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1089 (number)
1089 is the integer after 1088 and before 1090. It is a square number (33 squared), a nonagonal number, a 32-gonal number, a 364-gonal number, and a centered octagonal number. 1089 is the first reverse-divisible number. The next is 2178 , and they are the only four-digit numbers that divide their reverse. In magic 1089 is widely used in magic tricks because it can be "produced" from any two three-digit numbers. This allows it to be used as the basis for a Magician's Choice. For instance, one variation of the book test starts by having the spectator choose any two suitable numbers and then apply some basic maths to produce a single four-digit number. That number is always 1089. The spectator is then asked to turn to page 108 of a book and read the 9th word, which the magician has memorized. To the audience it looks like the number is random, but through manipulation, the result is always the same. In base 10, the following steps always yield 1089: # Take any three-digit num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Number
In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name ''square'' number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by ''n'' points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of ''n''; thus, square numbers are a type of Figurate number, figurate numbers (other examples being Cube (algebra), cube numbers and triangular numbers). In the Real number, real number system, square numbers are non-negative. A non-negative integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonagonal Number
A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular number, triangular and square numbers to the nonagon (a nine-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of nonagonal numbers are not rotationally symmetrical. Specifically, the ''n''th nonagonal number counts the dots in a pattern of ''n'' nested nonagons, all sharing a common corner, where the ''i''th nonagon in the pattern has sides made of ''i'' dots spaced one unit apart from each other. The nonagonal number for ''n'' is given by the formula: :\frac . Nonagonal numbers The first few nonagonal numbers are: :0 (number), 0, 1 (number), 1, 9 (number), 9, 24 (number), 24, 46 (number), 46, 75 (number), 75, 111 (number), 111, 154 (number), 154, 204 (number), 204, 261 (number), 261, 325 (number), 325, 396 (number), 396, 474 (number), 474, 559 (number), 559, 651 (number), 651, 750 (number), 750, 856 (number), 856, 96 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Octagonal Number
A centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are the same as the odd number, odd square numbers. Thus, the ''n''th odd square number and ''t''th centered octagonal number is given by the formula :O_n=(2n-1)^2 = 4n^2-4n+1 , (2t+1)^2=4t^2+4t+1. The first few centered octagonal numbers are :1 (number), 1, 9 (number), 9, 25 (number), 25, 49 (number), 49, 81 (number), 81, 121 (number), 121, 169 (number), 169, 225, 289, 361, 441, 529, 625, 729, 841, 961, 1089 (number), 1089, 1225 Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number. O_n is the number of 2x2 matrices with elements from 0 to n that their determinant is twice their Permanent (mathematics), permanent. See also * Octagonal number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reverse-divisible Number
In number theory, reversing the digits of a number sometimes produces another number that is divisible by . This happens trivially when is a palindromic number; the nontrivial reverse divisors are :1089, 2178, 10989, 21978, 109989, 219978, 1099989, 2199978, ... . For instance, 1089 × 9 = 9801, the reversal of 1089, and 2178 × 4 = 8712, the reversal of 2178... The multiples produced by reversing these numbers, such as 9801 or 8712, are sometimes called palintiples. Properties Every nontrivial reverse divisor must be either 1/4 or 1/9 of its reversal. The number of -digit nontrivial reverse divisors is 2F(\lfloor(d-2)/2\rfloor) where F(i) denotes the th Fibonacci number. For instance, there are two four-digit reverse divisors, matching the formula 2F(\lfloor(d-2)/2\rfloor)=2F(1)=2. History The reverse divisor properties of the first two of these numbers, 1089 and 2178, were mentioned by W. W. Rouse Ball in his ''Mathematical Recreations''. In ''A Mathematician's Apology'', G. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2178 (number)
2000 (two thousand) is a natural number following 1999 and preceding 2001. It is: :*the highest number expressible using only two unmodified characters in Roman numerals (MM) :*an Achilles number :*smallest four digit eban number :*the sum of all the nban numbers in the sequence Selected numbers in the range 2001–2999 2001 to 2099 * 2001 – sphenic number * 2002 – palindromic number in decimal, base 76, 90, 142, and 11 other non-trivial bases * 2003 – Sophie Germain prime and the smallest prime number in the 2000s * 2004 – Area of the 24tcrystagon* 2005 – A vertically symmetric number * 2006 – number of subsets of with relatively prime elements * 2007 – 22007 + 20072 is prime * 2008 – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 3 * 2009 = 74 − 73 − 72 * 2010 – number of compositions of 12 into relatively prime parts * 2011 – sexy prime with 2017, sum of eleven consecutive primes: 2011 = 157 + 163 + 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Trick
