The four color theorem is a mathematical theorem that states that‚ given a map‚ no more than four colors are required to color the regions of the map‚ so that no 2 regions that are touching (share a common boundary) have the same color. This theorem was proven by Kenneth Appel and Wolfgang Haken in 1976‚ and is unique because it was the first major theorem to be proven using a computer. This proof was first proposed in 1852 by Francis Guthrie when he was coloring the counties of England and realized
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1 10/10/01 Fermat’s Little Theorem From the Multinomial Theorem Thomas J. Osler (osler@rowan.edu) Rowan University‚ Glassboro‚ NJ 08028 Fermat’s Little Theorem [1] states that n p −1 − 1 is divisible by p whenever p is prime and n is an integer not divisible by p. This theorem is used in many of the simpler tests for primality. The so-called multinomial theorem (described in [2]) gives the expansion of a multinomial to an integer power p > 0‚ (a1 + a2 + ⋅⋅⋅ + an ) p = p k1 k2 kn a1 a2
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“The Arrow impossibility theorem and its implications for voting and elections” Arrow’s impossibility theorem represents a fascinating problem in the philosophy of economics‚ widely discussed for insinuating doubt on commonly accepted beliefs towards collective decision making procedures. This essay will introduce its fundamental assumptions‚ explain its meaning‚ explore some of the solutions available to escape its predictions and finally discuss its implications for political
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a NOR gate. DeMorgan’s theorems state the same equivalence in "backward" form: that inverting the output of any gate results in the same function as the opposite type of gate (AND vs. OR) with inverted inputs De Morgan’s theorem is used to simplify a lot expression of complicated logic gates. For example‚ (A + (BC)’)’. The parentheses symbol is used in the example. _ The answer is A BC. Let’s apply the principles of DeMorgan’s theorems to the simplification of
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HYDROLOGY & HYDRAULIC ENGINEERING I LABORATORY REPORT 3 TITLE : BERNOULLI’S THEOREM APPARATUS NAME : ID. NO. : SECTION : 02 EXPERIMENT DATE : 10th December 2009 SUBMISSION DATE : 17th December 2009 GROUP NO. : 2 GROUP MEMBERS : LECTURER : LAB INSTRUCTOR : TABLE OF CONTENT Content | Page | Summary | 2 | Objective | 2 | Theory | 3 - 5 | Equipment/ description of experimental apparatus | 6 | Procedure | 6 | Data and observation | 6a | Analysis | 7‚8
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A Brief History of the Pythagorean Theorem Just Who Was This Pythagoras‚ Anyway? Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece‚ and did much traveling through Egypt‚ learning‚ among other things‚ mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group‚ the Brotherhood of Pythagoreans‚ which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols‚ rituals and prayers. In addition
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central The Central Limit Theorem A long standing problem of probability theory has been to find necessary and sufficient conditions for approximation of laws of sums of random variables. Then came Chebysheve‚ Liapounov and Markov and they came up with the central limit theorem. The central limit theorem allows you to measure the variability in your sample results by taking only one sample and it gives a pretty nice way to calculate the probabilities for the total ‚ the average and the proportion
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Fermat’s Last Theorem Fermat’s Last Theorem states that no three positive integers‚ for example (x‚y‚z)‚ can satisfy the equation x^n+y^n=z^n if the integer value of n is greater than 2. Fermat’s Last Theorem is an example a Diophantine
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La Perouse field report Earth and Environmental science - Angus Kwan The area of La Perouse is a place featuring incredible landscapes‚ historical sites that has significant natural and cultural heritage to Australia. In this report i will be conducting research and primary investigation of the following topics in the coastal area of La Perouse and Botany Bay. • Geological features and history that it provides • The type of soils present how it effects vegetation. • The dominant flora and fauna
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Describe the role of courts in the criminal justice process. The courts serve as the venue where disputes are then settled and justice is administered. In Australian courts the adversarial system of trial is used to determine guilt‚ this is two sides‚ one representing the accused the other the state‚ debate over the guilt of the accused; this is mediated by a neutral third party‚ the judge or magistrate. Guilt is determined by the judge‚ magistrate or a jury. Punishment for the accused if found
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