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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]
There are 19 lines of text on the tablet's obverse and six on its reverse. The reverse also contains a diagram consisting of the rectangle of the problem and one of its diagonals. Along that diagonal is written its length in sexagesimal notation; the area of the rectangle is written in the triangular region below the diagonal. [5]
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.
More generally, if the quadrilateral is a rectangle with sides a and b and diagonal d then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d 2, the right hand side of Ptolemy's relation is the sum a 2 + b 2.
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.
The inscribed square problem, also known as the square peg problem or the Toeplitz' conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square? This is true if the curve is convex or piecewise smooth and in other special cases. The problem was proposed by Otto Toeplitz in 1911. [1]
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 ...
Euler's quadrilateral theorem or Euler's law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem.