10 Mathematical Equations That Changed The World
Get ready to dust off your old math textbooks and have your mind blown because these equations will make you see numbers in a new light. If you have ever asked how math has helped anyone, I am here to show you how ten equations out of many have changed the world.
Einstein’s theory of Special Relativity
Einstein’s theory of special relativity fundamentally changed our understanding of space and time, introducing time dilation and length contraction and disproving the idea that time and space are absolute.
The theory impacted physics, and cosmology, led to new understandings of light, energy, and matter, laid the foundations for quantum mechanics and general relativity, and has been applied in GPS, particle physics, and nuclear energy.
The Pythagorean theorem
This theorem plays a vital role in trigonometry and geometric shapes and is used in computer graphics, image processing, and algorithm design. The theorem also has practical applications in architecture, engineering, and navigation. It has been used to design bridges and buildings and calculate distances and angles for navigation.
It has also been used in physics and astronomy to calculate the distance between celestial bodies and the properties of orbits. It has been used to model the behavior of subatomic particles, black holes’ properties, and spacetime curvature. It has also been used to calculate the speed of light and the properties of gravitational waves.
The wave equation
The wave equation describes the behavior of particles at atomic and subatomic levels and provides a framework for understanding wave-like properties of matter and energy states of a system. It led to the wave function, which describes the probability of a particle’s position and momentum; it is used in physics to understand wave behavior in optics, electromagnetism, and quantum mechanics.
The wave equation models wave behavior in mediums like air, water, and solids; it’s used in telecommunications to model radio wave propagation and forms the basis of modern wireless communication. In engineering, it’s used to design and analyze structures exposed to dynamic loadings, such as bridges, buildings, and offshore platforms.
The Navier-Stokes equations
The Navier-Stokes equations describe fluid flow and have played a crucial role in fluid dynamics; they are used to understand and predict phenomena such as airflow around airplanes and ocean currents.
The equation has practical applications in the design of hydrodynamic machinery, weather patterns simulation, and prediction of fluid behavior in industrial processes; it is recognized as one of the most important equations in classical physics.
The Einstein field equations
Albert Einstein’s theory of general relativity revolutionized our understanding of gravity as a curvature of spacetime caused by mass or energy, leading to discoveries about black holes, the expansion of the universe, and the nature of time and space; it has practical applications in the development of GPS and other technologies and continues to shape our understanding of the universe.
Newton’s Law of Gravity
Isaac Newton’s law of gravity explained the motion of the planets and other celestial bodies and provided a mathematical framework for understanding the behavior of gravity. It also led to the development of new technologies, such as the marine chronometer, which significantly improved navigation at sea.
It paved the way for Einstein’s theory of general relativity; it was a crucial step in the development of modern physics and has had implications in many fields, such as astronomy, engineering, and technology.
The Maxwell equation
James Clerk Maxwell’s equations, formulated in the 19th century, unified the previously separate phenomena of electricity and magnetism and described the behavior of light as an electromagnetic wave. This led to a deeper understanding of the nature of electromagnetic radiation and the development of technologies such as radio, television, and radar.
Additionally, the equations predicted the existence of radio waves, which led to the discovery of new forms of electromagnetic radiation, such as X-rays and microwaves. The equations also played a crucial role in the development of quantum mechanics and the theory of special relativity and continue to be used in fields such as electrical engineering, optics, and electromagnetism.
The Euler-Lagrange formula
Euler’s formula connects the number of vertices, edges, and faces of a convex polyhedron and applies to all such shapes. It enabled a deeper understanding of the properties of three-dimensional figures and the examination of how structures respond to stress.
In physics, the formula was used to explore the stability and strength of structures, especially in mechanics. It also had a significant impact on computer graphics and computer-aided design. Additionally, it influenced other fields, such as materials science, aerospace engineering, and architecture.
The Information Theory
Information theory, developed by Claude Shannon in 1948, deals with studying the representation, processing, and transmission of information. It is considered one of the foundations of the modern digital age. It provides the theoretical foundation for data compression, error-correcting codes, and digital signal processing, which are essential for modern communication systems such as cell phones, the internet, and satellite communications.
It concepts like entropy and mutual information are used in computer science fields such as machine learning, artificial intelligence, and computer vision; in cryptography, it provides the mathematical foundation for modern cryptographic techniques; in biology, it is used to understand information processing in biological systems; and in economics, it is used in fields such as game theory, decision theory, and behavioral economics.
The Second Law of Thermodynamics
The second law of thermodynamics, also known as entropy, is a fundamental principle that describes the relationship between energy, entropy, and the direction of natural processes. It is used to understand the efficiency of heat engines and the maximum theoretical efficiency of power plants and other energy-conversion devices. In engineering, it is used to design and analyze heat transfer systems, refrigeration systems, and other thermal systems.
In chemistry, it is used to understand the direction of chemical reactions and the maximum theoretical yield of chemical processes. In biology, it is used to understand the efficiency of biochemical processes, such as photosynthesis and cellular respiration. In information theory, it is used to understand the limits of information storage and data compression. In cosmology, it helps to understand the ultimate fate of the universe and the concept of entropy increase.
