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IM 67118, also known as Db 2-146, is an Old Babylonian clay tablet in the collection of the Iraq Museum that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal.
The diagonals of a cube with side length 1. AC' (shown in blue) is a space diagonal with length , while AC (shown in red) is a face diagonal and has length .. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.
A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals [4] (therefore only two sides are parallel). It is a special case of an antiparallelogram , and its angles are not right angles and not all equal, though opposite angles are equal.
One edge, face diagonal or space diagonal must be divisible by 29. One edge, face diagonal or space diagonal must be divisible by 37. In addition: The space diagonal is neither a prime power nor a product of two primes. [9]: p. 579 The space diagonal can only contain prime divisors that are congruent to 1 modulo 4. [9]: p. 566 [10]
Placing the point P on any of the four vertices of the rectangle yields the square of the diagonal of the rectangle being equal to the ... pp. 147, 159 (problem 6.16 ...
Crossed rectangle: an antiparallelogram whose sides are two opposite sides and the two diagonals of a rectangle, hence having one pair of parallel opposite sides. Crossed square: a special case of a crossed rectangle where two of the sides intersect at right angles.
YBC 7289 is a Babylonian clay tablet notable for containing an accurate sexagesimal approximation to the square root of 2, the length of the diagonal of a unit square. This number is given to the equivalent of six decimal digits, "the greatest known computational accuracy ... in the ancient world". [ 1 ]
An alternative view (covering both simple and self-intersecting shapes) is to define a rectangle as an equiangular quadrilateral. Rectangles may be used in periodic tilings of the plane. Another popular subject in recreational mathematics is the tiling of rectangles by polygons, ranging from simple puzzles to unsolved problems.
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