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65 (number)
65 (sixty-five) is the natural number following 64 and preceding 66. In mathematics 65 is the nineteenth distinct semiprime, (5.13); and the third of the form (5.q), where q is a higher prime. 65 has a prime aliquot sum of 19 within an aliquot sequence of one composite numbers (65, 19, 1,0) to the prime; as the first member' of the 19-aliquot tree. It is an octagonal number. It is also a Cullen number. Given 65, the Mertens function returns 0. This number is the magic constant of a 5x5 normal magic square: \begin 17 & 24 & 1 & 8 & 15 \\ 23 & 5 & 7 & 14 & 16 \\ 4 & 6 & 13 & 20 & 22 \\ 10 & 12 & 19 & 21 & 3 \\ 11 & 18 & 25 & 2 & 9 \end. This number is also the magic constant of n-Queens Problem for n = 5. 65 is the smallest integer that can be expressed as a sum of two distinct positive squares in two (or more) ways, 65 = 82 + 12 = 72 + 42. It appears in the Padovan sequence, preceded by the terms 28, 37, 49 (it is the sum of the first two of these). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is, a magic square which contains the numbers 1, 2, ..., ''n''2 – the magic constant is M = n \cdot \frac. For normal magic squares of orders ''n'' = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order ''n'' is . The largest magic constant of normal magic square which is also a: *triangular number is 15 (solve the Diophantine equation where ''y'' is divisible by 4); *square number is 1 (solve the Diophantine equation where ''y'' is even); * generalized pentagonal number is 171535 (solve the Diophantine equation where '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sapphire Jubilee
In 2017, the term sapphire jubilee or blue sapphire jubilee was coined for the celebrations to mark the 65th anniversary of the reign of Queen Elizabeth II (see Sapphire Jubilee of Elizabeth II). Previously, the sapphire wedding anniversary was understood to be the 45th, and this would be expected to carry over to regnal anniversaries as with silver, golden, and diamond jubilees. 65-year reign anniversaries in recent history See also * Hierarchy of precious substances * List of longest-reigning monarchs * List of current reigning monarchs by length of reign * Wedding anniversary A wedding anniversary is the anniversary of the date that a wedding took place. Couples often mark the occasion by celebrating their relationship, either privately or with a larger party. Special celebrations and gifts are often given for partic ... References {{jubilee 2017 neologisms Jubilees Sapphire Jubilee of Elizabeth II ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chicken 65
Chicken 65 is a spicy, deep-fried chicken dish originating from Hotel Buhari, Chennai Chennai, also known as Madras (List of renamed places in India#Tamil Nadu, its official name until 1996), is the capital city, capital and List of cities in Tamil Nadu by population, largest city of Tamil Nadu, the southernmost states and ..., India, as an entrée, or quick snack. The flavour of the dish can be attributed to red chillies, but the exact set of ingredients for the recipe can vary. It is prepared using boneless chicken and is usually served with an onion and lemon garnish. Vegetarian variants like "Paneer 65" or "Gobhi 65" use paneer or cauliflower instead. While the name "Chicken 65" is universally used to refer to the dish, there are many different theories claiming its origins. Origins Although Chicken 65 is well established as being the invention of A. M. Buhari of the Buhari Hotel chain, its popularity as a dish has spawned several myths about its origin and na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
South India
South India, also known as Southern India or Peninsular India, is the southern part of the Deccan Peninsula in India encompassing the states of Andhra Pradesh, Karnataka, Kerala, Tamil Nadu and Telangana as well as the union territories of Lakshadweep and Puducherry, occupying 19.31% of India's area () and 20% of India's population. It is bound by the Bay of Bengal in the east, the Arabian Sea in the west and the Indian Ocean in the south. The geography of the region is diverse, with two mountain ranges, the Western and Eastern Ghats, bordering the plateau heartland. The Godavari, Krishna, Kaveri, Penna, Tungabhadra and Vaigai rivers are important non-perennial sources of water. Chennai, Bengaluru, Hyderabad, Coimbatore and Kochi are the largest urban areas in the region. The majority of the people in South India speak at least one of the four major Dravidian languages: Telugu, Tamil, Kannada and Malayalam. During its history, a number of dynastic kingdoms ruled ove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Triple
A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle. A primitive Pythagorean triple is one in which , and are coprime (that is, they have no common divisor larger than 1). For example, is a primitive Pythagorean triple whereas is not. Every Pythagorean triple can be scaled to a unique primitive Pythagorean triple by dividing by their greatest common divisor. Conversely, every Pythagorean triple can be obtained by multiplying the elements of a primitive Pythagorean triple by a positive integer (the same for the three elements). The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a^2+b^2=c^2; thus, Pythagorean triples describe the three integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stirling Number Of The Second Kind
In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of ''n'' objects into ''k'' non-empty subsets and is denoted by S(n,k) or \textstyle \left\. Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the study of partitions. They are named after James Stirling. The Stirling numbers of the first and second kind can be understood as inverses of one another when viewed as triangular matrices. This article is devoted to specifics of Stirling numbers of the second kind. Identities linking the two kinds appear in the article on Stirling numbers. Definition The Stirling numbers of the second kind, written S(n,k) or \lbrace\textstyle\rbrace or with other notations, count the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. Equivalently, they count the number of different equivalence relations with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padovan Sequence
In number theory, the Padovan sequence is the integer sequence, sequence of integers ''P''(''n'') defined. by the initial values P(0) = P(1) = P(2) = 1, and the recurrence relation P(n) = P(n-2)+P(n-3). The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... The Padovan sequence is named after Richard Padovan who attributed its discovery to Netherlands, Dutch architect Hans van der Laan in his 1994 essay ''Dom. Hans van der Laan: Modern Primitive''.Richard Padovan. ''Dom Hans van der Laan: modern primitive'': Architectura & Natura Press, . The sequence was described by Ian Stewart (mathematician), Ian Stewart in his Scientific American column ''Mathematical Recreations'' in June 1996. He also writes about it in one of his books, "Math Hysteria: Fun Games With Mathematics". . ''The above definition is the one given by Ian Stewart and by MathWorld. Other sources may start the sequence at a different place, ... [...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] |
Eight Queens Puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century. In the modern era, it is often used as an example problem for various computer programming techniques. The eight queens puzzle is a special case of the more general ''n'' queens problem of placing ''n'' non-attacking queens on an ''n''×''n'' chessboard. Solutions exist for all natural numbers ''n'' with the exception of ''n'' = 2 and ''n'' = 3. Although the exact number of solutions is only known for ''n'' ≤ 27, the asymptotic growth rate of the number of solutions is approximately (0.143 ''n'')''n''. History Chess composer Max Bezzel published the eight queens puzzle in 1848. Franz Nauck published the first solutions in 1850. W. W. Rouse Ball (1960) "The Eight Queens Problem" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Square
In mathematics, especially History of mathematics, historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The "order" of the magic square is the number of integers along one side (''n''), and the constant sum is called the "magic constant". If the array includes just the positive integers 1,2,...,n^2, the magic square is said to be "normal". Some authors take "magic square" to mean "normal magic square". Magic squares that include repeated entries do not fall under this definition and are referred to as "trivial". Some well-known examples, including the #Sagrada Família magic square, Sagrada Família magic square and the #Parker square, Parker square, are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant, this gives a semimagic square (sometimes called orthomagic square). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
0 (number)
0 (zero) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently division by zero has no meaning in arithmetic. As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya. Common names for th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
