Mathematics is all around us, and it has shaped our understanding of the world in countless ways.In 2013, mathematician and science author Ian Stewart published a book on 17 Equations That Changed The World.
1) The Pythagorean Theorem: This theorem is foundational to our understanding of geometry. It describes the relationship between the sides of a right triangle on a flat plane: square the lengths of the short sides, a and b, add those together, and you get the square of the length of the long side, c.
This relationship, in some ways, actually distinguishes our normal, flat, Euclidean geometry from curved, non-Euclidean geometry. For example, a right triangle drawn on the surface of a sphere need not follow the Pythagorean theorem.
2) Logarithms: Logarithms are the inverses, or opposites, of exponential functions. A logarithm for a particular base tells you what power you need to raise that base to to get a number. For example, the base 10 logarithm of 1 is log(1) = 0, since 1 = 100; log(10) = 1, since 10 = 101; and log(100) = 2, since 100 = 102.
The equation in the graphic, log(ab) = log(a) + log(b), shows one of the most useful applications of logarithms: they turn multiplication into addition.
Until the development of the digital computer, this was the most common way to quickly multiply together large numbers, greatly speeding up calculations in physics, astronomy, and engineering.
3) Calculus: The formula given here is the definition of the derivative in calculus. The derivative measures the rate at which a quantity is changing. For example, we can think of velocity, or speed, as being the derivative of position - if you are walking at 3 miles per hour, then every hour, you have changed your position by 3 miles.
4) Law of Gravity: Newton's law of gravitation describes the force of gravity between two objects, F, in terms of a universal constant, G, the masses of the two objects, m1 and m2, and the distance between the objects, r. Newton's law is a remarkable piece of scientific history - it explains, almost perfectly, why the planets move in the way they do. Also remarkable is its universal nature - this is not just how gravity works on Earth, or in our solar system, but anywhere in the universe.
Newton's gravity held up very well for two hundred years, and it was not until Einstein's theory of general relativity that it would be replaced.
5) The square root of -1: Mathematicians have always been expanding the idea of what numbers actually are, going from natural numbers, to negative numbers, to fractions, to the real numbers. The square root of -1, usually written i, completes this process, giving rise to the complex numbers.
Mathematically, the complex numbers are supremely elegant. Algebra works perfectly the way we want it to - any equation has a complex number solution, a situation that is not true for the real numbers
6) Euler's Polyhedra Formula: Polyhedra are the three-dimensional versions of polygons, like the cube to the right. The corners of a polyhedron are called its vertices, the lines connecting the vertices are its edges, and the polygons covering it are its faces.
A cube has 8 vertices, 12 edges, and 6 faces. If I add the vertices and faces together, and subtract the edges, I get 8 + 6 - 12 = 2.
Euler's formula states that, as long as your polyhedron is somewhat well behaved, if you add the vertices and faces together, and subtract the edges, you will always get 2. This will be true whether your polyhedron has 4, 8, 12, 20, or any number of faces.
Euler's observation was one of the first examples of what is now called a topological invariant - some number or property shared by a class of shapes that are similar to each other. The entire class of "well-behaved" polyhedra will have V + F - E = 2. This observation, along with with Euler's solution to the Bridges of Konigsburg problem, paved the way to the development of topology, a branch of math essential to modern physics..
Now to know more watch this video till the end.
Thanks for watching..
Social accounts link
Instagram- / scienceandmyths
Facebook Page- / scienceandmyths
Physics के 17 ऐसे सवाल जिनको कोई नहीं जान पाया | biggest unanswered questions of physics
FAIR-USE COPYRIGHT DISCLAIMER This video is meant for Educational/Inspirational purpose only. We do not own any copyrights, all the rights go to their respective owners. The sole purpose of this video is to inspire, empower and educate the viewers.