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Square. In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90- degree angles, π/2 radian angles, or right angles ). It can also be defined as a rectangle with two equal-length adjacent sides.
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In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. [ 2] It was popularized in English by Hugo Steinhaus in the 1950 edition of his book Mathematical ...
In two dimensions, 2x 1 + 2x 2 is the perimeter of a rectangle with sides of length x 1 and x 2. Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square.
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference . Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
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