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Centered Polygonal Number
In mathematics, the centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers of dots with a constant number of sides. Each side of a polygonal layer contains one more dot than each side in the previous layer; so starting from the second polygonal layer, each layer of a centered ''k''-gonal number contains ''k'' more dots than the previous layer. Examples Each centered ''k''-gonal number in the series is ''k'' times the previous triangular number, plus 1. This can be formalized by the expression \frac +1, where ''n'' is the series rank, starting with 0 for the initial 1. For example, each centered square number in the series is four times the previous triangular number, plus 1. This can be formalized by the expression \frac +1. These series consist of the * centered triangular numbers 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, ... (), * centered square numbers 1, 5, 13, 25, 41, 61, 85, 113, 145, 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Proof Centered Polygonal Numbers
The visual system is the physiological basis of visual perception (the ability to detect and process light). The system detects, transduces and interprets information concerning light within the visible range to construct an image and build a mental model of the surrounding environment. The visual system is associated with the eye and functionally divided into the optical system (including cornea and lens) and the neural system (including the retina and visual cortex). The visual system performs a number of complex tasks based on the ''image forming'' functionality of the eye, including the formation of monocular images, the neural mechanisms underlying stereopsis and assessment of distances to (depth perception) and between objects, motion perception, pattern recognition, accurate motor coordination under visual guidance, and colour vision. Together, these facilitate higher order tasks, such as object identification. The neuropsychological side of visual information process ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Triangular Number 19
In typesetting and page layout, alignment or range is the setting of text flow or image placement relative to a page, column (measure), table cell, or tab (and often to an image above it or under it). The type alignment setting is sometimes referred to as text alignment, text justification, or type justification. The edge of a page or column is known as a ''margin'', and a gap between columns is known as a ''gutter''. Basic variations There are four basic typographic alignments: * flush left—the text is aligned along the left margin or gutter, also known as ''left-aligned'', ''ragged right'' or ''ranged left''; * flush right—the text is aligned along the right margin or gutter, also known as ''right-aligned'', ''ragged left'' or ''ranged right''; * justified—text is aligned along the left margin, with letter-spacing and word-spacing adjusted so that the text falls flush with both margins, also known as ''fully justified'' or ''full justification''; * centered—text is ali ... [...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] |
Bunyakovsky Conjecture
The Bunyakovsky conjecture (or Bouniakowsky conjecture) gives a criterion for a polynomial f(x) in one variable with integer coefficients to give infinitely many prime values in the sequencef(1), f(2), f(3),\ldots. It was stated in 1857 by the Russian mathematician Viktor Bunyakovsky. The following three conditions are necessary for f(x) to have the desired prime-producing property: # The leading coefficient is positive, # The polynomial is irreducible over the rationals (and integers), and # There is no common factor for all the infinitely many values f(1), f(2), f(3),\ldots. (In particular, the coefficients of f(x) should be relatively prime. It is not necessary for the values f(n) to be pairwise relatively prime.) Bunyakovsky's conjecture is that these conditions are sufficient: if f(x) satisfies (1)–(3), then f(n) is prime for infinitely many positive integers n. A seemingly weaker yet equivalent statement to Bunyakovsky's conjecture is that for every integer polyno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygonal Number
In mathematics, a polygonal number is a Integer, number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate numbers. Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, who investigated and discussed properties of Pronic number, oblong, Triangular Number, triangular, and Square number, square numbers. Definition and examples The number 10 for example, can be arranged as a triangle (see triangular number): : But 10 cannot be arranged as a square (geometry), square. The number 9, on the other hand, can be (see square number): : Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number): : By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorization, factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow primality test, method of checking the primality of a given number , called trial division, tests whether is a multiple of any integer between 2 and . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Proof Centered Hexagonal Numbers Sum
The visual system is the physiological basis of visual perception (the ability to perception, detect and process light). The system detects, phototransduction, transduces and interprets information concerning light within the visible range to construct an imaging, image and build a mental model of the surrounding environment. The visual system is associated with the eye and functionally divided into the optics, optical system (including cornea and crystalline lens, lens) and the nervous system, neural system (including the retina and visual cortex). The visual system performs a number of complex tasks based on the ''image forming'' functionality of the eye, including the formation of monocular images, the neural mechanisms underlying stereopsis and assessment of distances to (depth perception) and between objects, motion perception, pattern recognition, accurate motor coordination under visual guidance, and colour vision. Together, these facilitate higher order tasks, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RedDot
OpenText Corporation (styled as opentext) is a global software company that develops and sells information management software. OpenText, headquartered in Waterloo, Ontario, Canada, is Canada's fourth-largest software company as of 2022, and recognized as one of Canada's top 100 employers 2025 by Mediacorp Canada Inc. OpenText software applications manage content and unstructured data for large companies, government agencies, and professional service firms. OpenText's main business offerings include data analytics, enterprise information management, AI, cloud solutions, security, and products that address information management requirements, including management of large volumes of content, compliance with regulatory requirements, and mobile and online experience management. OpenText employs 22,900 people worldwide, and is a publicly traded company, listed on the Toronto Stock Exchange and the NASDAQ (OTEX). History Timothy Bray, with the University of Waterloo professors Fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RedDot
OpenText Corporation (styled as opentext) is a global software company that develops and sells information management software. OpenText, headquartered in Waterloo, Ontario, Canada, is Canada's fourth-largest software company as of 2022, and recognized as one of Canada's top 100 employers 2025 by Mediacorp Canada Inc. OpenText software applications manage content and unstructured data for large companies, government agencies, and professional service firms. OpenText's main business offerings include data analytics, enterprise information management, AI, cloud solutions, security, and products that address information management requirements, including management of large volumes of content, compliance with regulatory requirements, and mobile and online experience management. OpenText employs 22,900 people worldwide, and is a publicly traded company, listed on the Toronto Stock Exchange and the NASDAQ (OTEX). History Timothy Bray, with the University of Waterloo professors Fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
