
	Where results make sense

Topic: Polygonal number

Related Topics

Partition function (number theory)

Integer partition

Triangular number

Fermat polygonal number theorem

Square (geometry)

Constitutional monarchy

1770

1771

	What's Special About This Number?
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is the number of planar partitions of 12.
	www.stetson.edu /~efriedma/numbers.html (7292 words)

	Triangular numbers
		Polygonal numbers are really just the number of vertexes in a figure formed by a certain polygon.
		The second number is equal to the number of vertexes of the polygon.
		The third polygonal number is made by extending two of the sides of the polygon from the second polygonal number, completing the larger polygon and placing vertexes and other points where necessary.
	milan.milanovic.org /math/english/triangular/triangular.html (465 words)

	Math Forum: Ask Dr. Math FAQ: Glossary of Numbers
		A happy number is a number for which the sum of the squares of the digits eventually equals 1.
		A polygonal number is the number of equally spaced dots needed to draw a polygon.
		A triangular number is the number of dots needed to draw a triangle.
	mathforum.org /dr.math/faq/faq.number.glossary.html (1533 words)

	Polygonal number
		Ancient mathematicians discovered that numbers could be arranged in certain ways when they were represented by pebbles or seeds.
		The method 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.
		Polygons with higher numbers of sides, such as pentagons and hexagons, can also be represented as arrangements of dots (by convention 1 is the first polygonal number for any number of sides).
	publicliterature.org /en/wikipedia/p/po/polygonal_number.html (545 words)

	PlanetMath: polygonal number
		From these equations, we can deduce that all generalized polygonal numbers are nonnegative integers.
		Polygonal numbers were studied somewhat by the ancients, as far back as the Pythagoreans, but nowadays their interest is mostly historical, in connection with this famous result:
		This is version 2 of polygonal number, born on 2003-09-02, modified 2003-09-03.
	planetmath.org /encyclopedia/PolygonalNumber.html (215 words)

	All You Ever Wanted to Know About Pascal's Triangle and more
		For example, in row 3, 1 is the zeroth element, 3 is element number 1, the next three is the 2nd element, and the last 1 is the 3rd element.
		The sum of the numbers in the consecutive rows shown in the diagram are the first numbers of the Fibonnacci Sequence.
		Square Numbers are another type of Polygonal Numbers They are found in the same diagonal as the triangular numbers.
	ptri1.tripod.com (1016 words)

	Pages of Shades - Legends, Myth & More...
		The beastly palindromic prime number 16661 is such a number, since it is the 1928'th prime, and 1 + 6 + 6 + 6 + 1 = 1 + 9 + 2 + 8.
		The number 666 is equal to the sum of the digits of its 47th power, and is also equal to the sum of the digits of its 51st power.
		A polygonal number is a positive integer of the form P(k,n) = n((k - 2)n + 4 - k)/2 where k is the 'order' of the polygonal number (k=3 gives the triangular numbers, k=4 the squares, k=5 the pentagonal numbers, etc.), and n is its index.
	www.angelfire.com /realm/shades/demons/numberofthebeast.htm (2045 words)

	NationMaster - Encyclopedia: Polygonal number
		Ancient mathematicians discovered that numbers could be arranged in certain ways when they were represented by pebbles or seeds; such numbers, which can be made from figures, are generally called figurate numbers.
		The number 10, for example, can be arranged as a triangle (see triangular number): A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments.
		A triangular square number is a number which is both a triangular number and a perfect square.
	www.nationmaster.com /encyclopedia/Polygonal-number (1703 words)

	What's special about this number? (4)
		is the number of planar partitions of 10.
		is the number of planar partitions of 11.
		is is a triangular number, a hexagonal number.
	www.archimedes-lab.org /numbers/Num70_200.html (3708 words)

	Polygonal number - Glasgledius (Site not responding. Last check: )
		Ancient mathematicians discovered that numbers could be arranged in certain ways when they were represented by pebbles or seeds.
		The method 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.
		Polygons with higher numbers of sides, such as pentagons and hexagons, can also be represented as arrangements of dots (by convention 1 is the first polygonal number for any number of sides).
	www.glasglow.com /E2/po/Polygonal_number.html (505 words)

	The Number of the Beast
		A Smith number is an integer in which the sum of its digits is equal to the sum of the digits of its prime factors.
		The nth doubly-triangular number is, among other things, the number of ways to paint the vertices of a square using a set of n colors, where the colors are distinct but rotations and reflections of a given colored square are considered the same.
		If these 148 numbers (the first 148 digits of 1/149) are written as the top row of a 148x148 square grid, and then the digits of 2/149 as the second row, then 3/149 and so on, the result is a 148x148 pseudo-magic square, in which every row and column sums to 666.
	users.aol.com /s6sj7gt/mike666.htm (2724 words)

	polygonal - Search Results - MSN Encarta
		Apse, recess in a building, generally a semicircular or polygonal projection from the exterior of a church, roofed with a vault.
		A polygonal number is a type of figurate number that is a generalization of triangular, square, etc...
		A polygonal number is a type of figurate number that is a generalization of triangular, square...
	encarta.msn.com /polygonal.html (175 words)

