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190 (number)
190 (one hundred ndninety) is the natural number following 189 and preceding 191. In mathematics 190 is a triangular number, a hexagonal number A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ..., and a centered nonagonal number, the fourth figurate number (after 1, 28, and 91) with that combination of properties. It is also a truncated square pyramid number. See also * 190 (other) References Integers {{Num-stub ... [...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] |
189 (number)
189 (one hundred ndeighty-nine) is the natural number following 188 and preceding 190. In mathematics 189 is a centered cube number and a heptagonal number. The centered cube numbers are the sums of two consecutive cubes, and 189 can be written as sum of two cubes in two ways: and The smallest number that can be written as the sum of two positive cubes in two ways is 1729. The largest prime number that can be represented in 256-bit arithmetic is the "ultra-useful prime" used in quasi-Monte Carlo methods and in some cryptographic Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More gen ... systems. See Appendix B. See also * The year AD 189 or 189 BC * List of highways numbered 189 * References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
191 (number)
191 (one hundred ndninety-one) is the natural number following 190 and preceding 192. In mathematics 191 is a prime number, part of a prime quadruplet of four primes: 191, 193, 197, and 199. Because doubling and adding one produces another prime number (383), 191 is a Sophie Germain prime. It is the smallest prime that is not a full repetend prime in ''any'' base from 2 to 10; in fact, the smallest base for which 191 is a full period prime is base 19 There are many different numeral systems, that is, writing systems for expressing numbers. By culture / time period "A ''base'' is a natural number B whose ''powers'' (B multiplied by itself some number of times) are specially designated wit ....Wolfram MathWorldPrimitive Root/ref> See also * 191 (other) References Integers {{num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangular Number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in the triangular arrangement with dots on each side, and is equal to the sum of the natural numbers from 1 to . The first 100 terms sequence of triangular numbers, starting with the 0th triangular number, are Formula The triangular numbers are given by the following explicit formulas: where \textstyle is notation for a binomial coefficient. It represents the number of distinct pairs that can be selected from objects, and it is read aloud as " plus one choose two". The fact that the nth triangular number equals n(n+1)/2 can be illustrated using a visual proof. For every triangular number T_n, imagine a "half-rectangle" arrangement of objects corresponding to the triangular number, as in the figure below. Copying this arrangement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Number
A hexagonal number is a figurate number. The ''n''th hexagonal number ''h''''n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex (geometry), vertex. The formula for the ''n''th hexagonal number :h_n= 2n^2-n = n(2n-1) = \frac. The first few hexagonal numbers are: :1 (number), 1, 6 (number), 6, 15 (number), 15, 28 (number), 28, 45 (number), 45, 66 (number), 66, 91 (number), 91, 120 (number), 120, 153 (number), 153, 190 (number), 190, 231 (number), 231, 276 (number), 276, 325 (number), 325, 378, 435, 496 (number), 496, 561 (number), 561, 630, 703, 780, 861, 946... Every hexagonal number is a triangular number, but only every ''other'' triangular number (the 1st, 3rd, 5th, 7th, etc.) is a hexagonal number. Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Nonagonal Number
A centered nonagonal number, (or centered enneagonal number), is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal number for ''n'' layers is given by the formula :Nc(n) = \frac. Multiplying the (''n'' - 1)th triangular number by 9 and then adding 1 yields the ''n''th centered nonagonal number, but centered nonagonal numbers have an even simpler relation to triangular numbers: every third triangular number (the 1st, 4th, 7th, etc.) is also a centered nonagonal number. Thus, the first few centered nonagonal numbers are : 1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946. The list above includes the perfect numbers 28 and 496. All even perfect numbers are triangular numbers whose index is an odd Mersenne prime. Since every Mersenne prime greater than 3 is congruent to 1 modulo In computing and mathematics, the modulo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figurate Number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The ancient Greek mathematicians already considered triangular numbers, polygonal numbers, tetrahedral numbers, and pyramidal numbers, ReprintedG. E. Stechert & Co., 1934 and AMS Chelsea Publishing, 1944. and subsequent mathematicians have included other classes of these numbers including numbers defined from other types of polyhedra and from their analogs in other dimensions. Terminology Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". In historical works about Greek mathematics the preferred term used to be ''figured number''. In a use going back to Jacob Bernoulli's Ars Conjectandi, the term ''figurate number'' is used for triangular numbers made up of successive integers, tetrahedral numbers made ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Square Pyramid
In geometry, a ; (: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A ''right frustum'' is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise, it is an ''oblique frustum''. In a ''truncated cone'' or ''truncated pyramid'', the truncation plane is necessarily parallel to the cone's base, as in a frustum. If all its edges are forced to become of the same length, then a frustum becomes a ''prism'' (possibly oblique or/and with irregular bases). Elements, special cases, and related concepts A frustum's axis is that of the original cone or pyramid. A frustum is circular if it has circular bases; it is right if the axis is perpendicular to both bases, and oblique otherwise. The height of a frustum is the perpendicular distance between the planes of the two bases. Cones and pyra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
190 (other)
190 A.D. is a year. 190 may also refer to: * 190 (number), the natural number following 189 and preceding 191 * U.S. Route 190, also known as the Ronald Reagan Memorial Highway, is an east–west United States highway in Louisiana and Texas * Mercedes-Benz 190 (other) * Interstate 190 (Massachusetts), runs for 19.26 miles (31.00 km) north from I-290 in Worcester, Massachusetts to Route 2 in Leominster, Massachusetts * Interstate 190 (New York), runs 28.34 miles (45.61 km) from I-90 near Buffalo, New York to Lewiston, New York via Niagara Falls * Interstate 190 (Illinois), Illinois Tollway system * Interstate 190 (South Dakota), an auxiliary Interstate Highway in the U.S. state of South Dakota * Connecticut Route 190 Route 190 is a state route in the northern part of the U.S. state of Connecticut. It starts at Connecticut Route 75, Route 75 in the town of Suffield, Connecticut, Suffield and proceeds eastward across the Connecticut River through the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
