Mathematical equations provide a unique window to the world. They help us understand reality and see things we didn’t notice before. So it’s no wonder that new developments in mathematics are often closely linked to advances in our understanding of the universe. Here we look at nine equations from history that have revolutionized the way we look at everything, from small particles to the vast universe.
One of the first majors trigonometry The rule that people learn at school is the relationship between the sides of a right triangle. Square the length of each of the two short sides and add them together to equal the square of the length of the longest side. This is usually written as a ^ 2 + b ^ 2 = c ^ 2 Known for at least 3,700 years, From the time of the ancient Babylonians.
The Greek mathematician Pythagoras allegedly wrote down the version of the equation used today. University of St Andrews In Scotland. The Pythagorean theorem helped extend the concept of numbers themselves, in addition to finding use in construction, navigation, mapping, and other important processes. In the 5th century BC, the Metapontam mathematician Hippasus noticed that a right-angled isosceles triangle with two base lengths of one unit has a hypotenuse, which is the square root of two. Irrational number.. (Up to that point, no one had encountered such a number in recorded history.) Hippasus is said to have been thrown into the sea for his discovery. It lasted forever without repeating after the decimal point, According to the article From Cambridge University.
F = ma and the law of gravity
Sir Isaac Newton, a British celebrity, Discovery that destroys the world..He is in it Second law of movement, This indicates that the force is equal to the mass of the object multiplied by its acceleration, usually written as F = ma. An extension of this law, combined with Newton’s other observations, led him in 1687 to explain what is now called his law. Universal gravitation.. It is usually written as F = G (m1 * m2) / r ^ 2. Where m1 and m2 are the masses of the two objects and r is the distance between them. G is a fundamental constant and its value must be discovered experimentally. These concepts have been used to understand many physical systems, such as the movement of planets in the solar system and the means of moving between planets using rockets.
Using Newton’s relatively new laws, 18th-century scientists began to analyze everything around them. In 1743, French polymath Jean le Rond d’Alambert derived an equation for the vibration or wave motion of a vibrating string, according to a paper published in the journal in 2020. Progress in historical research.. The equation can be written as:
1 / v ^ 2 * ∂ ^ 2y / ∂t ^ 2 = ∂ ^ 2y / ∂x ^ 2
In this equation, v is the velocity of the wave and the other part is the displacement of the wave in one direction. Wave equations extended to more than two dimensions allow researchers to predict water movements, seismic waves, and sound waves, which are the basis for: Schrodinger equation Of quantum physics that underpins many modern computer-based gadgets.
Even if you haven’t heard of the French Baron Jean Baptist Joseph Fourier, his work has influenced your life. This is because the formulas he wrote down in 1822 allowed researchers to break down complex and messy data into simple wave combinations that were much easier to analyze. The Fourier transform, as it is known, was a radical concept at the time, and many scientists refused to believe that complex systems could be reduced to such elegant simplicity. Yale Scientific.. However, the Fourier transform is a flagship product in many modern scientific fields such as data processing, image analysis, optics, communications, astronomy, and engineering.
Electricity and magnetism were still new concepts in the 1800s when scholars investigated how to capture and utilize these strange forces.Scottish scientist James Clerk Maxwell In 1864 he greatly enhanced his understanding of both phenomena when he published a list of 20 equations explaining how electricity and magnetism work and are interrelated. Maxwell’s equations, later refined into four, are now taught to first-year college physics students and provide the basis for all electronics in the modern world of technology.
E = mc ^ 2
Without the most famous equation of all, the list of transformation equations cannot be completed.First mentioned Albert Einstein In 1905, as part of his groundbreaking theory of special relativity, E = mc ^ 2 showed that matter and energy are two aspects of one thing. In this equation, E represents energy, m represents mass, and c represents the constant velocity of light. The concepts contained in such a simple statement are still difficult for many to envelop, but without E = mc ^ 2, we cannot understand how the stars and the universe work. Large Hadron Collider Examine the properties of the world of elementary particles.
It seems arrogant to think that we can create a set of equations that define the entire universe, which was done by Russian physicist Alexander Friedmann in the 1920s. Using Einstein’s theory of relativity, Friedman showed that the characteristics of the expanding universe can be expressed using two equations since the Big Bang.
They include the speed of light, the gravitational constant, in addition to all the important aspects of the universe, such as curvature, amount of matter and energy contained, speed of expansion, etc. Hubble’s constant, Capture the accelerated expansion of the universe. Einstein is famous for not like the idea of expanding or contracting the universe. This suggested that the general theory of relativity is caused by the influence of gravity.he I tried to add a variable In the results shown by the Greek letter Lambda, which acted against gravity to make the universe static. He later called it his greatest mistake, but decades later the idea was shattered and shown to exist in the form of a mysterious substance. Dark energy, Promoting the accelerated expansion of the universe.
Shannon’s Information Equation
Most people are familiar with the 0s and 1s that make up a computer bit. But this important concept would not have spread without the pioneering work of American mathematician and engineer Claude Shannon. In an important 1948 paper, Shannon presented an equation that indicates the maximum efficiency with which information can be transmitted. This is often given as C = B * 2log (1 + S / N). In the equation, C is the achievable capacity of a particular information channel, B is the bandwidth of the line, S is the average signal power, and N is the average noise power. (S over N indicates the system’s well-known signal-to-noise ratio.) The output of the equation is in bits per second. In a 1948 paper, Shannon acknowledged the idea of this bit as an abbreviation for the phrase “two-digit number” by mathematician John W. Tukey.
May Logistic Map
Very simple things can produce unimaginably complex results. This truth may not seem so radical, but it took scientists until the mid-20th century to fully understand the weight of ideas. In the meantime, when the field of chaos theory began, researchers began to understand how systems with only a small amount of feedback to themselves produced random and unpredictable behavior.Australian physicist, mathematician and ecologist Robert May wrote a paper and published it in a journal Nature In 1976, he popularized the equation xn + 1 = k * xn (1 – xn) under the title “Simple Mathematical Model with Very Complex Dynamics”.
Xn represents a certain amount in the system at the moment that feeds back to itself through the part specified by (1 – xn). K is a constant and xn + 1 indicates the system for the next moment. It’s very simple, but different values of k produce very different results, including those with complex and chaotic behavior. The May map is used to explain the population dynamics of the ecosystem and generate random numbers for computer programming.
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