	POLYGONAL NUMBERS - Online Information article about POLYGONAL NUMBERS (Site not responding. Last check: )
		general expression for the corresponding polygonal number is 2n[(n—I) (r—2)+2].
		Algebraically, polygonal numbers may be regarded as the sums of consecutive terms of the arithmetical progressions having 1 for the first See also:
		+- (2n—1) =n2; and generally for the polygonal number of the rth order we take the sums of consecutive terms of the series 1, 1+(r-2), 1+2 (r-2),.
	encyclopedia.jrank.org /PIG_POL/POLYGONAL_NUMBERS.html (412 words)

	Mind Over Mathematics: Geometric Numbers
		Each polygonal series, is unified, not with respect to each number of the series, but by the differences between those numbers, which are all congruent to unity relative to a modulus formed by the differences of the differences.
		Now the addition of unity, is found, not in the generation of the numbers themselves, but in the generation of the moduli, under which the differences between each polygonal number series are themselves made congruent to unity.
		The concept of number cannot be seperated from the content of number, which is a reflection of the domain in which that number is situated.
	members.tripod.com /~american_almanac/geometry.htm (5154 words)

	Figurate number Summary
		These numbers were studied, as were many kinds of numbers, for the sake of their supposed mystical properties rather than for their practical value.
		Figurate numbers were a concern of Pythagorean geometry, since Pythagoras is credited with initiating them, and the notion that these numbers are generated from a gnomon or basic unit.
		The tedium of increasing number of subtractions as the number grows is bypassed by a method similar to the standard way of square-rooting taught in school.
	www.bookrags.com /Figurate_number (2678 words)

	The 112th (JEHOVAH-ELOHIM) triangle 6328 (anagram or in ascending digits JESUS CHRIST) can be geometrically and ... (Site not responding. Last check: )
		polygonal numbers: the triangle (3 - 703), hexagon (2 + 3 - 2701), centred octagon (1 + 2 - 5625) and centred nonagon (1 + 2 + 3 - 6328).
		The three branches to the left and the central branch sum to 6808 and ignoring the zero the number is 688, the gematria of ‘Jesus’ in Matthew 1:1.
		A092311 (total number of largest parts in all partitions of n into odd parts) is 1119, equal to 373 x 3, the latter figure being the number of occurrences of ‘Logos’ in John 1:1 and the figure itself the Greek gematria of ‘John’.
	www.fivedoves.com /revdrnatch/112th_Triangle.htm (3095 words)

	Pascal's Triangle and Its Patterns
		If the first element in a row is a prime number (remember, the 0th element of every row is 1), all the numbers in that row (excluding the 1's) are divisible by it.
		The sum of the numbers in the consecutive rows shown in the diagram are the first numbers of the Fibonacci Sequence.
		When all the odd numbers (numbers not divisible by 2) in Pascal's Triangle are filled in (fl) and the rest (the evens) are left blank (white), the recursive Sierpinski Triangle fractal is revealed (see figure at right), showing yet another pattern in Pascal's Triangle.
	britton.disted.camosun.bc.ca /pascal/pascal.html (927 words)

	True or False?
		A repdigit number is an integer whose base-10 representation consists of a repeated non-zero digit (e.g., 11 or 222 or 555555).
		This is rather weird and wonderful, since among all the repdigit polygonal numbers the frequency of occurrence of the digit 6 is not significantly greater than any other digit.
		The number 121 has the following remarkable property: it is a perfect square, and it is a palindrome simultaneously in four of the bases in the range 2 to 10 (it's 121 in base 10, 171 in base 8, 232 in base 7, and 11111 in base 3).
	members.aol.com /s6sj7gt/mikeconj.htm (703 words)

	Abramovich, Fujii, and Wilson article
		Therefore the number of dots in the parallelogram is n(n+1), and the number of dots in the triangle is
		, are triangular; numbers 5151, 501501, 50015001, 5000150001,...
		One can visualize that any polygonal number of side m and of rank n is constituted with a triangular number of the same rank and m-3 (3 in the case of a hexagonal number) triangular numbers of the previous rank.
	jwilson.coe.uga.edu /Texts.Folder/AFW/AFWarticle.html (8748 words)

