KRITHIKADEVI (PEDAGOGY)

The paper written by Leonhard Euler on the Seven Bridges of Königsberg and published in 1736 is regarded as the first paper in the history of graph theory.[20] This paper, as well as the one written by Vandermonde on the knight problem, carried on with the analysis situs initiated by Leibniz. Euler's formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy[21] and L'Huilier,[22] and represents the beginning of the branch of mathematics known as topology. More than one century after Euler's paper on the bridges of Königsberg and while Listing was introducing the concept of topology, Cayley was led by an interest in particular analytical forms arising from differential calculus to study a particular class of graphs, the trees.[23] This study had many implications for theoretical chemistry. The techniques he used mainly concern the enumeration of graphs with particular properties. Enumerative graph theory then arose...

 Parts of a Circle Many objects that we come across in our daily life are ‘round’ in shape such as a coin, bangles, bottle caps, the Earth, wheels etc. In layman terms, the round shape is often referred to as a circle. A closed plane figure, which is formed by the set of all those points which are equidistant from a fixed point in the same plane, is known as a circle. In other words, a circle can be described as the locus of a point moving in a plane, in such a way that its distance from a fixed point is always constant. The fixed point is called the centre of the circle and the constant distance between any point on the circle and its centre is called the radius. Figure 1: Centre and Radius of circle figure Names of parts of a circle A circle can have different parts and based on the position and shape, these can be named as follows: Centre Radius Diameter Circumference Tangent Secant Chord Arc Segment Sector As we have already discussed the centre and radius of a circle. And the ...

In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1.[1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as S1 because it is a one-dimensional unit n-sphere. Unit circle Illustration of a unit circle. The variable t is an angle measure. Animation of the act of unrolling the circumference of a unit circle, a circle with radius of 1. Since C = 2πr, the circumference of a unit circle is 2π. If (x, y) is a point on the unit circle's circumference, then |x| and |y| are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and y satisfy the equation {\displaystyle x^{2}+y^{2}=1.} {\displaystyle x^{2}+y^{2}=1.} Since x2 = (−x)2 for all x, and since the reflection of any point on the unit circle about the x- or y-axis is also on the unit circle, the abov...

   Composite Numbers In Mathematics, composite numbers are numbers that have more than two factors. These numbers are also called composites. Composite numbers are just the opposite of prime numbers which have only two factors, i.e. 1 and the number itself. All the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers. For example, 6 is a composite number because it is divisible by 1, 2, 3 and even by 6. In this article, we will learn the definition of composite numbers, properties, smallest composite number, even and odd composite numbers, list of composite numbers, and difference between prime and composite numbers along with many solved examples in detail. Table of Contents: Definition Examples Properties List of composite numbers How to find composite number Types of Composite Number Odd Even Smallest Composite Number Difference Between Prime and Composite Numbers Prime Factorisation of composite number Solved Exa...

 History of Prime Numbers The prime number was discovered by Eratosthenes (275-194 B.C., Greece). He took the example of a sieve to filter out the prime numbers from a list of natural numbers and drain out the composite numbers. Students can practise this method by writing the positive integers from 1 to 100, circling the prime numbers, and putting a cross mark on composites. This kind of activity refers to the Sieve of Eratosthenes. Properties of Prime Numbers Some of the properties of prime numbers are listed below: Every number greater than 1 can be divided by at least one prime number. Every even positive integer greater than 2 can be expressed as the sum of two primes. Except 2, all other prime numbers are odd. In other words, we can say that 2 is the only even prime number. Two prime numbers are always coprime to each other. Each composite number can be factored into prime factors and individually all of these are unique in nature. Prime Numbers Chart Before calculators and c...

If you like Sudoku, there’s a good chance you’ll love KenKen. If you hate Sudoku, there’s a good chance you’ll love KenKen. Invented by Japanese mathematics teacher Tetsuya Miyamoto in 2004, KenKen is an elegant and rich logic puzzle with a few easy-to-understand rules, which helps explain why New York Times Puzzle Editor Will Shortz called it “The most addictive puzzle since Sudoku.” KenKen’s rules are straightforward: Fill in each square cell in the puzzle with a number between 1 and the size of the grid. For example, in a 4×4 grid, use the numbers 1, 2, 3, & 4. Use each number exactly once in each row and each column. The numbers in each “Cage” (indicated by the heavy lines) must combine — in any order — to produce the cage’s target number using the indicated math operation. Numbers may be repeated within a cage as long as rule 2 isn’t violated. No guessing is required. Each puzzle can be solved completely using only logical deduction. Harder puzzles require more complex deducti...

 Maths Project Ideas for Class 8 Class 8 secondary students can make some of the best working models based on these topics: Constructing different types of quadrilaterals Representation of rational numbers in number line Grouping, organizing and presentation of data using charts and graphs. Profit and loss for commodities and finding simple interest Playing with numbers Linear graphs (use matchsticks to represent) How to visualize 3D objects