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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.
		A "perfect" squared square is such a square such that each of the smaller squares has a different size.
		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.
	en.wikipedia.org /wiki/Squaring_the_square (437 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).
		Square dissections in which the squares need not be different sizes are called Mrs.
		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)

	Perfect square - Wikipedia, the free encyclopedia
		a positive integer which is the square of some other integer, i.e.
		This is not the same as a magic square.
		In general, the product of two numbers is equal to the square of their average minus their difference from the average squared.
	en.wikipedia.org /wiki/Perfect_square (205 words)

	Integer Bars: More About Multiplication
		Perfect Squares - Mathematically, a perfect square is when you multiply a two numbers that are the same.
		To use the integer bars to find a perfect square, you can follow the methods described in Activity 1 and you will end up with an image that is a perfect square.
		The perfect square on the left is made of 4 bars of size 4.
	www.arcytech.org /java/integers/multiplication2.html (572 words)

	mat052 (Site not responding. Last check: 2007-10-21)
		The square root will be a whole number, a fraction,or a decimal that is repeating or terminating.
		64 is a perfect square since it's square root is 8.
		is not a perfect square since 3 is not a perfect square.
	servercc.oakton.edu /~cshapero/online/chap5/diff-sq.htm (170 words)

	Numbers - Square Roots - In Depth (Site not responding. Last check: 2007-10-21)
		Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself.
		The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …
		Here are the square roots of all the perfect squares from 1 to 100.
	www.explore.math.com /school/subject1/lessons/S1U1L9DP.html (255 words)

	Perfect Magic Hypercubes
		It is analogous to a pandiagonal magic square but instead of moving a row or column from one side to the other and retaining the magic properties, you move any cube from one side to the other.
		It is analogous to a pandiagonal magic square but instead of moving a row or column from one side to the other and maintaining the magic properties, you may move any plane from one side to the other.
		The 3 squares that bisect each of these four cubes are also magic although that is not a requirement of a simple magic cube..
	members.shaw.ca /hdhcubes/cube_perfect.htm (4972 words)

	Simplifying, Adding, and Subtracting Radicals (Site not responding. Last check: 2007-10-21)
		Realize that, according to the properties of exponents, an expression can be a perfect square without actually having an exponent of 2.
		Some non-perfect squares can be represented in a simplified form by writing the radical as a product of an integer and a square root of the remaining factors.
		In fact, whenever we are faced with a radical expression, we should remove any factors that are perfect squares.
	cwx.prenhall.com /bookbind/pubbooks/tobey3/medialib/course_notes/ch07_rational_exponents/simplifying.htm (363 words)

	Perfect Squares (Site not responding. Last check: 2007-10-21)
		Suppose N > 1 is not a perfect square, and suppose that sqrt(N) = a/b for some positive integers a and b, and that b is the smallest positive integer denominator for which this is true.
		Theorem 1: If a is a non-zero integer, and b is an integer, and a is a perfect square, then the following statement is true: ab is a perfect square if and only if b is a perfect square.
		Prove that the area of a right triangle with integer sides is not a perfect square.
	mcraeclan.com /MathHelp/BasicNumberPerfectSquares.htm (381 words)

	Math Online Q and A: The interger 49 can be written as the sum of small (Site not responding. Last check: 2007-10-21)
		The interger 49 can be written as the sum of smaller perfect squares in a variety of ways.
		You are to express 49 as the sum of perfect squares in as many different ways as possible.
		You are trying to find as many other ways to express 49 as the sum of perfect squares.
	www.mathonline.org /mho/view.cgi?21283 (219 words)

	Numbers - Square Roots - First Glance (Site not responding. Last check: 2007-10-21)
		Remember, the square of a number is that number times itself.
		The perfect squares are the squares of the whole numbers.
		The square root of a number, n, written below is the number that gives n when multiplied by itself.
	www.math.com /school/subject1/lessons/S1U1L9GL.html (49 words)

	Ed Pegg's Math Games - Square Packing
		The puzzle is to find the smallest number of square portions of which the quilt could be composed and show how they might be joined together.
		Perfect Squares, which can be considered as quilts without any repeated squares.
		For 1 to n, the square of their sum is equal to the sum of their cubes (provable by induction).
	www.maa.org /editorial/mathgames/mathgames_12_01_03.html (1123 words)