	181 (number) at AllExperts
		181 is not a regular polygonal number in any way besides being 181-gonal, but it is a centered number in three different ways: it is a centered square number, centered pentagonal number and a star number.
		181 is the rider number given to Lance Armstrong in 1999 when he won his first of seven Tour de France victories consecutively.
		After winning his first he returned to each subsequent tour as rider number 1 which is traditionally given to the previous years' defending overall winner.
	en.allexperts.com /e/0/181_(number).htm (215 words)

	Exploring Pascal's Triangle and Other Recursive Patterns
		Each number is referred to as an element, and the number of elements in a row is always one more than the number of the row.
		A polygonal number sequence is a progression of numbers in which each term is based on the number of vertices in a given shape.
		Two is the number that is used to multiply each term with, and it is known as the common ratio.
	www.cfep.uci.edu /uci-sati/faculty/carole_bersani_full.html (2956 words)

	Repdigit Polygonal Numbers
		An efficient algorithm for finding repdigit polygonal numbers is presented and used to provide a complete characterization of all 1526 such numbers with 50 or fewer digits.
		The combination sequence is the sequence of combination numbers pertaining to the successive repdigits (which are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, etc., sequence A010785 in the On-Line Encyclopedia of Integer Sequences).
		Finally, define a simple RP number to be one generated from a simple (or trivial) primitive solution, and a fancy RP number to be one generated from a fancy primitive solution.
	www.cs.uwaterloo.ca /journals/JIS/keith.html (2807 words)

	dankois.com: Control-X: Polygonal numbers
		Polygonal numbers belong to one of the somewhat arcane branches of mathematics that concern themselves with the physical representation of abstract concepts.
		Which is to say, while I imagine there is some aesthetic pleasure to be had in determining a series of polygonal numbers, it seems unlikely that there's any deeper mathematical truths to be unearthed in the process.
		It was as if the agreement I'd had with numbers all my life had been revoked, and suddenly those simple numbers were behaving in all sorts of odd ways.
	www.dankois.com /2006/12/control-x-polygonal-numbers.html (1069 words)

	Modular toy building units - Patent 4209934
		The polygonal panel members can include triangular, rectangular, hexagonal and octagonal members and are provided with a pair of apertures substantially adjacent to each of their side edges.
		Even though the reinforcing ribs 60 are narrow relative to the overall dimension of the polygonal panel members, they are disposed essentially perpendicularly to the general plane defined by the polygonal panel member and increase the overall apparent thickness of the polygonal panel members.
		On the other side of the base plate 58, the hollow channel shaped member 80 extends a relatively large distance away from the polygonal panel member thereby assuring that the slide fitted rail 70 is relatively firmly mounted to the polygonal panel member and relative movement of the panel member is prevented.
	www.freepatentsonline.com /4209934.html (4528 words)

	666 - The Number of the Beast
		The nth triangular number is given by the formula T(n) = (n)(n+1)/2, and is equal to the sum of the numbers from 1 to n.
		The nth doubly-triangular number is, among other things, the number of ways to paint the vertices of a square using a set of n colors, where the colors are distinct but rotations and reflections of a given colored square are considered the same.
		If these 148 numbers (the first 148 digits of 1/149) are written as the top row of a 148x148 square grid, and then the digits of 2/149 as the second row, then 3/149 and so on, the result is a 148x148 pseudo-magic square, in which every row and column sums to 666.
	www.francesfarmersrevenge.com /stuff/conspiracy/666.htm (2604 words)

	HRM Educational Multimedia: REVIEWS: MATH-Grades 4-9
		The numbers and examples range from 10 to the 289 power as the number of combinations obtained when tossing a six-sided die 500 items to 10 to the negative 40,000 power as the probability that a monkey can randomly type Shakespeare's Hamlet.
		The pictures presented are the planet Jupiter, a hydrogen atom, Rub's Cube, the Statue of Liberty, a shrew, the sun, the George Washington Bridge, and a cell.
		The polygonal numbers presented are for the square, triangular, pentagonal, hexagonal, and cubic numbers.
	www.learningwave.com /msmathrvw14.html (571 words)

	Pascal's Triangle
		Blaise Pascal discussed combinatorial numbers of n things taken m at a time and determination of the probability of winning games by the numbers of his triangle in his Traité du triangle arithmétique, 1654.
		These are distinguishable from other series that are also figurate called polygonal numbers (which are fundamentally two-dimensional and compositions of triangular numbers).
		A result of the triangle's obvious symmetry is, any two neighboring figurate number series certainly share one number in common: the (n+1)th of the n-PT diagonal and the nth of the (n+1) diagonal.
	noticingnumbers.net /220PASCALStriangle.htm (751 words)

Try your search on: Qwika (all wikis)