MATHEMATICS ENCYCLOPEDIA

Once Professor G.H. Hardy visited Indian mathematician Srinivas Ramanujan in hospital in a taxi number 1729. Mr. Hardy described the conversation between them as: “I remember once going to see him when he was ill at Putney. I had ridden a taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. No, he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”” It can be written in following two forms: 1729 = 12 3 + 1 3 1729 = 10 3 + 9 3 There is also a film based on the above mathematicians, The film name is  "The man who kne w infinity" . See the poster belo w.

Definition of triangle: A plane figure bounded by three straight lines and three angles in a plane is called a triangle. Types of triangle on the basis of sides: Scalene triangle: A triangle with all the three sides of different lengths is called scalene triangle. Isosceles triangle: A triangle with two sides equal is called isosceles triangle. Equilateral triangle : A triangle whose all sides are equal is called equilateral triangle. Types of triangle on the basis of angles: Acute triangle:  Triangle in which each angle is acute , is called acute triangle. Obtuse triangle: Triangle in which one angle is obtuse , is called obtuse triangle. Right triangle: Triangle with one angle equal to 90 degree , is called right triangle. Theorems of triangles: The sum of three angles of a triangle is 180 degree. If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose a rectangle. Exterior angle theorem: If a s

Definition of angle: An angle is the union of two non-collinear rays with a common initial point. The two  rays forming an angle are called the "arms" of the angle and the common initial point is called the "vertex" of the angle. Angle measure axiom: Every angle has a measure. The unit of angle measure is a standard angle called a "degree". Types of angles: Acute angle:  An angle whose measure is less than 90 degree is called an acute angle. Obtuse angle: An angle whose measure is more than 90 degree but less than 180 degree is called an obtuse angle. Right angle:  An angle whose measure is 90 degree  is called a right angle. Straight angle: An angle measuring 180 degree is called Straight angle. Reflex angle: An angle whose measure is more than 180 degree is called reflex angle. Complete angle: An angle measuring 360 degree is called complete angle. Complementary angle: Two angles having their sum equal to 90 degree, are called c

Interior point of a line segment:  A point P is called an interior point of a line segment AB, if P lies between A and B but P is neither A nor B. Theorems on Euclid's geometry Theorem 1: Two distinct lines can't have more than one point in common. Theorem 2: Two lines which are both parallel to the same line, are parallel to each other. Theorem 3: If l, m, n are lines in the same plane such that l intersects m and m ॥ n ( m is parallel to n ), then l intersects n also. Theorem 4: If l and m are intersecting lines, l ॥ p and m ॥ q, then p and q also intersects. Theorem 5: If lines AB, AC, AD, and  AE are parallel to a line l, then points A, B, C, D and E are collinear.