Magic, which encompasses the subgenres of close-up magic, parlor magic, and stage magic, among others, is a performing art in which audiences are entertained by tricks, effects, or illusions of seemingly impossible feats, using natural means. It is to be distinguished from paranormal magic which are effects claimed to be created through supernatural means. It is one of the oldest performing arts in the world. Modern entertainment magic, as pioneered by 19th-century magician Jean-Eugène Robert-Houdin, has become a popular theatrical art form. In the late 19th and early 20th centuries, magicians such as John Nevil Maskelyne and David Devant, Howard Thurston, Harry Kellar, and Harry Houdini achieved widespread commercial success during what has become known as "the Golden Age of Magic", a period in which performance magic became a staple of Broadway theatre, vaudeville, and music halls. Meanwhile, magicians such as Georges Méliès, Gaston Velle, Walter R. Booth, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magician's Choice
In stage magic, a force is a method of controlling a choice made by a spectator during a trick. Some forces are performed physically using sleight of hand, such as a trick where a spectator appears to select a random card from a deck but is instead handed a known card by the magician. Other forces use equivocation (or "the magician's choice") to create the illusion of a free decision in a situation where all choices lead to the same outcome. Equivocation Equivocation (or the magician's choice) is a verbal technique by which a magician gives an audience member an apparently free choice but frames the next stage of the trick in such a way that each choice has the same end result. An example of equivocation can be as follows: A performer deals two cards on a table and asks a spectator to select one. If the spectator chooses the card on the left, the performer will hand the card to the spectator. If they pick the card on the right, the performer will take that card as his own and hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Book Test
The book test is a classic mentalism demonstration used by mentalists to demonstrate telepathy-like effects. The name refers to its early use as a test of mental powers. Effect An audience member (the "spectator") is called onstage to assist the mentalist. The spectator is shown one or more books, and asked to read a random passage from one of them. The passage may be revealed to the audience, or recorded in some other way for later comparison. The mentalist then typically presents a routine to establish an atmosphere or back story, and proceeds to read the spectator's mind to reveal elements relating to the passage read by the spectator. History Books have been used as props as long ago as the 1450s. In one particularly common trick, the " blow book", spectators would blow on the pages of a book which would then reveal images, colors, or text. However, these were not similar to modern book tests, as the "magic" was simply the change in appearance.When the history of book tests a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base. For base ten, the subscript is usually assumed and omitted (together with the enclosing parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems Generally, in a system with radix ''b'' (), a string of digits denotes the number , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octal
Octal (base 8) is a numeral system with eight as the base. In the decimal system, each place is a power of ten. For example: : \mathbf_ = \mathbf \times 10^1 + \mathbf \times 10^0 In the octal system, each place is a power of eight. For example: : \mathbf_8 = \mathbf \times 8^2 + \mathbf \times 8^1 + \mathbf \times 8^0 By performing the calculation above in the familiar decimal system, we see why 112 in octal is equal to 64+8+2=74 in decimal. Octal numerals can be easily converted from binary representations (similar to a quaternary numeral system) by grouping consecutive binary digits into groups of three (starting from the right, for integers). For example, the binary representation for decimal 74 is 1001010. Two zeroes can be added at the left: , corresponding to the octal digits , yielding the octal representation 112. Usage In China The eight bagua or trigrams of the I Ching correspond to octal digits: * 0 = ☷, 1 = ☳, 2 = ☵, 3 = ☱, * 4 = ☶, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexadecimal
Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen. Software developers and system designers widely use hexadecimal numbers because they provide a convenient representation of binary code, binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble). For example, an 8-bit byte is two hexadecimal digits and its value can be written as to in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value would be expressed in hexadecimal as . In programming, several notations denote hexadecimal numbers, usually involving a prefi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