	Lesson 3: Lecture 1 (Site not responding. Last check: 2007-10-21)
		By turning the statement around and reordering it a little, it says "If the first term is a square, the last term is a square and the middle term is twice the product of the two terms being squared, you have the square of a binomial.
		In that example, the clue is that the 4th term is a square preceded by a minus sign.
		Therefore you have a binomial square minus a monomial square.
	www.dis.dpi.state.nd.us /west/classes/math/ndsu/math/lesson3_lecture1.html (474 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		EMBED Equation.3 169 is a perfect square of 13 EMBED Equation.3 20 is not a perfect square.
		EMBED Equation.3 9 is a perfect square of 3 x2 is a perfect square of x 49 is a perfect square of 7 and we are subtracting Difference of Squares EMBED Equation.3 EX.
		EMBED Equation.3 y2 is a perfect square of y 25 is a perfect square of 5 36 is a perfect square of 6 and we are subtracting Difference of Squares EMBED Equation.3 EX.
	cfcc.net /jshands/MAT_070/MAT_070_5_5.doc (689 words)

	Special Factoring Lesson - II
		"Perfect square trinomials" are quadratics that you got by squaring a binomial.
		Recognizing the pattern to perfect squares isn't a make-or-break issue, but it can be a time-saver occasionally.
		The trick is really quite simple: If the first and third terms are squares, figure out what they're squares of.
	www.purplemath.com /modules/specfact2.htm (360 words)

	[No title]
		Then every 4x4 square drawn on the pattern will also be a pandiagonal magic square -- in other words, every straight line of four numbers will add up to 30.
		In general, a magic square is called pandiagonal if all its broken diagonals add up to the magic constant.
		If a pandiagonal square also has similar properties to the order-4 pandiagonals, it is called 'most-perfect': for example, the most-perfect order-8 square below has a magic constant of 252, and its 2x2 sub-squares add up to 126, and any two numbers that are n/2=4 cells apart add up to n^2-1=63.
	www.math.niu.edu /~rusin/known-math/98/ollerenshaw (876 words)

	[No title]
		The reduction of the contents inside the square root is accomplished (when possible) by a very straightforward strategy: (i) Factor the expression inside the square root completely.
		It is particularly important to ensure that the perfect squares that you identify are accurate, and the best way to do that is to show at least as much work as we did in the solution to Example 1 above.
		However, only perfect square factors of the entire expression in the radical are of any use to us here.
	www.math.bcit.ca /competency_testing/testinfo/testsyll11/basicalg/basops/radicals/simplif/simplif.doc (1362 words)

	Relations and sizes - Squares and square roots - In Depth (Site not responding. Last check: 2007-10-21)
		That's why we call raising a number to the second power "squaring the number." The perfect squares are squares of whole numbers.
		The square root of a number n is a number that, when multiplied by itself, equals n.
		We find 13 units to a side, so 13 is the square root of 169.
	www.math.com /school/subject3/lessons/S3U3L3DP.html (134 words)

	diffsqrs (Site not responding. Last check: 2007-10-21)
		A binomial is a Difference of Squares if both terms are perfect squares.
		is a perfect square, and so is 25, so yes we have a difference of squares.
		, the square root of 25 is 5.
	www.csun.edu /~ayk38384/notes/mod8/diffsqrs.html (268 words)

	Intermediate Test Prep (Grades7-8) More on Square Roots (Site not responding. Last check: 2007-10-21)
		From our perfect squares lesson we learned that when we square a whole number, or multiply it by itself, our product is a perfect square.
		However, their square roots are not whole numbers, they are decimals or fractional parts of whole numbers.
		Since 153 is between 144 and 169 in our perfect squares list, the square root of 153 is between 12 and 13 (12 and 13 are the square roots of 144 and 169).
	www.oswego.org /mtestprep/math8/a/squarerootsl.cfm (274 words)

	Perfect squares - Physics Help and Math Help - Physics Forums
		An integer num is called a perfect square modulo a if num = foo^2 mod a for some integer foo.
		thus for example, since 29 is congruent to the square 4 mod 5, we have 29 is a square mod 5, so then 5 is also a square mod 29, without having to find the square root.
		then if we ask whether 5 is a square, not mod 1234, but mod half of that, say mod 617, then since 617 is cong to 2 mod 5, and since 2 is not a square mod 5, it follows that 5 is not a square mod 617.
	www.physicsforums.com /showthread.php?threadid=57996 (886 words)

