In the vast mathematical universe, formulas occupy a central place. These famous equations are found in every mathematical theorem from ancient times to the recent discoveries of the 20th century. With every new mathematical equation comes new questions and new answers. The following is an anthology of some of the math equations that have changed the way we see the world.
🙋♂️Equation
🔢Equation or theory name
🔎What it does
Pythagorean Theorem
Helps solve problems involving right angles.
The Universal Law of Gravitation
It states that two bodies in the universe attract each other with a force that depends on their masses and the distance between them.
The Theory of Relativity
It explains the fundamental relationship between space, time, and gravity.
Area of a Circle
Calculates the area of a circle. Also helps measure wave forms, lens curvatures and light distribution.
Chaos Theory
Used to understand and predict possible behaviours of complex systems that are sensitive to initial conditions.
Euler's Identity
Useful in the analysis of waves and oscillations. Provides a connection between different areas of mathematics
ΔS=∫
The Second Law of Thermodynamics
It dictates the direction of potential energy transfers.
The Schrödinger Equation
Governs wave functions of non-relativistic quantum-mechanical systems.
Maxwell's Equations
These equations are the foundation of classical electromagnetism, classical optics, electric and magnetic circuits
This theorem, dating back to 530 BC, is one of the most famous math equations to exist.
The Pythagorean Theorem is one of the cornerstones of modern mathematics; it has significantly contributed to the development of mathematics as a discipline. Even after many years, the formula of this theorem remains ingrained in our memory.
Thanks to Pythagoras and his famous equation, we can calculate lengths, angles and determine whether a triangle is right-angled or not. This equation is just one of the many examples of how math is part of our daily life, whether we are aware of it or not.
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Pythagoras' Theorem
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The Pythagorean Theorem continues to be used in practical fields such as construction, architecture, and carpentry, among others.
Universal Law of Gravitation
Isaac Newton formulated the Universal Law of Gravitation in the 17th century. It states that two bodies in the universe attract each other with a force that depends on their masses and the distance between them.
This force is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between them. For example, the Earth attracts the Moon, and vice versa.
The same law applies to the attraction between an apple and the Earth, and the attraction between planets and the Sun. All of these relationships fall under the Universal Law of Gravitation.
Use this law to calculate planetary attraction.
If you wish to delve deeper into one of the most famous math equations and the principles of gravity, an online maths tutor can provide personalised guidance.
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The Universal Law of Gravitation
, where F = Gravitational force (N: Newtons) M = Mass of the first body (usually a planet, kg) m = Mass of the second body (kg) R = Distance between the bodies (meters) G = Gravitational constant
Remember: gravitational interaction is universal; it applies to all types of matter. Gravity only manifests as attraction; it does not account for the repulsion of bodies.
Theory of Relativity
Pure mathematics is, in its way, the poetry of logical ideas.
Albert Einstein
Albert Einstein's Theory of Relativity is the most famous among mathematical theories. It proves how important math is in real life and the main impact math can have on the course of history. And yet, no one fully understands it.
E represents energy, m the mass of a body and c the speed of light. Source: Artturi Jalli on Unsplash
This formula, which illustrates the theory of relativity (restricted relativity and general relativity) revolutionised our understanding of physics up to that point.
It remains crucial to this day, as it shows that matter can be converted into energy and vice versa. 🤓
Note that the mass of any object is a form of energy. In the formula, the mass (𝑚) of an object can be converted into energy (𝐸), and vice versa. The “c” represents the speed of light, and it is squared to indicate that even a small amount of mass can be transformed into a large amount of energy.
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The Theory of Relativity
, where E = energy m = mass c = velocity (the speed of light)
Restricted relativity introduced the idea that the speed of light was a universal constant that did not change. It further explains that the passage of time was not the same for bodies moving at different speeds.
To master these and other complex physics concepts, taking math lessons is the perfect next step. As you wait for your lessons to start, have a listen to this podcast, which explains Einstein's maths theories in great detail.
The Area of a Circle
A circle is a closed, flat curve where all points are equidistant from the centre. In simple terms, a circle is a closed line, like a ring or a tyre.
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The Area of a Circle
, where A = the area of the circle π = 3.1416 r = the radius of the circle
The radius is the distance between the circle's centre point and any point on its boundary.
Whether for practical purposes or in physics calculations, knowing the formula for calculating the area of a circle is essential. Thanks to this famous maths equation, we can study wave phenomena, electromagnetic fields, lenses, and the distribution of light in greater depth.
Chaos Theory is the science of the unexpected, the nonlinear, and the unpredictable. It is one of the most famous math theories.
This theory deals with nonlinear phenomena that are practically impossible to predict or control. Such factors include turbulence, weather, stock markets, brain states, and more. We describe them using fractal mathematics, which reflects the infinite complexity of nature.
