
	Where results make sense

Topic: Figurate number

	Figurate number Summary
		Figurative numbers are numbers which can be represented by dots arranged in various geometric patterns.
		Figurative numbers are not confined to those associated with plane figures.
		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.
	www.bookrags.com /Figurate_number (2678 words)

	Figurate number - Wikipedia, the free encyclopedia
		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.
		For example, the gnomon of the square number is the odd number, of the general form 2n + 1, n = 1, 2, 3,...
		The concepts of figurate numbers and gnomon implicitly anticipate the modern concept of recursion.
	en.wikipedia.org /wiki/Figurate_number (1549 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)

	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 (218 words)

	Pythagoras - Number (Site not responding. Last check: 2007-10-13)
		Number mysticism is not generally associated with "serious mathematics" but from the early Pythagoreans until the 19th century many venerated mathematicians practised some forms of numerology.
		To the Pythagoreans the holiest number of all was the number 10 or the tetractys.
		To Pythagoras and the early Pythagoreans, number was "atomistic", it existed as bundles of a fundamental elementary object - unity.
	www.mathgym.com.au /history/pythagoras/pythnum.htm (2721 words)

	Numerical Geometry
		Triangular Number is the sum of all the numbers from 1 to n.
		Square Numbers are also associated the polar concepts of Confinement (due to the limitations imposed by structure) and Expansion (in the sense of the Four Directions).
		This Number is the basis of the Unity Holograph which is built upon four nested word clusters that sum to multiples of the Number (= One = Love).
	www.biblewheel.com /GR/GR_Figurate.asp (1835 words)

	[No title]
		A figurate number is represention of number as a regular geometric pattern, say, of dots.
		Another label for these numbers is '''Pythgorean geometry''', since [[Pythagoras]] is credited with initiating them, with the notion that these numbers are generated from a [[gnomon]] or basic unit.
		The tedium of increasing number of subtractions as number grows is short-cut by a method similar to the standard way of square-rooting taught in school.
	members.fortunecity.com /jonhays/figurate.htm (1312 words)

	Figurate numbers - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-13)
		Another label for these numbers is Pythgorean geometry, since Pythagoras is credited with initiating them, and the notion that these numbers are generated from a Gnomon or basic unit.
		Cubes of natural numbers or positive integers can be generated from S = 1, 3, 5, 6, 7,..., 2n + 1,...., n = 1,2, 3,..., by "moving sums", similar to the "moving averages" of Statistics:
		School children construct figurate numbers from pebbles, bottle caps, etc. As a bonus, children can use figurate numbers to discover the Commutative law and associative law for addition and multiplication -- laws usually dictated to them -- by buiding rows and tables of dots.
	www.peacelink.de /index.php?title=Figurate_number&redirect=no (1424 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.
		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.
		Here is a chart of proportional relationships as occur between figurate numbers (first defined by Gerolamo Cardano in 1570, Edwards p.
	noticingnumbers.net /220PASCALStriangle.htm (751 words)

	figurate number
		A number sequence found by creating consecutive geometrical figures from arrangements of equally spaced points.
		The points can be arranged in one, two, three, or more dimensions.
		There are many different kinds of figurate numbers, such as polygonal numbers and tetrahedral numbers.
	www.daviddarling.info /encyclopedia/F/figurate_number.html (112 words)

	Reference.com/Encyclopedia/Figurate number
		The gnomon is the piece which needs to be added to a figurate number to transform it to the next biggest one.
		School children construct figurate numbers from pebbles, bottle caps, etc. As a bonus, children can use figurate numbers to discover the commutative law and associative law for addition and multiplication -- laws usually dictated to them -- by building rows and tables of dots.
		Using asterisks in place of dots or bottle caps or pebbles the additive commutativity of 2 + 3 = 3 + 2 = 5 becomes:
	www.reference.com /browse/wiki/Figurate_number (1429 words)

	Cubic Number
		cubic number is a figurate number of the form
		The hex pyramidal numbers are equivalent to the cubic numbers (Conway and Guy 1996).
		There is a finite set of numbers which cannot be expressed as the sum of distinct positive cubes: 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26,...(Sloane's A001476).
	www.m-brella.be /math/topics/CubicNumber.html (1510 words)

	Euler-Pascal/Cube
		The algorithm that generates formulas for power values (that is Worpitzky's Identity of 1883) logically also generates formulas for values that are summations of powers (where Bernoulli numbers come into play) as well as shells or nexus number series and more.
		of Euler's Triangle and may be the figurate number relationships that Fermat and Pascal were discussing for sums of powers (Pengelley p.
		The number of summations from an initial Euler Triangle row is “enumerated” by the value that is z.
	noticingnumbers.net /300SeriesCube.htm (398 words)

Try your search on: Qwika (all wikis)