Greek mathematician and philosopher. Pythagoras was responsible for important developments in the history of mathematics‚ astronomy‚ and the theory of music. The thing that Pythagoras is probably the most famous for is the Pythagorean Theorem. The Pythagorean Theorem is used in the field of mathematics and it states the following: the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two other sides. This means that if one makes a square (with all sides equal in
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Pythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I ’ll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion‚ a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears
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Gauss Markov Theorem In the mode [pic]is such that the following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify
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Geometry Definitions‚ Postulates and Theorems Definitions Name Complementary Angles Supplementary Angles Theorem Vertical Angles Transversal Corresponding angles Same-side interior angles Alternate interior angles Congruent triangles Similar triangles Angle bisector Segment bisector Legs of an isosceles triangle Base of an isosceles triangle Equiangular Perpendicular bisector Altitude Definition Two angles whose measures have a sum of 90o Two angles whose measures have a sum of 180o A statement
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Speed limits are posted for reasons that will help you through your life. School zones are one of the most important reasons. I am going to explain my beliefs on limitations for the speed limits. In most cases‚ people don’t like to drive the speed limit. School zones‚ in my opinion‚ are the most important. When traveling through school zones‚ doing the speed limit‚ you have the ability to stop faster when something out of the blue happens‚ a child running out in the street chasing a ball kicked
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huge role in the conviction of The Central Park Five. Within the week of April 19-22‚ 1989. there were twenty-eight other first degree rapes or attempted rapes. Although sexual violence is a problem that has been occurring for a (long) time‚ these twenty-nine raped did not have the “wow factor” to make the front page of every newspaper in the nation. The Location of the Central Park captured the writers of huge newspapers. During the late 1980’s early 1990’s‚ Central Park was viewed as a “peaceful place”
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properties of actual procedures for aggregating preferences via voting rules. The problem is finding a social choice function that satisfies normative criteria and establishing equilibrium under voting rules. (Mueller‚ 3‚ 1989) Arrow’s Impossibility Theorem set out to prove that democratic social choice processes were inherently flawed and had no way to be fixed. In order for a person to vote there must be a social welfare function that satisfies unrestricted domain‚ positive association‚ independence
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GLOBAL BUSINESS FINANCE CIA ARTICLE REVIEW DONE BY: BHAKTI SHETH-1111120 SANGITHA S. - 1111222 THE LIMITS OF BIMETALLISM By Christopher M. Meissner ‚ University of California‚ Davis and NBER ARTICLE REVIEW Bimetallism refers to a monetary standard or system based upon the use of two metals‚ traditionally gold and silver‚ rather than one (monometallism). This paper focuses on the factors which led to the decline of bimetallism as an international monetary standard. In the late
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ATTERBERG LIMIT AND MOISTURE CONTENT Introduction: This report is to establish the Atterberg limit of s oil sample after performing and analyzing the tests performed in laboratory. Atterberg limit is used to differentiate between silt & clay ‚ in various categories‚ and also to establish boundaries between each state of soil‚ i.e soild‚ semi-solid‚ plastic & liquid‚ and the change in soil behavior. The method of Cone Penetrometer was
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Push It to the Limit Many things cross your mind while you’re traveling down the road. But have you ever wondered why do we have speed limits? Or maybe you do and you’re the grandma driver that everyone is stuck behind in a no passing zone. Everyone has their own speeds so why shouldn’t you be able to go how fast or how slow you wanted to go. Should we strike down every sign that the government has put up to regulate the speed limit in the thousands of highways around the country? And should we
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