Chaos Theory encompasses, for example, the butterfly effect. This effect is often described as a butterfly flapping its wings in Australia causing a hurricane in Chile.
These waves represent chaos.
The butterfly effect means that small changes in initial conditions can lead to drastic changes in outcomes.
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Chaos Theory
There exists no definitive, unifying Chaos Theory equation. Chaos Theory mathematics involves repetitions of simple mathematical formulas like this one.
Chaos Theory in mathematics contradicts the idea of using math for poker or gambling. Even small errors in measuring the state of the system will be greatly amplified, making any prediction useless. Chaos is one of the most interesting math theories, as this clip explains.
Euler's Identity
Swiss polymath Leonhard Euler gave humanity what many mathematicians and experts consider one of the most remarkable equations ever devised.
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Euler's Identity
, where e = the base of natural logarithms i = the imaginary unit π = 3.1416 1 and 0 = integers
The elegance of Euler's Identity lies in its simplicity, but this formula isn't just a stunning example of mathematical beauty. It connects five important mathematical constants in a single formula.
💡This simplicity gives Euler's Identity a major impact on areas such as engineering, number theory, and complex functions, among others.
The Second Law of Thermodynamics
The first Law of Thermodynamics specifies that energy can be exchanged between physical systems as heat and work.
Source: Roman Mager on Unsplash
The second law introduces another quantity, known as entropy. It is a principle of change since it determines which direction potential energy transformations are possible.
This law states that it is impossible for a process's only result to be the transfer of heat from a colder body to a hotter one.
The Second Law of Thermodynamics is a physical principle that imposes a restriction on the direction of heat transfer processes between bodies. In 1873, Ludwig Boltzmann and Max Planck developed the theory from the generalisation of experimental facts.
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Second Law of Thermodynamics
ΔS=∫ , where ΔS = change of entropy dQ = amount of heat transferred T = the absolute temperature at which the transfer occurs.
To put this Law into a real-world context, think of an iced drink. You'll note that the ice melts, it will NOT freeze the drink.
The Schrödinger Equation
Austrian physicist Erwin Schrödinger had many brilliant ideas, including the one about his cat being dead and alive at the same time. His love of felines notwithstanding, he delivered one of the most famous formulas in quantum mechanics.
Source: Monstera Production on Unsplash
Schrödinger's Equation is essential for understanding how particles change over time. It helps describe the different states in which a particle can be found.
This equation poses a profound question: Does matter exist only in the possible physical states (solids, liquids, gases)?
At the philosophical level, Schrödinger's Equation invites us to reflect on the nature of matter and how we perceive it. On the practical side, it was very useful for the advancement of nuclear energy, as well as for computing and laser applications. Engaging with a maths tutor can illuminate these concepts further.
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The Schrödinger Equation
The Schrödinger equation explains the changes over time of a particle. It describes the states of a particle, from which it is possible to describe any state, while posing a deep philosophical problem. These types of math enigmas are very common, and this equation is a door to answers that will eventually be found.
Maxwell's Equations
The four Maxwell's Equations (pictured above) form one of the most important foundations of modern physics. These equations are significant for both electrodynamics and the theory of relativity. This statistic delivers proof of the following:
Number of Maths papers published each year
30 000
A fair number of them use at least one of those equations. The establishment of Maxwell's Equations is considered the pinnacle of classical physics. All equations for calculating electromagnetism can be derived from them.
These equations describe the interaction between electric and magnetic fields and their relationship with electric fields and charges. Both the electric and magnetic fields can be represented using field line diagrams. These equations have defined the importance of math in the modern world, making it evident that math is an integral part of our society.
All these famous math equations have something in common:
They are simple, elegant, and concise.
They help connect fundamental mathematics with simpler concepts.
Each has extensive applications in everyday life and across various disciplines.
Although mathematics can be somewhat complex, these equations remain compelling.
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Sophia Birk
A vagabond traveller whose first love is the written word, I advocate for continuous learning, cycling, and the joy only a beloved pet can bring.
prof prem raj pushpakaran writes — let us celebrate eDay (Euler’s number or Napier’s constant) on February 7 !!!!
me
im downn
John
I’m grateful to know these
Frequently asked questions
🏆What is the most famous equation?
The equation E = Mc2 is the most famous equation. at least of twentieth- century physics.
😍What's the most beautiful equation?
According to Science4All, in 1988, a Mathematical Intelligencer poll voted Euler's identity as the most beautiful feat of all of mathematics. In one mystical equation, Euler had merged the most amazing numbers of mathematics: e i π + 1 = 0
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prof prem raj pushpakaran writes — let us celebrate eDay (Euler’s number or Napier’s constant) on February 7 !!!!
im downn
I’m grateful to know these