Chinese remainder theorem The Chinese remainder theorem is a result about congruences in number theory and its generalizations in abstract algebra. It was first published in the 3rd to 5th centuries by Chinese mathematician Sun Tzu. In its basic form‚ the Chinese remainder theorem will determine a number n that when divided by some given divisors leaves given remainders. For example‚ what is the lowest number n that when divided by 3 leaves a remainder of 2‚ when divided by 5 leaves a remainder
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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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Kirchhoff’s Law Kirchhoff’s current law (KCL) imposes constraints on the currents in the branches that are attached to each node of a circuit. In simplest terms‚ KCL states that the sum of the currents that are entering a given node must equal the sum of the currents that are leaving the node. Thus‚ the set of currents in branches attached to a given node can be partitioned into two groups whose orientation is away from (into) the node. The two groups must contain the same net current. In general
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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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Sir Isaac Newton William Tyler Seal 4th Famous Scientist Ms. Bass May 1‚ 2013 Sir Isaac Newton was born on January 4‚ 1963. In his early years‚ he attended school in Lincolnshire at King ’s School. Briefly‚ his mother took him out of school with hopes of him becoming a farmer‚ but Newton failed miserably and went back to school to get his basic education. His uncle pressed his mother to allow Newton to go to college at Cambridge ’s Trinity College. At first‚ he was taught the standard
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Sarah DeGarso Isaac Newton Isaac Newton made a multitude of discoveries that are still relevant in today’s academia. Many people have referred to him as one of the most important scientist that has ever lived. He is mostly known by his Theory of Universal Gravity and laws of motion‚ Newton’s laws‚ but he also influenced the areas of math and optics. Newton had a passion for alchemy and astrology. Today Newton’s laws of motion and gravity theory are still taught in schools as one of the most fundamental
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The newtons theroy of it should be trueDuring the first half of the 19th century‚ scientists such as John Herschel‚ Fox Talbot‚ and William Swan studied the spectra of different chemical elements in flames. Gradually‚ the idea that each element produces a set of characteristic emission lines was established. Each element has several prominent‚ and many lesser‚ emission lines in a characteristic pattern. Sodium‚ for example‚ has two prominent yellow lines (the so-called D lines) at 589.0 and 589.6
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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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development‚ but the two most recognized discoverers of calculus are Isaac Newton and Gottfried Wilhelm Leibniz. Although the credit is currently given to both men‚ there was a time when the debate over which of them truly deserved the recognition was both heated and widespread. Evidence also shows that Newton was the first to establish the general method called the "theory of fluxions" was the first to state the fundamental theorem of calculus and was also the first to explore applications of both
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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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