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Topic: Triangular number

Related Topics

Square number

Perfect number

Fermat polygonal number theorem

Polygonal number

Harmonic divisor number

Natural number

Rational number

Real number

Imaginary number

Prime number

Arithmetic series

15 (number)

Complex number

Sum

Fundamental theorem of algebra

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	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).
		The Number 19 is the number of Physical Manifestation.
	www.biblewheel.com /GR/GR_Figurate.asp (1576 words)

	Fascinating Triangular Numbers By Shyam Sunder Gupta
		Numbers such that d(n), the number of divisors of n, is greater than for any smaller n are called highly composite numbers.
		Number of divisors of all triangular numbers less than 28 is less than 6.
		Numbers such that s(n), the sum of aliquot divisors of n, is greater than n are called Abundant numbers.
	www.shyamsundergupta.com /triangle.htm (1716 words)

	Pythagoras, A History With Quotes From the Old Greek (Site not responding. Last check: 2007-11-06)
		Number was studied by Pythagoras, the early Greeks, and Plato during their studies of the Divine, the creation, and its principles.
		“And further, discerning in numbers the conditions and reasons of harmonies also; since, moreover, other things seemed to be like numbers in their entire nature, and numbers were the first of every nature, they assumed that the elements of numbers were the elements of all things, and that the whole heavens were harmony and number.
		And thus he asserted that God is a monad, and examining the nature of number with especial care, he said that the universe produces melody and is put together with harmony, and he first proved the motion of the seven stars to be rhythm and melody.
	www.thearchimedeandual.com /platonic/Greek/Pythagoras/pythagoras.htm (5043 words)

	More about Palindromic Triangulars
		Triangular numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
		Now combine two properties and the palindromic triangular numbers and their basenumbers are born.
		While extending the list with the next higher palindromic triangular may be very difficult to accomplish, searching for extra features in the existing ones is something that we all could embark on.
	www.worldofnumbers.com /triangle.htm (1605 words)

	Games and Puzzles Journal #41: Diamond Solitaire
		Because it is on a triangular lattice the corners of the board are restricted to multiples of 60°.
		The number of moves, however, can be less than this, and an interesting question is to find the solution with the least number of moves.
		Peg solitaire on a triangular lattice is a fascinating game, and one that has not been studied to the extent that "normal" (square lattice) peg solitaire has.
	www.gpj.connectfree.co.uk /gpjw.htm (3577 words)

	Everything about January 1 (Site not responding. Last check: 2007-11-06)
		For any number x: :x·1 = 1·x = x (This expresses the fact that 1 is the multiplicative identity.) As a consequence of this, 1 is a 1-automorphic number in any place-based numbering system.
		One is currently considered neither a prime number, nor a composite number - although it used to be considered prime.
		In some sports, one is the number of a specific position: in rugby union, the number of the loosehead prop; in baseball, the number representing the pitcher's position; in football, the number of the goalkeeper.
	wikimiki.org /en/January+1 (7985 words)

	id:A001110 - OEIS Search Results
		Numbers that are both triangular and square: a(n) = 34a(n-1) - a(n-2) + 2.
		A. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p.
		a(2) = ((17+12sqrt(2))^2+(17-12sqrt(2))^2-2)/32 = (289+24sqrt(2)+288+289-24sqrt(2)+288-2)/32 = (578+576-2)/32 = 1152/32 = 36 and 6^2 = 36 = 89/2 = >a(2) is both the sixth square and the 8th triangular* number
	www.research.att.com /projects/OEIS?Anum=A001110 (430 words)

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