study? Start with Flashcards 7 22 terms by shweta101 Pythagorean Theorem In a right triangle‚ the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. (a^2 + b^2 = c^2 (Page 433) Pythagorean Triple A set of 3 positive integers A‚ B‚ and C that satisfy the equation A^2 + B^2 = C^2 [Ex. (3‚4‚5) (5‚12‚13) (8‚ 15‚17) and (7‚24‚25)] (Page 435) Converse of the Pythagorean Theorem If the square of the length of the longest side of a triangle (hypotenuse) is equal to
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Early trigonometry The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. But pre-Hellenic societies lacked the concept of an angle measure and consequently‚ the sides of triangles were studied instead‚ a field that would be better called "trilaterometry".[6]The Babylonian astronomers kept detailed records on the rising and setting of stars‚ the motion of the planets‚ and the solar and lunar eclipses‚ all of which required
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compass-and-straightedge construction. Several fundamental theorems about triangles are attributed to Thales‚ including the law of similar triangles (which Thales used famously to calculate the height of the Great Pyramid) and "Thales’ Theorem" itself: the fact that any angle inscribed in a semicircle is a right angle. (The other "theorems" were probably more like well-known "axioms"‚ but Thales proved Thales’ Theorem using two of his other theorems; it is said that Thales then sacrificed an ox to celebrate
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MTH 405 Midterm 16/3/2011 1. A specific area for the area of various polygons is the one for the area of a regular polygon. The setup and initial steps to creating the proof require a geometric approach that would otherwise make proving a big challenge. For example‚ a polygon with n sides is broken up into a collection of n congruent triangles‚ this geometric setup is key in reaching an easy solution for the area. The algebraic aspect comes into play when it comes to deriving the equation
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measurements in a bell-shaped distribution lie within standard deviations of the mean. • • We are asked to use Chebyshev’s theorem to determine the minimum percentage of the students’ commute distances that lie between and . To do this‚ we can express the values and in terms of their distance from the mean (in standard deviations) and then apply Chebyshev’s theorem. We are told that the mean is and the standard deviation is . Note that and or‚ equivalently‚ and
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in math. He is best remembered for his number theory‚ in particular for Fermat’s Last Theorem. This theorem states that: xn + yn = zn has no non-zero integer solutions for x‚ y and z when n is greater than 2. Fermat almost certainly wrote the marginal note around 1630‚ when he first studied Diophantus’s Arithmetic. It may well be that Fermat realized that his prove was wrong‚ however‚ since all his other theorems were stated and restated in challenge problems that Fermat sent to other mathematicians
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In today’s world‚ there are a multitude of mathematical theorems and formulas. One theorem that is particularly renowned is the Pythagorean Theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of any right triangle. While most people have heard of or even used the Pythagorean Theorem‚ many know little of the man who proved it. Pythagoras was born in 570 BC in Samos‚ Greece. His father‚ Mnesarchus‚ was a merchant from Tyre who traveled
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References: • Besanko D. et al (2010)‚ “Economics of Strategy”‚ Wiley 2010 • Coase R. (1937)‚ “The Nature of the Firm” • Vedpuriswar A. V (2003)‚ “The Vertical Boundaries of the Firm” Available at www.vedpuriswar.org • Tan K. (2009)‚ “The Firm” Available at www.econ.ohio-state.edu 1.Introduction
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Geometry Notes Second Semester I. Area‚ Surface Area and Volume & Circumference Circumference is the linear distance around the outside of a circular object. • C = π • d or π • 2r. • d = diamater or (radius • 2) • r = radius II. Perimeter Perimeter is the distance around a figure. * It is found by adding the lengths of all the sides. * Finding perimeter on the coordinate plane may require the use of the distance formula: (2 x width) + (2 x height) III. Regular Polygon • A regular
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numbers and encountered irrational numbers. We continue our discussion on real numbers in this chapter. We begin with two very important properties of positive integers in Sections 1.2 and 1.3‚ namely the Euclid’s division algorithm and the Fundamental Theorem of Arithmetic. Euclid’s division algorithm‚ as the name suggests‚ has to do with divisibility of integers. Stated simply‚ it says any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is
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