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Topic: Triangular

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	Fascinating Triangular Numbers By Shyam Sunder Gupta
		There are pairs of triangular numbers such that the sum and difference of numbers in each pair are also triangular numbers e.g.
		For example 36 is a triangular number and s(36) = 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55, which is greater than 36.
		So the sum of two triangular numbers is equal to the number formed from concatenation of index of these two triangular numbers.
	www.shyamsundergupta.com /triangle.htm (1716 words)

	Triangular - definition from Biology-Online.org
		(Science: botany) Oblong or elongated, and having three lateral angles; as, a triangular seed, leaf, or stem.
		Triangular compasses, compasses with three legs for taking off the angular points of a triangle, or any three points at the same time.
		(Science: mathematics) Triangular numbers, the series of numbers formed by the successive sums of the terms of an arithmetical progression, of which the first term and the common difference are 1.
	www.biology-online.org /dictionary/Triangular (171 words)

	Triangular Brilliant Diamonds Shape: Diamond Source of Virginia Loose Diamonds Education
		Triangular Brilliant cut is often called a Trillion was first designed in Amsterdam by Leon Finker in 1978 and is cut into the shape of a wedge.
		They produced a triangular diamond with curved sides instead of straight ones and were an early version of what is now the Trielle.
		The Triangular Brilliant, whether branded or not, is most often sold as matched side stones for rings.
	www.diamondsourceva.com /Education/Shape/diamonds-shape-triangular-brilliant.asp (484 words)

	PlanetMath: triangular matrix
		Note that upper triangular matrices and lower triangular matrices must be square matrices.
		A triangular matrix is a matrix that is an upper triangular matrix or lower triangular matrix.
		In fact, triangular matrices are so useful that much computational linear algebra begins with factoring (or decomposing) a general matrix or matrices into triangular form.
	planetmath.org /encyclopedia/RightTriangular.html (306 words)

	Triangular numbers
		The triangular number is a polygonal number : a number that can be represented by a regular geometric arrangement of equally spaced points.
		The triangular numbers can be found in the third diagonal of Pascal`s triangle, starting at row 3 as shown in the diagram.
		The first triangular number is 1, the second is 3, the third is 6, the forth is 10, and so on.
	milan.milanovic.org /math/english/triangular/triangular.html (465 words)

	Çiçek pasaj enr. - Triangular hip scarves - ClicShop
		Triangular shakti-style chiffon hip scarf in shades of purple and blue, decorated with silver and ma...
		Triangular hipscarf made with royal blue chiffon, decorated with silver and blue beads and silver fa...
		Triangular hip scarf made of chiffon with motif in shades of pink decorated with pink and silver bea...
	www.clicshop.com /Stores/cicekpasaj/c147652.2.html (221 words)

	Triangular Number Activities, HOML SLCC/Meramec (Site not responding. Last check: )
		For example, the 9th triangular number is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
		The 10th triangular number is 1+ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 which is the same as the 9th triangular number but with 10 added on.
		This should lead to the generalization that the nth triangular number can be calculated by multiplying n by the next natural number (called "the successor") and then dividing by 2.
	www.stlcc.cc.mo.us /mc/dept/math/homl/tritable.htm (735 words)

	PlanetMath: triangular numbers
		The triangular numbers are defined by the series
		th triangular number is simply the sum of the first
		This is version 2 of triangular numbers, born on 2002-02-02, modified 2002-02-02.
	planetmath.org /encyclopedia/TriangularNumbers.html (217 words)

	Spielboy Issue 5
		Triangular numbers are positive integers such that the given number of dots can be arranged to make an equilateral triangle.
		Triangular numbers work the same way, though the base of the pyramid is a triangle (having 3 sides) and not a square or pyramid shape (having 4 sides).
		The triangular number of 4 is the number and arrangement of bowling pins.
	www.spielboy.com /triangularnumbers.php (1091 words)

	Roy Lawaetz - The Modular Triangular System
		But historically the triangular aesthetic as represented by the Taino Zemi stones never had a chance to be developed in a modern context.
		But now she has also dared to branch into the creative end, giving feedback, dialogue, constructive criticism, encouragement and most of all she has a quality of persistence that is exceptional.
		She understands that "The Modular Triangular System" is an expansive approach for the Support.
	www.roylawaetz.com /interview.htm (2939 words)

	Triangular Square Numbers
		The aim of this investigation is to investigate numbers that are both square and triangular.
		Note: The original triangular number is the number that is entered into the triangular formula to produce the triangular square number.
		The square roots of the triangular square numbers were analysed because they are smaller and so easier to handle.
	www.courseworkhelp.co.uk /A_Level/Maths/2.htm (1449 words)

