeless, spaceless, and impersonal theologies.
This medial triangle is sometimes also known as auxiliary triangle (Dixon, 1991). The medial triangle DEF consists of the vertices/ Now let KLM be the mid points of DE, DF, and EF respectively. By joining these points we get another triangle KLM i.e. the medial triangle of DEF. Therefore, K= (k1, k2)
Composition of transformation refers to a case when two or more transformations are combined to another new transformation. In a composition, the first transformation maps the object to an image which is then transformed by the subsequent transformation.
Currently, the study has advanced to include other branches of mathematics such as number theory, algebra, and topology. Riemannian geometry for example is among the latest braches of geometry. Each of the above fields of specialization
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