Found 6 Articles for Maths Theorems

Introduction Binomial Theorem for Positive Integral Indices states that “the total number of terms in the expansion is one more than the index”. The nth row of this array gives the coefficients in the expansion of $\mathrm{(a\:+\:b)^{n}}$ in descending powers of a and ascending powers of b; this array is known as the Pascal’s triangle after French mathematician Blaise Pascal (1623-1662). The triangle is, in fact, much older; it appeared as early as in 1303 in the works of the Chinese mathematician Chu Shin-Chien. Indeed, this was described by Indian mathematician Halayudha in 10th century A.D. as Meru Prastara, 700 ... Read More

Introduction A chord is a line segment connecting any two points located on the circumference of the circle . The circle is a well-known two-dimensional shape used in Euclidean geometry. It has various components, including chord, radius, diameter, etc. In this tutorial, we will discuss the definition, formulae, and some theorems related to the chord of a circle. Circles The circle is a two-dimensional figure drawn on a plane in such a way that each point on the circle is equidistant to a fixed point. The fixed point is known as the center of the circle. The dimension of ... Read More

Introduction The remainder theorem is used to find the remainder when a polynomial is divided by another polynomial. Polynomials are algebraic expressions consisting of different algebraic terms & these terms are joined together by mathematical operators like addition (+) & subtraction(-). The concept of polynomials is used in almost every field of mathematics. Also, the polynomial is considered one of the important branches of calculus. It also has wide applications in science. It is a central concept of algebra & algebraic geometry. It is used to form polynomial equations & word problems for analysing & solve difficult problems. In this ... Read More

Introduction Basic proportionality theorem was proposed by a famous Greek mathematician, Thales, hence, it is also referred to as the Thales theorem. Triangle is one of the basic geometrical shapes with three sides & three angles. In geometry you have studied different properties & theorems of the triangle. In this tutorial, we will study one of the most important properties i.e., similarity & basic proportionality theorem. Two triangles are said to be similar if their angles are congruent & corresponding sides are in proportion. '$\mathrm{\sim}$' symbol is used to represent similar triangles. There are several methods for finding whether triangles ... Read More

Introduction The midpoint theorem in geometry helps in determining the sides of triangles that are missing values. It establishes a link between a triangle's sides and the line segment created by any two of the triangle's sides' midpoints. A line that connects two places has a midpoint in the middle of the line. The centre of a line is located halfway between its two endpoints. A line connecting these two places has a midpoint at the point where it is divided into two equal pieces. A second line that was drawn to divide the two regions in half also runs ... Read More

Introduction Rolle’s theorem and Lagrange’s mean value theorem are interpreted on a function over an interval if the function satisfies the condition of continuity over a given closed interval and the condition of differentiability over a given open interval. The continuity of a function over a closed interval is defined as the function's graph that should not contain any break over the interval. The differentiability of a function over an open interval is defined as the function should be differentiable at every point in the interval. Continuity and Differentiability Continuity: Let’s take a function 𝑓(𝑥) with a domain and ... Read More