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Topic: Squaring the square

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	Squaring the square - Wikipedia, the free encyclopedia
		A square with sides equal to a unit length multiplied by an integer is called an integral square.
		They transformed the square tiling into an equivalent electrical circuit, by considering the squares as resistors that connected to their neighbors at their top and bottom edges, and then applied Kirchhoff's circuit laws and circuit decomposition techniques to that circuit.
		A "simple" squared square is one where no subset of the squares forms a rectangle or square, otherwise it is "compound".
	en.wikipedia.org /wiki/Squaring_the_square (462 words)

	Squaring the square: Definition and Links by Encyclopedian.com - All about Squaring the square
		Of course squaring the square is a trivial task unless additional conditions are set.
		They transformed the square tiling into an equivalent electrical circuit, and then applied Kirchhoff's laws and circuit decomposition[?] techniques to that circuit.
		A "simple" squared square is one where no subset of the squares forms a rectangle.
	www.encyclopedian.com /sq/Squaring-the-square.html (399 words)

	Squaring the square
		A square with integral sidelength is called an integral square.
		Other possible conditions that lead to interesting results are nowhere neat squared squares and no-touch squared squares (see tiling).
		Squared Squares and Squared Rectangles - Tilings of Squared Squares and Squared Rectangles, constructed using javascript.
	www.nebulasearch.com /encyclopedia/article/Squaring_the_square.html (442 words)

	Square - Definition of Square by Webster Dictionary
		It is of several forms, as the T square, the carpenter's square, the try-square., etc.
		The act of squaring, or quarreling; a quarrel.
		The units of square measure are squares whose sides are the linear measures; as, square inches, square feet, square meters, etc.
	www.webster-dictionary.net /definition/square (805 words)

	Square Down: Free quilt instructions
		When making a quilt block that is made from a triangle of one fabric stitched to a triangle of another fabric, you face the challenge of completing a block that is diagonally divided, is straight on the sides, and is exactly the right size.
		This means that you will place the quilter's square over the top of your quilt block, with the diagonal line on the quilter's square directly on top of the diagonal line on the quilt block.
		The finished block is then squared down to the correct size (in this case, 2.5" x 2.5" - as shown by the small marks on the quilter's square).
	craftandfabriclinks.com /instructions/squaredown.html (312 words)

	Circuit and method for fast squaring by breaking the square into a plurality of terms - Patent 6260056
		It is desirable to increase the squaring speed and reduce the size of the squaring circuit.
		In accordance with the invention, a squaring circuit includes an input terminal that is configured to carry a k-bit input bit group representing a k-bit input value.
		A left hand squaring circuit is configured to receive the left hand m-bit portion and generate a first term bit group representing a square of the left hand value.
	www.freepatentsonline.com /6260056.html (2208 words)

	Squaring the square -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		A (A hand tool consisting of two straight arms at right angles; used to construct or test right angles) square with sides equal to a unit length multiplied by an integer is called an integral square.
		The squaring-the-square problem consists of (The application of tiles to cover a surface) tiling one integral square using only other integral squares.
		Other conditions that lead to interesting results are nowhere neat squared squares and no-touch squared squares (see (The application of tiles to cover a surface) tiling).
	www.absoluteastronomy.com /encyclopedia/s/sq/squaring_the_square.htm (483 words)

	The Hindu : Education Plus Coimbatore : Vedic mathematics is simple
		To find the square of a number that is closer to 10, 100, 1000, use the following principle: The square of 99 is 9801.
		The last two digits are obtained by the square of difference between the nearest `0' number and the base number; (100-99)to the power of 2=01.
		How to get the square of a number that is not closer to 10, 100, 1000 etc? The square of 43 is 1849.
	www.hinduonnet.com /edu/2004/11/29/stories/2004112900180600.htm (924 words)

	THE ABACUS HANDBOOK (Site not responding. Last check: 2007-10-21)
		The square number refers to the number from which the square root is to be extracted.
		In preparing to find the square root of a number, whether it be on paper or on the abacus, the number is normally separated into pairs of digits.
		In the event the square number is not a perfect square, when the decimal is reached further groups of 00 may be added and the process continued.
	www.gis.net /~daveber/Abacus/SquareRoot.html (2573 words)

	The Cricket Square (Site not responding. Last check: 2007-10-21)
		The wicket should be smooth and flat with no undulations or holes present, with a binding strength to provide an acceptable bounce and pace when the ball pitches 2-3 meters in front of the popping crease.
		Squaring corners of square using the 3-4-5 method of triangulation
		This is usually the first operation (water first if square is hard and dry), working in two or more directions if using mechanical aids to thoroughly remove all dead material (thatch or mat).
	www.boughton-loam.co.uk /cricket.html (644 words)

