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A Knowledge Hub by Rahul Anand
Mathematical Marvels: Insights from the Field
Pythagoras’ theorem
Pythagoras’ theorem is stated as : The sum of the areas of the two squares on the perpendicular(p) and base(b) of a right-angle triangle is equal to the area of the square on the hypotenuse(h). i.e. p2 + b2 = h2
Sides of a Triangle
A right-angle triangle is a triangle in which one of the angles measures 90°. Right-angled triangles have wide applications in mathematics and physics and as such, it became convenient to have specific names for their sides so that the problem statement in mathematics…
Trigonometric functions in terms of a unit circle context
The trigonometric functions can be described on an x-y coordinate plane (Euclidean plane) using a circle of radius 1 unit and cutting a sector that subtends an angle θ at the centre. Refer to the diagram below for details.
Relation between radian and degree
By definition, L (length of arc) = ( \dfrac { \mathrm{θ_{deg} } } {360} ) × Circumference (arc length is proportional to angle, one complete arc subtends 360° at center) Also, Circumference = 2 ? r Hence, L = ( \dfrac { \mathrm{θ_{deg} } } {360} ) × 2 ? r …
Odd numbers
A number not divisible by 2 is called an odd number. Any number whose unit digit(last digit) is either 1,3,5,7 or 9 is an odd number. The set of all odd numbers is represented as Odd numbers = { 2n+1: n ∈ Z } where Z is the set of all integers. When an even…
Even Numbers
A number divisible by 2 is called an even number. All numbers whose unit digit(last digit) is either 0,2,4,6 or 8 is an even numbers. The set of all even numbers is represented as follows: Even numbers = { 2n: n ∈ Z } where Z is the set of all integers. Zero is…
Cartesian Product
The cartesian product of two sets A and B is defined as a set formed by all the possible ordered pairs of elements from A and B, such that the first element comes from set A and the second element comes from set B. The cartesian product is denoted as A × B. Let a and…
Ordered Pairs
An ordered pair is a 2-tuple formed by taking two elements (generally numbers but can be alphabets, characters, words or symbols). The general form of representation is (a, b) where a and b represent two distinct objects. The important thing with ordered pairs is that…
Calculus Castle
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Insight into the Laws of Physics
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NUMERICAL SOLUTIONS IN PHYSICS
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Atom to Atom: Insights from the Chemical Universe
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Life’s Mysteries Revealed: Exploring Biology
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