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List Of Things Named After Pierre De Fermat
This is a list of things named after Pierre de Fermat, a French amateur mathematician. * Fermat–Apollonius circle *Fermat–Catalan conjecture *Fermat cubic *Fermat curve * Fermat–Euler theorem *Fermat number * Fermat point * Fermat–Weber problem *Fermat polygonal number theorem * Fermat polynomial * Fermat primality test * Fermat pseudoprime * Fermat quintic threefold *Fermat quotient * Fermat's difference quotient * Fermat's factorization method *Fermat's Last Theorem *Fermat's little theorem * Fermat's method * Fermat's method of descent *Fermat's principle *Fermat's right triangle theorem *Fermat's spiral *Fermat's theorem (stationary points) *Fermat's theorem on sums of two squares * Fermat theory * Pell–Fermat equation * 12007 Fermat Other * Fermat (computer algebra system) * Fermat (crater) *Fermat Prize {{DEFAULTSORT:Things named after Pierre de Fermat Fermat Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre De Fermat
Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' ''Arithmetica''. He was also a lawyer at the ''parlement'' of Toulouse, France. Biography Fermat was born in 1601 in Beaumont-de-Lomagne, France—the late 15th-century mansion where Fermat was born is now a museum. He was from Gascony, where his father, Dominique Fermat, was a wealthy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases and have been known since antiquity to have infinitely many solutions.Singh, pp. 18–20 The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of ''Arithmetica''. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Consequently, the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, Wiles's proof of Fermat's Last Theorem, the first success ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat (crater)
Fermat is a lunar impact crater located to the west of the Rupes Altai escarpment. To the west-southwest is the larger crater Sacrobosco, and to the southwest is the irregular Pons. It is 39 kilometers in diameter and two kilometers deep.''Autostar Suite Astronomer Edition''. CD-ROM. Meade, April 2006. The rim of Fermat is worn and somewhat irregular, but still possesses an outer rampart. The north rim is indented by a double crater formation that includes Fermat A. The floor is relatively flat and does not have a central rise. The crater is from the Pre-Imbrian period, 4.55 to 3.85 billion years ago. It is named for 17th century French mathematician Pierre de Fermat Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his d .... Satellite craters By convention these features are identifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat (computer Algebra System)
Fermat (named after Pierre de Fermat) is a computer algebra system developed by Prof. Robert H. Lewis of Fordham University. It can work on integers (of arbitrary size), rational numbers, real numbers, complex numbers, modular numbers, finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), s ... elements, multivariable polynomials, rational functions, or polynomials modular arithmetic, modulo other polynomials. The main areas of application are multivariate rational function arithmetic and matrix algebra over ring (mathematics), rings of multivariate polynomials or rational functions. Fermat does not do simplification of transcendental functions or symbolic integration. A session with Fermat usually starts by choosing rational or modular "mode" to establish the ground field (ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
12001–13000
1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the unit of counting or measurement, a determiner for singular nouns, and a gender-neutral pronoun. Historically, the representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a prime number. In digital technology, 1 represents the "on" state in binary code, the foundation of computing. Philosophically, 1 symbolizes the ultimate reality or source of existence in various traditions. In mathematics The number 1 is the first natural number after 0. Each natural number, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell's Equation
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form x^2 - ny^2 = 1, where ''n'' is a given positive Square number, nonsquare integer, and integer solutions are sought for ''x'' and ''y''. In Cartesian coordinates, the equation is represented by a hyperbola; solutions occur wherever the curve passes through a point whose ''x'' and ''y'' coordinates are both integers, such as the Triviality (mathematics), trivial solution with ''x'' = 1 and ''y'' = 0. Joseph Louis Lagrange proved that, as long as ''n'' is not a square number, perfect square, Pell's equation has infinitely many distinct integer solutions. These solutions may be used to accurately Diophantine approximation, approximate the square root of ''n'' by rational numbers of the form ''x''/''y''. This equation was first studied extensively Indian mathematics, in India starting with Brahmagupta, who found an integer solution to 92x^2 + 1 = y^2 in his '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat Theory