	Function and Relation Library -- Squaring and Square Root Functions (Site not responding. Last check: 2007-10-21)
		The slope of the squaring function is 2x, twice the value of the x at a given point.
		Squaring is useful in determining areas of plane figures.
		The square root function is important because it is the inverse function for squaring.
	www.mathnstuff.com /math/spoken/here/2class/300/fx/library/quadrat.htm (534 words)

	Games and Puzzles Journal #35
		When the rectangle itself is a square the problem is known as Squaring the Square and a comprehensive theory was developed by four mathematicians at Cambridge by which they showed a relationship between the elements of dissections and the currents in certain electrical networks.
		The sum of the duplicated squares in C1 and C2 (92 + 208) is equal to the sum of the two duplicated pairs in C3 (97 + 203).
		A dissection of a rectangle in two different ways but with a corner square in one equal to a corner square in the other will yield two different tripolar networks and one of these can be used with the dual of the other.
	www.gpj.connectfree.co.uk /gpjq.htm (1024 words)

	MSN Encarta - Search Results - Circle in the Square
		Circle in the Square, influential, independent theater company based in New York City, dedicated to the production of serious American and European...
		Square Roots : measuring chords of a circle
		combining like terms, equations with squares (quadratic equations), evaluating or simplifying expressions, multiplication, order of operations,...
	ca.encarta.msn.com /Circle_in_the_Square.html (162 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Fill a 63x63 square with either square, and then use 3 7x63's and 4 9x63's to make a 57x63, and make another 57x63 on the other side, and you have a 57x57 square left.
		It's the small squares that cause problems -- typically you can't complete the border because the two subsquare sizes you chose can't be combined in a way that adds up to the small square's size (needed for part of the border).
		Sometimes the small square left over may be a factor of the main square, or the "blocks" simply don't fit in the square at all (such as when trying to tile a 60x60 with 7's and 9's, in imitation of the 120x120 tiling).
	www.mathematik.uni-bielefeld.de /~sillke/PENTA/square-tiling-gcd (657 words)

	[No title]
		Perfect Square Dissection Square which can be Dissected into a number of smaller squares with no two equal is called a Perfect Square Dissection (or a Squared Square).
		If no subset of the Squares form a Rectangle, then the perfect square is called ``simple.'' Lusin claimed that perfect squares were impossible to construct, but this assertion was proved erroneous when a 55-Square perfect square was published by R. Sprague in 1939 (Wells, 1991).
		There is a simple notation to describe perfect squares in which brackets are used to group adjacent squares with flush tops, and then the groups are sequentially placed in the highest (and leftmost) possible slots.
	www.math.niu.edu /~rusin/known-math/98/square_dissect (1278 words)

	Let's Talk ShopBot: Setting Y-axis square to X-axis (Site not responding. Last check: 2007-10-21)
		During the assembly of the y-gantry, squareness is only one of the (easier) issues to deal with.
		I'm needing near-perfect square for the bulkheads of my Didi26 sailboat (Dixdesign.com) at the worst a 0.25mm diagonal error when I cross triangulate a 2000mmx1200mm rectangle (use a 0.125" drill bit on my 'A' axis for these corners.
		Then type MO ( motors off ) and tweak the carriage to the known to be square stops, then type an X move away from the stops to energize the motors.
	www.talkshopbot.com /messages/7/522.html (815 words)

	What does it mean to Square something - SEDS Forums
		The area of square of A + the area of square of B = The area of square C. The square of one kilogram is one kilogram.
		The square of the value was then literally as the area of the square which had sides of length proportional to the value.
		For instance squaring zero goes nowhere, squaring one stays the same, squaring the square root of negative one has cyclic magnitude and polarity.
	forums.seds.org /showthread.php?t=430 (1356 words)

	Dot Grid Use (Site not responding. Last check: 2007-10-21)
		Multiply the length of a side of the square by the denominator of the photo scale.
		Estimate the land area represented by the square by squaring the length of a side found in step 3.
		Use the dot grid to count the dots that are included in the square.
	botweb.uwsp.edu /plantecology/DotGrid.html (241 words)

	New View of Statistics: Ordinal Dependent Variables
		You can't back-transform an effect (such as a difference between means) into a count by squaring it, but you can get a feel for the magnitude as a count relative to the mean by adding the value of the effect appropriately to the mean of the square-rooted counts, then squaring it.
		Now take the square root and find the inverse sine (arcsine) of the resulting number; in other words, find the angle whose sine is the square root of the proportion.
		The appropriate standard deviation is the root-mean square error from the analysis of the transformed variable, because this error should take into account the weighting factors.
	www.sportsci.org /resource/stats/counts.html (965 words)