	Most-Perfect Magic Squares (Site not responding. Last check: 2007-10-21)
		A special type of pandiagonal magic square was described in an 1897 paper by Eamon McClintock of Toronto University.
		There is a unique principle reversible square in each set in which all the rows, reading left to right, and all the columns reading top to bottom, contain integers in ascending order, and the top row begins with the integers 1and 2.
		The other reversible squares for this order are simply the 15 rearrangements of the rows and/or columns of these three.
	www.geocities.com /~harveyh/most-perfect.htm (858 words)

	5.6 Special Factoring (Site not responding. Last check: 2007-10-21)
		perfect square trinomial: A perfect square trinomial is a trinomial that factors into a binomial squared.
		Notice that the first and third terms are perfect squares.
		perfect square: A perfect square is anything that is multiplied by itself twice.
	www.suu.edu /faculty/peterson_s/math1010/special_factoring.htm (193 words)

	Problem 48. Simple perfect prime squared rectangles
		Also (which I have not seen) there is W.T.Tutte "The quest of the perfect square", Amer.
		There's Chapter 34 "Electrical networks and squared squares" on pages 449-460 of J.H. van Lint and R.M. Wilson's "A Course in Combinatorics", Cambridge University Press (England), 1992 (ISBN 0 521 41057 6 hardback, ISBN 0 521 42260 4 paperback) but it does not give any algorithms.
		It also illustrates transformation techniques whereby, for example, squares and L-shapes in one squared square can sometimes be moved around or added to to produce another square sometimes with a different number of elements.
	www.primepuzzles.net /problems/prob_048.htm (1096 words)

	[No title]
		4 x 4, 4 • 4, 4 (4), and 4 2 All of these represent the same value; 16 We call products of this form perfect squares; 5x5, 62, 7 • 7, 12 (12) the result (the product) is also called a perfect square; 1, 4, 9, 16, 25,...
		You should be familiar with as many perfect squares as possible beginning with 1x1 through 25 x 25.
		You should also realize that perfects squares of some larger numbers are easy to calculate without having to memorize.
	www.angelo.edu /faculty/jmontema/PerfectSquares.doc (250 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Abstract: We have developed a method for constructing and enumerating all squares of any size, n, in an interesting class of magic squares, which we call most-perfect.
		This is the first time, in the thousand years during which magic squares have challenged mathematicians, that a method of construction, let alone enumeration, has been found for a whole class of magic square.
		In most-perfect squares integers come in complementary pairs along the diagonals and any 2x2 block of four adjacent integers add to the same sum.
	www.cs.man.ac.uk /~dbree/Reviews/mp-cs.html (220 words)

	Trinomial Squares (Site not responding. Last check: 2007-10-21)
		square of a sum or the square of a difference.
		The square root of the first term is 4x.
		The result is 3y which is the square root of the
	www.tpub.com /math1/11c.htm (652 words)

	day 1
		The teacher tells the students that they will be learning about perfect squares and square roots today.
		A. Show examples of a perfect square on the board.
		Choose which problems are perfect squares from the board.
	home.olemiss.edu /~mkyarbor/day_11.htm (179 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-21)
		Date: 02/16/2002 at 14:17:15 From: Stacey Subject: Perfect squares with congruences Prove that there is no perfect square a^2 whose last digits are 35.
		Date: 02/17/2002 at 17:42:47 From: Doctor Paul Subject: Re: Perfect squares with congruences What if I asked you to prove that there is no perfect square a^2 whose last digit is 7?
		Just square each of the 100 residue classes mod 100 and show that none of them yields 35.
	mathforum.org /library/drmath/view/56081.html (375 words)

	flooble :: perplexus :: forums
		My understanding is that a perfect square is essentially the square of an integer.
		Since zero is an integer, then presumably it's square is perfect.
		I agree with fwaff, I always remember this because the first differences between them are the odd numbers: 1 3 5 7, and without zero, you wouldn't have the 1.
	www.flooble.com /perplexus/forum.php?fid=6&tid=40 (346 words)

	(GCG531) Perfect Squares and a Semicircle by Geometry (Site not responding. Last check: 2007-10-21)
		(GCG531) Perfect Squares and a Semicircle by Geometry
		Point A is the vertex of a perfect square and 2 masked men can sometimes be seen here.
		Point B is a short walk from here at (N 42 28.820, W 71 11.339) and has the same properties as point A. Using AB as a diameter, imagine a semicircle drawn on the map toward the northeast direction.
	www.geocaching.com /seek/cache_details.aspx?guid=87103981-adb7-4512-8244-d688611a910c (604 words)

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