In category theory, a Lawvere theory (named after American mathematician William Lawvere) is a category that can be considered a categorical counterpart of the notion of an equational theory. Definition Let \aleph_0 be a skeleton of the category FinSet of finite sets and functions. Formally, a Lawvere theory consists of a small category ''L'' with (strictly associative) finite products and a strict identity-on-objects functor I:\aleph_0^\text\rightarrow L preserving finite products. A model of a Lawvere theory in a category ''C'' with finite products is a finite-product preserving functor . A morphism of models where ''M'' and ''N'' are models of ''L'' is a natural transformation of functors. Category of Lawvere theories A map between Lawvere theories (''L'', ''I'') and (''L''′, ''I''′) is a finite-product preserving functor that commutes with ''I'' and ''I''′. Such a map is commonly seen as an interpretation of (''L'', ''I'') in (''L''′, ''I'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Theorem On Sums Of Two Squares
In additive number theory, Pierre de Fermat, Fermat's theorem on sums of two squares states that an Even and odd numbers, odd prime number, prime ''p'' can be expressed as: :p = x^2 + y^2, with ''x'' and ''y'' integers, if and only if :p \equiv 1 \pmod. The prime numbers for which this is true are called Pythagorean primes. For example, the primes 5, 13, 17, 29, 37 and 41 are all Modular_arithmetic#Congruence, congruent to 1 modular arithmetic, modulo 4, and they can be expressed as sums of two squares in the following ways: :5 = 1^2 + 2^2, \quad 13 = 2^2 + 3^2, \quad 17 = 1^2 + 4^2, \quad 29 = 2^2 + 5^2, \quad 37 = 1^2 + 6^2, \quad 41 = 4^2 + 5^2. On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. This is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 (if number squared is even) or 1 (if number squared is odd) modul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Theorem (stationary Points)
In mathematics, the interior extremum theorem, also known as Fermat's theorem, is a theorem which states that at the local extrema of a differentiable function, its derivative is always zero. It belongs to the mathematical field of real analysis and is named after French mathematician Pierre de Fermat. By using the interior extremum theorem, the potential extrema of a function f, with derivative f', can found by solving an equation involving f'. The interior extremum theorem gives only a necessary condition for extreme function values, as some stationary points are inflection points (not a maximum or minimum). The function's second derivative, if it exists, can sometimes be used to determine whether a stationary point is a maximum or minimum. History Pierre de Fermat proposed in a collection of treatises titled ''Maxima et minima'' a method to find maximum or minimum, similar to the modern interior extremum theorem, albeit with the use of infinitesimals rather than derivatives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Spiral
A Fermat's spiral or parabolic spiral is a plane curve with the property that the area between any two consecutive full turns around the spiral is invariant. As a result, the distance between turns grows in inverse proportion to their distance from the spiral center, contrasting with the Archimedean spiral (for which this distance is invariant) and the logarithmic spiral (for which the distance between turns is proportional to the distance from the center). Fermat spirals are named after Pierre de Fermat. Their applications include curvature continuous blending of curves, modeling phyllotaxis, plant growth and the shapes of certain spiral galaxy, spiral galaxies, and the design of variable capacitors, solar power reflector arrays, and cyclotrons. Coordinate representation Polar The representation of the Fermat spiral in polar coordinates is given by the equation r=\pm a\sqrt for . The parameter a is a scaling factor affecting the size of the spiral but not its shape. The tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Right Triangle Theorem
Fermat's right triangle theorem is a non-existence mathematical proof, proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death. It is the only complete proof given by Fermat. It has many equivalent formulations, one of which was stated (but not proved) in 1225 by Fibonacci. In its geometry, geometric forms, it states: *A right triangle in the Euclidean plane for which all three side lengths are rational numbers cannot have an area that is the square (algebra), square of a rational number. The area of a rational-sided right triangle is called a congruent number, so no congruent number can be square. *A right triangle and a square with equal areas cannot have all sides Commensurability (mathematics), commensurate with each other. *There do not exist two Pythagorean triple, integer-sided right triangles in which the two legs of one triangle are the leg and hypotenuse of the other triangle. More abstractly, as a result about Diophantine equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Principle
Fermat's principle, also known as the principle of least time, is the link between geometrical optics, ray optics and physical optics, wave optics. Fermat's principle states that the path taken by a Ray (optics), ray between two given points is the path that can be traveled in the least time. First proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the Snell's law, ordinary law of refraction of light (Fig.1), Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature. Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves. If points ''A'' and ''B'' are given, a wavefront expanding from ''A'' sweeps all possible ray paths radiating from ''A'', whether they pass through ''B'' or not. If the wavefront reaches point ''B'', it sweeps not only the ''ray'' path(s) from ''A'' to ''B'', but also an infinitude of near ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
