MATHEMATICS ENCYCLOPEDIA

Perfect cuboid is an Euler brick having  integer side lengths integer face diagonal integer space diagonal The problem of finding such a cuboid is also called the brick problem, diagonals problem, perfect box problem, perfect cuboid problem, or rational cuboid problem. No perfect cuboid is known. Equivalent to solution of Diophantine equations: a 2 + b 2 = d 2 a 2 + c 2 = e 2 b 2 + c 2 = f 2 A lso an extra following equation has to be added: a 2 + b 2 + c 2 = g 2 ( space diagonal equation ) where a, b, c are the edges and d, e, f are the diagonals. The space diagonal is g.

Oxford dictionary definition: A four sided figure. Cambridge dictionary definition: A flat shape with four straight sides. A quadrilateral is a four sided figure bounded by four line segments and four angles in a plane. 'Quad' means four and 'lateral' means sides.   Consecutive or adjacent sides: Two sides of quadrilateral are consecutive, if they have a common point ( vertex ). Example: AB & BC, CD & DA etc. Opposite sides: Two sides of a quadrilateral are opposite, if they have no common end-point ( vertex ). Example: AB & CD, BC & AD etc. Consecutive angle: Two angles are consecutive, if they have a common arm. Example: ∠A & ∠B, ∠C & ∠D etc. Opposite angles: Two angles are opposite, if they don't have a common arm. Example: ∠A & ∠C, ∠B & ∠D etc. Angle sum property of quadrilateral The sum of all the four angles of a quadrilateral is 360 degree. ∠A + ∠B + ∠C + ∠D = 360°. Different types of quadrilaterals

Definition of circle: A circle is a collection of those points in a plane that are at a given constant distance from a given fixed point in the plane. The fixed point is called the centre and the given constant distance is called the radius of the circle. A circle with centre O and radius r is usually denoted by C ( O, r ).  Thus in set notation we write C ( O, r ) = { X : OX = r } Position of point with respect to a circle: A point P is said to lie inside, outside or on the circle C ( O, r ) according as OP < r, OP > r, or OP = r respectively. Concentric circles: Circles having same centre with different radii are called concentric circles. Arc of a circle: A continuous piece of a circle is called an arc. Central angle: Let C ( O, r ) be any circle, then angle whose vertex is O is called the central angle. Chord: A line segment joining any two points on a circle is called a chord of the circle. Diameter: A chord passing through the centre of a circle is kn