2 SLIDES - NO SOUND - SILENCE

• Report rights infringement
• published: 07 Mar 2016
• views: 42

2 SLIDES - NO SOUND - SILENCE. The number two has many properties in mathematics. An integer is called even if it is divisible by 2. For integers written in a numeral system based on an even number, such as decimal and hexadecimal, divisibility by 2 is easily tested by merely looking at the last digit. If it is even, then the whole number is even. In particular, when written in the decimal system, all multiples of 2 will end in 0, 2, 4, 6, or 8. Two is the smallest and the first prime number, and the only even prime number for this reason it is sometimes called "the oddest prime". The next prime is three. Two and three are the only two consecutive prime numbers. 2 is the first Sophie Germain prime, the first factorial prime, the first Lucas prime, the first Ramanujan prime, and the first Smarandache-Wellin prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. It is also a Stern prime, a Pell number, the first Fibonacci prime, and a Markov number—appearing in infinitely many solutions to the Markov Diophantine equation involving odd-indexed Pell numbers. It is the third Fibonacci number, and the third and fifth Perrin numbers. Despite being prime, two is also a superior highly composite number, because it is a natural number which has more divisors than any other number scaled relative to the number itself. The next superior highly composite number is six. Vulgar fractions with only 2 or 5 in the denominator do not yield infinite decimal expansions, as is the case with all other primes, because 2 and 5 are factors of ten, the decimal base. Two is the base of the simplest numeral system in which natural numbers can be written concisely, being the length of the number a logarithm of the value of the number (whereas in base 1 the length of the number is the value of the number itself); the binary system is used in computers. For any number x: x + x = 2 · x addition to multiplication x · x = x2 multiplication to exponentiation xx = x↑↑2 exponentiation to tetration In general: Two is the only number x such that the sum of the reciprocals of the powers of x equals itself. In symbols Taking the square root of a number is such a common mathematical operation, that the spot on the root sign where the exponent would normally be written for cubic roots and other such roots, is left blank for square roots, as it is considered tacit. The square root of 2 was the first known irrational number. The smallest field has two elements. Two is a primorial, as well as its own factorial. Two often occurs in numerical sequences, such as the Fibonacci number sequence, but not quite as often as one does. Two is also a Motzkin number, a Bell number, an all-Harshad number, a meandric number, a semi-meandric number, and an open meandric number. Two is the number of n queens problem solutions for n = 4. With one exception, all known solutions to Znám's problem start with 2. The number of domino tilings of a 2×2 checkerboard is 2. In n-dimensional space for any n, any two distinct points determine a line. For any polyhedron homeomorphic to a sphere, the Euler characteristic is χ = V − E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. As of June 2015, there are only two known Wieferich primes in base 2. With the exception of the sequence 3, 5, 7, the maximum number of consecutive odd numbers that are prime is two. **************************** Baseball: In baseball scorekeeping, 2 is the position of the catcher. Football: In American football, a safety has a two-point value. Also, a two-point conversion is a point after touchdown (PAT) attempt where the ball crosses the goal line via run or pass. (In six-man football, however, the traditional PAT kick is worth two points, whereas a PAT via pass or run is only one point.) In Association football, the scoring of two goals by one individual in a single match is referred to as a brace. The successor of a brace is the "hat-trick", three goals scored by one player. Basketball: In standard basketball, the value of any made shot taken from inside the three-point arc in normal play is 2 points. In the half-court 3x3 variant, made shots taken from outside the "three-point" arc are worth 2 points. **************************************** Baseball is a bat-and-ball game played between two teams of nine players each who take turns batting and fielding. The batting team attempts to score runs by hitting a ball that is thrown by the pitcher with a bat swung by the batter, then running counter-clockwise around a series of four bases: first, second, third, and home plate. A run is scored when a player advances around the bases and returns to home plate.