Pythagorean Theorem Diana Lorance MAT126 Dan Urbanski March 3‚ 2013 Pythagorean Theorem In this paper we are going to look at a problem that can be seen in the “Projects” section on page 620 of the Math in our World text. The problem discusses Pythagorean triples and asks if you can find more Pythagorean triples than the two that are listed which are (3‚4‚ and 5) and (5‚12‚ and 13) (Bluman‚ 2012). The Pythagorean theorem states that for any right triangle‚ the sum of the squares of the length
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Stokes’ theorem In differential geometry‚ Stokes’ theorem (or Stokes’s theorem‚ also called the generalized Stokes’ theorem) is a statement about the integration of differential forms on manifolds‚ which both simplifies and generalizes several theorems from vector calculus. The general formulation reads: If is an (n − 1)-form with compact support on ‚ and denotes the boundary of with its induced orientation‚ and denotes the exterior differential operator‚ then. The modern Stokes’ theorem is a
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Taylors Theorem: Taylor’s theorem gives an approximation of a n times differentiable function around a given point by a n-th order Taylor-polynomial. For analytic functions the Taylor polynomials at a given point are fixed order truncations of its Taylor’s series‚ which completely determines the function in some locality of the point. There are numerous forms of it applicable in different situations‚ and some of them contain explicit estimates on the approximation error of the function by its Taylor-polynomial
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BINOMIAL THEOREM : AKSHAY MISHRA XI A ‚ K V 2 ‚ GWALIOR In elementary algebra‚ the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem‚ it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc‚ where the coefficient of each term is a positive integer‚ and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in the binomial expansion are known as binomial coefficients.
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In mathematics‚ the Pythagorean theorem — or Pythagoras’ theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas‚ it states: In any right-angled triangle‚ the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). The theorem can be written as an equation relating the lengths
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The binomial theorem is a simplified way of finding the expansion of a binomial to a certain power. We can of course find the expanded form of any binomial to a certain power by writing it and doing each step‚ but this process can be very time consuming when you get into let’s say a binomial to the 10th power. Example: (x+y)^0=1 of course because anything to the power if 0 equal 1 (x+y)^1= x+y anything to a power of 1 is just itself. (x+y)^2= (x+y)(x+y) NOT x^2+y^2. So expand (x+y)(x+y)=x^2+xy+yx+y^2
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bernoulli’s theorem ABSTRACT / SUMMARY The main purpose of this experiment is to investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tape red duct and to measure the flow rate and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The apparatus used is Bernoulli’s Theorem Demonstration Apparatus‚ F1-15. In this experiment‚ the pressure difference taken is from h1- h5. The
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Experiment No. 1: Bernoulli’s Theorem Object: To verify Bernoulli’s theorem for a viscous and incompressible fluid. Theory: In our daily lives we consume a lot of fluid for various reasons. This fluid is delivered through a network of pipes and fittings of different sizes from an overhead tank. The estimation of losses in these networks can be done with the help of this equation which is essentially principle of conservation of mechanical energy. Formal Statement: Bernoulli’s Principle is
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new centre of order for the now chaotic world‚ as old aesthetics and beliefs simply did not seem to fit anymore. This sense of aloneness and being unstuck from reality is a quintessential trait of early 20th century texts. By examining the work of Thomas Hardy and William Butler Yeats (two contemporary poets of the time)‚ a real sense of the estrangement experienced comes across. Many social and political crises around the turn of the century aided the development of Modernism (approximately 1890
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