	The Ultimate Cubing the cube - American History Information Guide and Reference
		In combinatorics and recreational mathematics, cubing the cube refers to the analogue in three dimensions of squaring the square: that is, given a cube C, to divide it into finitely many smaller cubes, not all congruent.
		Unlike the case of squaring the square, a hard but soluble question, cubing the cube is impossible.
		In fact if you take a squared square, and consider the smallest square S in it, and stand cubes of the same side on each of the squares, they 'tower over' the cube standing at S.
	www.historymania.com /american_history/Cubing_the_cube (179 words)

	Squaring Up Your Quilt
		If each unit is squared as you complete it, the final blocks will be nearly perfect when sewn together.
		Notice that the 4 1/2" line is well within the fabric on the two outer edges, the diagonal line matches the line in the block and the edges extend beyond the ruler.
		When squaring a half square triangle, the diagonal line will rest on the center seam line.
	www.quiltuniversity.com /squaring_up.htm (903 words)

	Radicals Lesson - I
		You can factor the insides of a square root, and then split the square root according to the factors.
		So far we have dealt only with square roots, but you would manipulate other radicals in much the same way.
		In the same way, when there is no number on the radical, the radical is understood to be the square root; to indicate other roots, you insert a number, called the "index", inside that little "hook" on the front of the radical symbol.
	www.purplemath.com /modules/radicals.htm (670 words)

	Squaring the square : Squaring the square problem (Site not responding. Last check: 2007-10-21)
		Squaring the square : Squaring the square problem
		terms defined : Squaring the square : Squaring the square problem
		It tendencies as respected this subject, for any material variation growing counties in England thirty per cent, at least at a.
	www.termsdefined.net /sq/squaring-the-square-problem.html (457 words)

	Squaring Up a Square
		To check a square for accuracy, insert the blade so that it is sticking out as far as possible.
		Place the square against a jointed surface and, using a very sharp pencil, draw a fine line the length of the blade.
		Most heads that are out of square can be adjusted by filing the raised center ridge that the blade slides on.
	www.taunton.com /finewoodworking/pages/w00127.asp (287 words)

	From Marti Michell Quilt Templates : : Squaring Up Ruler (Site not responding. Last check: 2007-10-21)
		Squaring up is very different from just plain measuring.
		The entire ruler is gridded using the same symbols as our two larger rulers, but in addition, there is a shadow that follows every inch mark, turns a corner and connects to make seeing squares very easy.
		When those two exposed edges are trimmed, the fabric piece is rotated so that the trimmed sides line up with the correct measurement and the untrimmed sides are ready to be perfected.
	www.frommarti.com /6squareup.html (244 words)

	Macintosh HD:Documents:Kee:honsberger2:Document.html (Site not responding. Last check: 2007-10-21)
		Instead of carrying as many unknowns as there are squares in the subdivision, we shall try to label neighbouring squares so that they fit together in the sketch; thus we shall have fewer unknowns to eliminate later.
		A squaring or tiling in which no two squares are the same size is said to be "perfect".
		So many perfect squares have been found that experts in the field suspect that tiled rectangles of unequal sides are the harder to come by.
	www.math.uwaterloo.ca /ideas/honsberger2 (2379 words)

	The Inside Approach - How It Works!
		To hit solid, accurate shots, the clubface must be square or squaring at impact and the club must be approaching the ball from an "inside" path.
		The path in which the club is swung directly influences one’s ability to square the clubface and thus be consistent.
		If you happen to square the clubface when swinging from out-to-in, you may hit a "pull." (Often, you may find that you pull your short irons and slice you longer irons, and especially your driver).
	info.insideapproach.com /inside.html (853 words)

	Is a square a rectangle? (Site not responding. Last check: 2007-10-21)
		A square was defined as a parallelogram with 4 congruent sides and 4 right angles.
		This is the square, a special case, but still a rectangle.
		No. The property is now automatic for squares, because squares are 'included' in the properties of rectangles, and in the word 'rectangle'.
	mathcentral.uregina.ca /QQ/database/QQ.09.99/jaireh1.html (526 words)

	Kevin's Website: Math and Science #1
		Kevin had finished an assignment early at school and the teacher said he could fill the remaining time by writing a paper on anything he wanted.
		Well, squaring is when you multiply a number by itself.
		Square Roots (V) Square roots are the opposite of square numbers.
	www.lehuanet.com /kevin/pelec01.htm (296 words)

	New York's Premier Alternative Newspaper. Arts, Music, Food, Movies and Opinion (Site not responding. Last check: 2007-10-21)
		Just as we were beginning to digest the news that Coney Island is to become a giant indoor mall, along comes word that Washington Square Park is slated for a $16 million makeover.
		As a result of Duchamp's so-called Washington Square Revolution, the city locked the door at the base of the Arch.
		Almost 80 years and a few dozen major social, artistic and intellectual movements later, the entire park is to be locked at night, presumably to protect undergraduates from rapists and drug dealers.
	www.nypress.com /18/20/pagetwo/newshole2.cfm (494 words)

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