	Session 7, Part C: Figurate Numbers
		The first triangular number is 1, the second is 3, and so on.
		Describe a rule relating the number of dots on the side of a triangle (the independent variable) and the total number of dots (the dependent variable).
		Describe any similarities and differences between your rules and graphs for the square and triangular numbers.
	www.learner.org /channel/courses/learningmath/algebra/session7/part_c/triangular.html (233 words)

	other alopecias - congenital triangular alopecia
		Congenital triangular alopecia is a patch of hair loss in the temple area of the scalp found mainly in very young children anytime from birth up to 5 years of age.
		The affected area is often roughly triangular shaped but may be oval in some individuals.
		The cause of congenital triangular alopecia is not known, but its presence is not usually associated with any adverse disease state.
	www.keratin.com /af/af005.shtml (317 words)

	Triangular Barracks Site Monument
		The triangular barracks were the quarters for kamikaze pilots [1] at the end of the Pacific War.
		The wooden barracks, built half underground where only the triangular roofs could be seen, were camouflaged with large trees put on top of the roofs.
		The triangular barracks were the quarters of kamikaze pilots.
	wgordon.web.wesleyan.edu /kamikaze/monuments/sankakuheisha/index.htm (543 words)

	triangular. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
		Of, relating to, or shaped like a triangle.
		Having a triangle for a base: a triangular pyramid.
		Relating to or involving three entities, such as three people, objects, or ideas.
	www.bartleby.com /61/44/T0344400.html (94 words)

	The Reality Of Triangular UFOs
		During his investigation, he walked around (and touched) a hovering, dark colored, triangular craft in a clearing in the forest.
		Some were indeed triangular while others were described as discoid.
		This incident was witnessed by at least thirty military personnel who surrounded the craft after it made a spectacular landing in a clearing.
	www.rense.com /general51/TRI.HTM (1055 words)

	George Bell's Triangular Peg Solitaire Page
		A triangular board is a null-class board unless n is of the form 3i+1, i.e.
		Triangular boards that are not null-class are also characterized by having a unique central hole, and the total number of holes is not a multiple of 3.
		This 10-hole board is not null-class, but is the smallest triangular board on which a single vacancy to single survivor problem is actually solvable.
	www.geocities.com /gibell.geo/pegsolitaire/tindex.html (7171 words)

	803 Triangular
		The Nederman 803 Series Triangular Exhaust Extraction Nozzle is constructed of heavy duty EPDM rubber which reduces surface heat build up on the nozzle and protect the vehicle from scrapes or paint damage.
		The 803 Series Triangular Exhaust Extraction Nozzle is secured to the vehicle by a fully adjustable, quick release locking clamp which will ensure positive attachment to vehicle exhaust pipe.
		The 803 Series Triangular Exhaust Extraction Nozzle is equipped with two ports: one will enable sampling of exhaust gases while attached to the exhaust pipe and the other port will allow the return of the sample gas into the exhaust system.
	www.nedermanusa.com /gofer.php?&target=TriangularExhaustNozzle.html (199 words)

	Triangular Waveform
		The triangular wave form shows the signal that is sent to the solenoid coil of the system.
		The triangular wave form is changing polarity all of the time; and, thereby, inducing a voltage all of the time.
		The current to the Triangular Wave System solenoid is changing 100% of the time; therefore, there is an induced voltage applied to the particles 100% of the time; rather than a small percentage of the time with a square wave generator.
	www.triangularwave.com /a1a2.htm (348 words)

	Triangular numbers (Site not responding. Last check: )
		So, 10 is the fourth triangular number since it's the number of dots in a triangle of side length 4.
		For instance, the 5th triangular number is 5 more than 10, the 4th triangular number.
		Imagine a triangular arrangement of marbles, each one inch in diameter, to make a big triangle whose side is the length of a football field, 100 yards.
	aleph0.clarku.edu /~djoyce/triangle (857 words)

	Triangular Arbitrage (Site not responding. Last check: )
		The triangular arbitrage strategy generates a profit of $1,000.
		Also note that triangular arbitrage is a risk-free strategy since there is no uncertainty about the prices at which you will buy and sell the currencies, and of course all the three steps should be executed simultaneously.
		Triangular arbitrage forces a quoted cross exchange rate to be appropriately priced vis-à-vis the rates of the given two currency values with respect to the dollar.
	www.bsu.edu /classes/rrathina/course/unit3_3.htm (172 words)

	triangular - Search Results - MSN Encarta
		- with triangular base: having a base in the shape of a triangle
		We know of his achievements only from his disciples, the...
		The Atlantic slave trade became part of a prosperous trading cycle known as the triangular trade.
	ca.encarta.msn.com /triangular.html (143 words)

	Robert J. Sternberg's Homepage (Site not responding. Last check: )
		I have proposed a triangular theory of love, according to which love has three components: intimacy, passion, and commitment.
		I have proposed a duplex theory of hate, according to which hate has both triangular and story components.
		The triangular components are negation of intimacy, passion, and commitment.
	www.yale.edu /rjsternberg (1335 words)

	Tests for Triangular Matrices
		The triangular test paths, xTR, xTP, and xTB, include a number of pathological test matrices for testing the auxiliary routines xLATRS, xLATPS, and xLATBS, which are robust triangular solves used in condition estimation.
		To generate unit triangular matrices of predetermined condition number, we choose a special unit triangular matrix and use plane rotations to fill in the zeros without destroying the ones on the diagonal.
		The tests performed for the triangular routines are similar to those for the general and symmetric routines, including tests of the inverse, solve, iterative refinement, and condition estimation routines.
	www.netlib.org /lapack/lawn41/node35.html (351 words)

	Triangular trade
		The profits made from the global trade of sugar, tea and coffee were the major driving force behind the triangular trade.
		Powerful trading interests tried to prevent any regulation or abolition of the slave trade using a fierce campaign of misinformation, lies and delaying tactics.
		In order to expose the truth publicly about the triangular trade it was necessary to show conditions on the ships and plantations.
	www.nmm.ac.uk /freedom/viewTheme.cfm/theme/triangular (577 words)

	Triangular Numbers
		They are triangular numbers like every perfect number.
		It is fun to find out which triangular numbers also appear in the new sequences.
		Here you also have the question, which triangular numbers repeat in the new sequences.
	www.mathematische-basteleien.de /triangularnumber.htm (717 words)

	Three sides to city’s manhole story
		In reality, says Pollock of the DPW, Nashua’s triangular lids can’t fall down into the sewers despite what geometry says, because Nashua Foundries built them slightly tapered so the hole is just a little too small to fit the lid.
		Draw lines from one side to the other of a Rouleaux triangle, through the center, and their length will never vary; so it has no dimension shorter than any other that could be used to squeeze the lid through the hole.
		It’s a slow process and triangular covers will remain around for years to come, but like VCRs and afternoon newspapers, they’re on the downward slope to extinction.
	www.drainspotting.com /mirror/nhtelegraph-2003-11-26 (1066 words)

	Conjecture 34. n & n2, Triangular Numbers
		While visiting the wonderful page by Shyam Sunder Gupta, about Triangular Numbers I got interested by his affirmation that 1 and 6 are the only known triangular numbers such that their respective squares are also triangular numbers and his challenge to find the third one.
		Finding a triangular number which has a triangular square is equivalent to finding a positive integer m such that T(m)^2 is triangular, where T(m) = the m-th triangular number.
		Hence, an NSC for T(m) = m(m+1)/2 to have a triangular square is for the equation
	www.primepuzzles.net /conjectures/conj_034.htm (1018 words)

	Efficient algorithms for computing triangular decompositions (Site not responding. Last check: )
		It shows also that, since the triangular decompositions of Lazard satisfy better algebraic properties, they are generally more expensive to compute than those of Kalkbrener.
		Laz91] This is achieved by relaxing some properties of the triangular decompositions of Lazard during the computations, until a triangular decomposition is obtained.
		Mor99] is the first one, among those computing triangular decompositions of Lazard, to be completely proved.
	www.csd.uwo.ca /faculty/moreno/node4.html (558 words)

	Definition of triangular - Merriam-Webster Online Dictionary
		Learn more about "triangular" and related topics at Britannica.com
		Find more about "triangular" instantly with Live Search
		See a map of "triangular" in the Visual Thesaurus
	www.m-w.com /cgi-bin/dictionary?book=Dictionary&va=triangular (36 words)

	Triangular number that are also square
		I just stumbled across your site and noticed your page on triangular and square numbers.
		I couldn't help dropping this note to point out the curious fact that there is also an infinite set of numbers which are simultaneously both triangular and square.
		Armando Guarnaschelli from Argentina found a very simple recurrence relation that generates all triangular numbers that are also square.
	www.cut-the-knot.org /do_you_know/triSquare.shtml (312 words)

	Math Forum: Pascal's Triangle
		Triangular numbers can be thought of as the numbers of dots you need to make a triangle:
		The triangular numbers are found in the third diagonal of
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /workshops/usi/pascal/pascal_triangular.html (79 words)

	Compute discharge for triangular open channel with sudden drop using ISO 4371 equation (Site not responding. Last check: )
		Compute discharge, depth, top width, or channel angle for a horizontal triangular open channel with a sudden drop-off.
		This web page describes using the end-depth method for analysis or design of a triangular channel that freely discharges.
		· Triangular cross-section for a distance at least 20h upstream of the drop-off.
	www.lmnoeng.com /Waterfall/TriangularWaterfall.htm (417 words)

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