Exactly what is a square?
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A square is a quadrilateral (4-sided polygon) with sides of equal length, all joined at 90-degree (also called "right") angles to each other.\n\nSince the square has area, it is definitely the area within the lines that constitutes the square, not the lines themselves.
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This is impossible:\nProof. Let the area of each identical square equal n^2 (so each side is n). Since the large square is has 3 of these pieces, its area is 3n^2. Thus, each of its side is sqrt(3)n. However, you can never divide the square to do this (since sqrt(3) is irrational).
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Draw a picture - a square with corners (0,0), (2,0), (0,2), (2,2), showing the range of possible values for x and y.\nNow, what part of that square has the difference < 1? Its a hexagon to be precise; its the entire square except for a little triangle at the top left, and a little triangle at the bottom right. The two sloping sides go from (0,1) to (1,2) and (1,0) to (2,1).\nThose triangles each have area 1*1/2 = 0.5, so area 1 combined.\nSo the total area left is 4-1 = 3, so the answer is 3/4.
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This is a good one.\nAccording to the definition in geometry a vertex is a corner.\n\nA triangle has 3 vertices \nA square has 4 vertices  \n \nSo far it is a piece of cake.\n\nSo how many corners does a sphere have? \n\nIf we have to approximate a sphere (actually I’m thinking of a circle but for our argument it is good enough) we would need infinitely many edges (or sides) and therefore would generate infinite number of vertices since a vertex is formed between every two edges. \n\nSo a sphere has infinite number of vertices. \n\nSome people would say that it has a zero vertices since there are no corners to a sphere. But now you know better don’t you?
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ok, lets make this simple.\n\nIf a shape can be folded over itself and cover itself exactly, the article is said to be symmetrical and the "fold line" is said to be an axis of symmetry.\n\nA square is a symmetrical shape with 4 axis of symmetry, the two diagnals and one line drawn across it half way up, one line drawn down through it, half way across it.\n\nA circle has an infinate nubber of axis of symmetry, each one being a diameter.\n\nOne way to look at this axis is to think of it as a mirror placed on a plain geometrical shape, the reflection is the other half of the shape.
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It is said that the area of a circle is Pi R square.  Pie are not square. Pie are round, cornbread are square.
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A perfect square integer is one that can be expressed as k^2, where k is an integer.\n\n^ means raised to the power\n \nExamples of such numbers are 1,4,9,16,25,36,49,64,81,100,.....etc
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Perfect Squares\n\nEdit: First Four to be precise
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The answer is +/- the square root of 119, over 8.  Divide both sides of the equation by 8, and you get X squared = 119/64.  Take the square root of this and you have the answer.  64 is a perfect square, but 119 isn't.  If it had been 121 on top, your answer would be +/- 11/8.
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Alway true:\n- a square is a rhombus \n- a rhombus is a kite\n\nA square has four sides that are equal, and that is the definition of a rhombus.  It's a special rhombus with angles of 90 degrees.\n\nA rhombus has all four sides the same length, while a kite has two sides and two sides the same length.  Thus a rhombus is just a special kite with all sides the same.\n\nNot necessarily true:\n- a rhombus is a square (only if 90 degrees)\n- a kite is a rhombus (only if the sides are the same)\n- a rhombus is a rectangle (only if 90 degrees)\n- a rectangle is a rhombus (only if 90 degrees and sides the same length, e.g. a square)\n- a kite is a parallelogram (only if all sides the same)\n- a kite is a rectangle (only if a square)
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draw the same square if the square is on the origin...because the rotation of a square for every 90 degree will produce the exact same figure, again assuming the square is on the origin
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Anytime you square something i.e. 2 squared.  In retail we use it to calculate margins\n\nhope this helps
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the ratio is 1:2 or 1/2\n\noh, by the way it goes like this:\n\nassuming the length of each side of square A is a, then the area is a^2.\n\nsince, the vertices of the smaller square (A) is the midpoint of the sides of the big square(B), using the diagonal of square A, we can find the sides of the bigger square.\n\nThe diagonal is a*squareroot of 2, in which when we square to get the area ===>  gives us 2a^2.\nThus, the ratio is between Square A' area (a^2) and B's area (2a^2) is 1:2 or 1/2
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fancy description of a rectangle.\n\nIf it had four congruent sides, it would be a square.
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are the circles inside the square?\nif they are...\none side of the square is 8m\nso you divide that by two since there two circles side by side.\ndiameter of circle = 4m and you half this to get radius which is 2m. \nTo get area of a circle use pi.\nArea of circle =pi x radius squared\n                      = pi x 4
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It is named "magic square" and they are very well investigated.\nExapmple of it's history and other information is, for example, in the first attached wiki article.\n\nThere are 275,305,224 such 5x5 squares.\nMethods for building them can be found in a references of this wiki article.\nFor example, 2nd attached URL is a link to an application, which can generate you a lot of them.\n\nNow, some examples:\n\n01 02 17 23 22\n19 15 08 16 07\n20 14 13 12 06\n21 10 18 11 05\n04 24 09 03 25\n\n\n01 02 17 23 22\n20 16 08 15 06\n19 12 13 14 07\n21 11 18 10 05\n04 24 09 03 25\n\n\n01 02 17 23 22\n20 16 08 15 06\n21 12 13 14 05\n19 11 18 10 07\n04 24 09 03 25\n\n\n01 02 17 23 22\n21 15 08 16 05\n19 14 13 12 07\n20 10 18 11 06\n04 24 09 03 25\n\nand so on
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See a magic square in\nhttp://en.wikipedia.org/wiki/Magic_square