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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.
m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...
A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular. A parallelogram is a special case of a trapezium (known as a trapezoid in North America) in which both pairs of opposite sides are parallel and equal in length. A trapezium is a convex quadrilateral which has at least one pair of parallel ...
For example, 6 and 35 factor as 6 = 2 × 3 and 35 = 5 × 7, so they are not prime, but their prime factors are different, so 6 and 35 are coprime, with no common factors other than 1. A 24×60 rectangle is covered with ten 12×12 square tiles, where 12 is the GCD of 24 and 60.
One pair of opposite sides is parallel and equal in length. Adjacent angles are supplementary. Each diagonal divides the quadrilateral into two congruent triangles. The sum of the squares of the sides equals the sum of the squares of the diagonals. (This is the parallelogram law.) It has rotational symmetry of order 2. The sum of the distances ...
The first direction is also true for rectangles, i.e.: If a rectangle s is maximal, then each pair of adjacent edges of s intersects the boundary of P. The second direction is not necessarily true: a rectangle can intersect the boundary of P in even 3 adjacent sides and still not be maximal as it can be stretched in the 4th side.
162 (one hundred [and] sixty-two) is the natural number between 161 and 163. In mathematics. Having only 2 and 3 as its prime divisors, 162 is a 3-smooth number.
For the general quadrilateral (with four sides not necessarily equal) Euler's quadrilateral theorem states + + + = + +, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that x = 0 {\displaystyle x=0} for a parallelogram, and so the general formula simplifies to the parallelogram law.