17 equations that changed the world
There is always "mathematics" behind the technology, it is no exaggeration to say that a modern advanced society was not realized without the development of mathematics. From numerous theorems and equations that have been created since BC, Mathematician Ian Stuart published his book "In Pursuit of the Unknown: 17 Equations That Changed the World"We've carefully selected 17 equations that are said to have changed the world.
Mathematical equations: 17 that changed the world.
◆01: Pythagorean theorem (Theorem of Sanchigata)
"The square of the hypotenuse of a right triangle equals the sum of the squares of the other sides" that supports the foundation of geometryPythagorean theoremThe existence of "survey and navigation technology developed.
◆02: The sum of the product of the antilogarithm and the logarithm in the logarithm
The relationship between the exponent and the inverse functionLogarithm"Contributed to the rapid development of science such as calculation of orbits of celestial bodies and calculation slides because we can calculate the product of huge numbers with familiar numbers.
◆03: Differential / integral
NewtonEstablished by "Differential integrationIs a subject given as one field as analytics in mathematics, Newton is called "the best paper in the history of science"Principia"And used it as a tool to explain" law of movement ".
In 1687, NewtonKepler's lawIntoEquation of motionAnd "Law of universal gravitationWe announced. Using this law, the mass of the earth can be easily measured.
◆05: Complex number (imaginary unit)
It becomes "-1" when squaredImaginary unit iExpanding the real number concept by devising "Complex number"Was born, which led us to the development of electromagnetism and quantum mechanics of today.
◆06: Euler's polyhedron theorem
For the relation of vertex (V), side (E), and plane (F) in the polyhedron, the relationship "V - E + F = 2"Euler's polyhedron theorem) Found by Euler. This discoveryTopologyIt will be the beginning of.
◆07: Normal distribution (probability density function)
It is indispensable in probability theory and statisticsnormal distributionIs the greatest mathematician of the 19th centuryGaussWas devised.
◆08: Wave equation
In order to deal with wave theory theoretically it is better to give a mathematical expression "Wave equation"The solution developed to solve the wave equation opened the door to understanding other differential equations.
◆09: Fourier transform
It is possible to decompose and convert a wave into a well-known waveform such as a sinusoidal wave "Fourier transform"In familiar places, it is also applied to medical instruments such as cuts of high frequency sounds that can not be heard in music CDs, and CT scans.
◆10: Navier - Stokes equation
"Fluid motion"Navier - Stokes equation(NS equation) "is an equation used in fluid dynamics. The NS equation is thought to be able to decide a lot of phenomena such as motion of fluid, but solving the NS equation itself is quite difficult, so decide by substituting an approximate solution obtained by simplifying the condition so that it can be solved Is common. To those who have found a solution to the NS equation or who proved that the equation can not be solvedClay Mathematics InstituteFrom1 million dollar prizeIs given.
◆11: Maxwell's equation
Newton's Law of Motion · The law of universal gravitation is called the fundamental equation of classical mechanics, whereas the basic equation of classical electromagnetics is called "Maxwell's equation"is. The relationship between electric field, magnetic field, magnetic flux density, and current density is expressed by four equations.
◆12: The second law of thermodynamics (entropy increasing law)
"Second law of thermodynamicsBy describing the direction of energy movement and energy quality,Type II perpetual engineIt was confirmed that it was impossible to realize, and then thermodynamics developed greatly.
◆13: Special Relativity Theory (Equality of Mass and Energy)
EinsteinThat energy is equal to the product of the mass and the square of the speed of lightEquality of mass and energy"Was discovered. This discovery,Atomic bombIt is applied to the development of Einstein in the later years.
◆14: Schroedinger equation
"Schroedinger equation"Is a fundamental equation in quantum mechanics (wave dynamics). The Schroedinger equation describing the microscopic world is essential for technologies such as semiconductor, laser and nuclear power generation.
◆15: Information Theory
The concept of "the amount of information obtained when an event with a low probability of occurrence occurs is large" is not inconsistent with the intuitive information concept. For example, the information that "Yokozuna / Shiho Pen lost" is easier to understand than "information that Shira Pen won" that "the amount of information is large". Shannon expresses such an intuitive concept mathematically "Information theory", Devised the average information amount as" entropy "in accordance with thermodynamics and quantified the uncertainty of the information source. Information theory is applied to data compression technology and network communication technology.
◆16: Chaos theory
"When butterflies flutter in Brazil, a tornado occurs in Texas"Butterfly effectIs a term that refers to a phenomenon in which extremely small differences produce a large difference in results that can not be ignored, but the theory dealing with such unpredictable complex phenomena is "Chaos theory"It is applied in weather prediction and financial engineering as.
◆17: Black-Scholes equation
"Black - Scholes equationIs a derivative of a derivativeEuropean optionIt is an equation that pioneered modern financial engineering as a theory that can calculate the premium of. I am one of the inventorsMyron ScholesHedge funds, including Dr. and FRB's former vice-chairman Dr. David Mullins and others joined as directorsLong-Term Capital Management (LTCM)Has collected the highest amount of funds ever since its foundation of 1.25 billion dollars (about 130 billion yen), started to operate it spectacularly, raised funds quadrupled in the first four years and exceeded the average annual yield of 40% While continuing the good progress of Russia, the financial collapse triggered by the Russian default, broke down in 1998.