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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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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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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Fermat’s last theorem Currently holding the world record for longest standing math problem ever‚ Fermat’s last theorem went unsolved for 365 years. Fermat’s last theorem was one of the largest white whales in the study of math. Over the centuries‚ thousands were puzzled by the impossible problem. From its conception to its solution‚ Fermat’s last theorem was one of the most difficult to solve yet easy to understand problems in mathematics. First‚ I will discuss the theorem and how it was introduced
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LAST THEOREM I am going to do my project in the field of number theory. Number theory‚ a subject with a long and rich history‚ has become increasingly important because of its application to computer science and cryptography. The core topics of number theory are such as divisibility‚ highest common factor‚ primes‚ factorization‚ Diophantine equations and so on‚ among which I chose Diophantine equations as the specific topic I would like to go deep into. Fermat ’s Last Theorem states
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mathematics that developed from simple measurements. A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics‚ such as Fermat’s Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle‚ the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. A particularly simple one is the scaling relationship
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THE WIZARD OF OZ 2 The Wizard of Oz Scarecrow’s Speech on Pythagorean Theorem The Pythagorean theorem is one of the earliest theorems known to ancient civilization. The well-known theorem is named after the Greek mathematician and philosopher‚ Pythagoras. In the Wizard of Oz‚ after the Scarecrow gets a brain‚ he states the Pythagorean theorem. However‚ he mistakenly says it applies to an isosceles triangle when it applies to a right triangle. He not only says the wrong triangle
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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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4.14 TRIANGLES Triangles are three-sided shapes that lie in one plane. Triangles are a type of polygons. The sum of all the angles in any triangle is 180º. Triangles can be classified according to the size of its angles. Some examples are : Acute Triangles An acute triangle is a triangle whose angles are all acute (i.e. less than 90°). In the acute triangle shown below‚ a‚ b and c are all acute angles. Sample Problem 1: A triangle has angles 46º‚ 63º and 71º. What type of triangle is this? Answer:
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