Related Research Articles
In mathematics, especially 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 , the magic square is said to be "normal". Some authors take "magic square" to mean "normal magic square".
The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers.
19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.
111 is the natural number following 110 and preceding 112.
The square root of 2 is a real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as or . It is an algebraic number, and therefore not a transcendental number. Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property.
In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four main space diagonals are equal, the so-called magic constant of the cube, denoted M3(n). If a magic cube consists of the numbers 1, 2, ..., n3, then it has magic constant (sequence A027441 in the OEIS)
In mathematics, a perfect magic cube is a magic cube in which not only the columns, rows, pillars, and main space diagonals, but also the cross section diagonals sum up to the cube's magic constant.
In mathematics, a magic hypercube is the k-dimensional generalization of magic squares and magic cubes, that is, an n × n × n × ... × n array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the same. The common sum is called the magic constant of the hypercube, and is sometimes denoted Mk(n). If a magic hypercube consists of the numbers 1, 2, ..., nk, then it has magic number
A pandiagonal magic square or panmagic square is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the 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, ..., n2 – the magic constant is .
In mathematics, a magic cube of order is an grid of natural numbers satisying the property that the numbers in the same row, the same column, the same pillar or the same length- diagonal add up to the same number. It is a -dimensional generalisation of the magic square. A magic cube can be assigned to one of six magic cube classes, based on the cube characteristics. A benefit of this classification is that it is consistent for all orders and all dimensions of magic hypercubes.
A magic series is a set of distinct positive integers which add up to the magic constant of a magic square and a magic cube, thus potentially making up lines in magic tesseracts.
181 is the natural number following 180 and preceding 182.
In recreational mathematics and the theory of magic squares, a broken diagonal is a set of n cells forming two parallel diagonal lines in the square. Alternatively, these two lines can be thought of as wrapping around the boundaries of the square to form a single sequence.
A magic graph is a graph whose edges are labelled by the first q positive integers, where q is the number of edges, so that the sum over the edges incident with any vertex is the same, independent of the choice of vertex; or it is a graph that has such a labelling. The name "magic" sometimes means that the integers are any positive integers; then the graph and the labelling using the first q positive integers are called supermagic.
Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui. It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameters are identical. One of his magic circles was constructed from the natural numbers from 1 to 33 arranged on four concentric circles, with 9 at the center.
The Siamese method, or De la Loubère method, is a simple method to construct any size of n-odd magic squares. The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère, as he was returning from his 1687 embassy to the kingdom of Siam. The Siamese method makes the creation of magic squares straightforward.
Sriramachakra is a mystic diagram or a yantra given in Tamil almanacs as an instrument of astrology for predicting one's future. The geometrical diagram consists of a square divided into smaller squares by equal numbers of lines parallel to the sides of the square. Certain integers in well defined patterns are written in the various smaller squares. In some almanacs, for example, in the Panchangam published by the Sringeri Sharada Peetham or the Pnachangam published by Srirangam Temple, the diagram takes the form of a magic square of order 4 with certain special properties. This magic square belongs to a certain class of magic squares called strongly magic squares which has been so named and studied by T V Padmakumar, an amateur mathematician from Thiruvananthapuram, Kerala. In some almanacs, for example, in the Pambu Panchangam, the diagram consists of an arrangement of 36 small squares in 6 rows and 6 columns in which the digits 1, 2, ..., 9 are written in that order from left to right starting from the top-left corner, repeating the digits in the same direction once the digit 9 is reached.
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol, or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, statistics, and calculus.
9855 is an odd, composite, four-digit number. The number 9855 is the magic constant of an n × n normal magic square as well as n-Queens Problem for n = 27. It can be expressed as the product of its prime factors: