Hello Friends today we are going to talk about top 10 Equations that change the world… I hope you would enjoy it, so lets strt…
10. 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.
9. 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 : x2 + 4 = 0 has no real number solution, but it does have a complex solution: the square root of -4, or 2i. Calculus can be extended to the complex numbers, and by doing so, we find some amazing symmetries and properties of these numbers. Those properties make the complex numbers essential in electronics and signal processing.
8. Fourier Transform :
The Fourier transform is essential to understanding more complex wave structures, like human speech. Given a complicated, messy wave function like a recording of a person talking, the Fourier transform allows us to break the messy function into a combination of a number of simple waves, greatly simplifying analysis.The Fourier transform is at the heart of modern signal processing and analysis, and data compression.
7. 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, m and m, 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.
6. The Callan-Symanzik equation :
The Callan-Symanzik equation is a vital first-principles equation from 1970, essential for describing how naive expectations will fail in a quantum world,” said theoretical physicist Matt Strassler of Rutgers University.
The equation has numerous applications, including allowing physicists to estimate the mass and size of the proton and neutron, which make up the nuclei of atoms.
Basic physics tells us that the gravitational force, and the electrical force, between two objects is proportional to the inverse of the distance between them squared. On a simple level, the same is true for the strong nuclear force that binds protons and neutrons together to form the nuclei of atoms, and that binds quarks together to form protons and neutrons. However, tiny quantum fluctuations can slightly alter a force’s dependence on distance, which has dramatic consequences for the strong nuclear force.It prevents this force from decreasing at long distances, and causes it to trap quarks and to combine them to form the protons and neutrons of our world,” Strassler said. “What the Callan-Symanzik equation does is relate this dramatic and difficult-to-calculate effect, important when [the distance] is roughly the size of a proton, to more subtle but easier-to-calculate effects that can be measured when [the distance] is much smaller than a proton.
5. Chaos Theory :
This equation is May’s logistic map. It describes a process evolving through time – xt+1, the level of some quantity x in the next time period – is given by the formula on the right, and it depends on x t, the level of x right now. k is a chosen constant. For certain values of k, the map shows chaotic behavior: if we start at some particular initial value of x, the process will evolve one way, but if we start at another initial value, even one very very close to the first value, the process will evolve a completely different way.
We see chaotic behavior – behavior sensitive to initial conditions – like this in many areas. Weather is a classic example – a small change in atmospheric conditions on one day can lead to completely different weather systems a few days later, most commonly captured in the idea of a butterfly flapping its wings on one continent causing a hurricane on another continent.
4. Maxwell’s Equations:
This set of four differential equations describes the behavior of and relationship between electricity (E) and magnetism (H).Maxwell’s equations are to classical electromagnetism as Newton’s laws of motion and law of universal gravitation are to classical mechanics – they are the foundation of our explanation of how electromagnetism works on a day to day scale. As we will see, however, modern physics relies on a quantum mechanical explanation of electromagnetism, and it is now clear that these elegant equations are just an approximation that works well on human scales.
3. Schrodinger’s Equation:
This is the main equation in quantum mechanics. As general relativity explains our universe at its largest scales, this equation governs the behavior of atoms and subatomic particles.
Modern quantum mechanics and general relativity are the two most successful scientific theories in history – all of the experimental observations we have made to date are entirely consistent with their predictions. Quantum mechanics is also necessary for most modern technology – nuclear power, semiconductor-based computers, and lasers are all built around quantum phenomena.
2. Second Law of Thermodynamics:
This states that, in a closed system, entropy (S) is always steady or increasing. Thermodynamic entropy is, roughly speaking, a measure of how disordered a system is. A system that starts out in an ordered, uneven state – say, a hot region next to a cold region – will always tend to even out, with heat flowing from the hot area to the cold area until evenly distributed.
The second law of thermodynamics is one of the few cases in physics where time matters in this way. Most physical processes are reversible – we can run the equations backwards without messing things up. The second law, however, only runs in this direction. If we put an ice cube in a cup of hot coffee, we always see the ice cube melt, and never see the coffee freeze.
Einstein radically altered the course of physics with his theories of special and general relativity. The classic equation E = mc states that matter and energy are equivalent to each other. Special relativity brought in ideas like the speed of light being a universal speed limit and the passage of time being different for people moving at different speeds.
General relativity describes gravity as a curving and folding of space and time themselves, and was the first major change to our understanding of gravity since Newton’s law. General relativity is essential to our understanding of the origins, structure, and ultimate fate of the universe.
Note : This list is based on research All the Equations in physics is important this is just 10 that is more important and revolutionary so we added that in list. If you want to know more details about these equations then stay connected with us because we are going to write about it in the future…
Thank you for reading ….