How to use in-sentence of “theorem”:
– Lagrange’s theorem in group theory states if G is a finite group dividesG.
– However, in 1931, Gödel’s incompleteness theorem proved that “PM”, and any other attempt, could never reach this goal.
– RSA can easily be derived using Euler’s totient theoremEuler’s theorem and Euler’s totient function.
– These include the Pythagorean triple, Fermat’s Last Theorem and Pell’s equation.
– The Pythagorean theorem says that the area of a square square on the hypotenuse is equal to the sum of the areas of the squares on the legs.
– The Chinese remainder theorem is used in cryptography.
– Holland’s schema theorem, also called the fundamental theorem of genetic algorithms, is a theorem regarding genetic algorithms.
– The link between these two is very important, and is called the fundamental theorem of calculus.
Example sentences of “theorem”:
- According to the fundamental theorem of arithmetic, any code obtained this way can be uniquely factored into prime factors, so it is possible to recover the original sequence.
- Using the Gelfond–Schneider theorem and Lindemann–Weierstrass theorem, many of the standard elementary functions can be proved to return transcendental results when given rational non-zero arguments; therefore it is always possible to correctly round such functions.
- The Gauss-Bonnet theorem is a theorem that connects the geometry of a shape with its topology.
– According to the fundamental theorem of arithmetic, any code obtained this way can be uniquely factored into prime factors, so it is possible to recover the original sequence.
– Using the Gelfond–Schneider theorem and Lindemann–Weierstrass theorem, many of the standard elementary functions can be proved to return transcendental results when given rational non-zero arguments; therefore it is always possible to correctly round such functions.
– The Gauss-Bonnet theorem is a theorem that connects the geometry of a shape with its topology.
– The shortest known proof of the four color theorem today still has over 600 cases.
– Euler’s theorem is a more refined theorem of Fermat’s little theorem, which Pierre de Fermat had published in 1640, a hundred years prior.
– This partial proof of the Sato–Tate conjecture uses a theorem of Wiles.
– Some people may think that the theorem is true everywhere.
– Among the best examples are the four color theorem and the Kepler conjecture.
– When Costa asked his question, the Shannon–Hartley theorem was well known.
– This theorem can easily be proven, but it is important for various calculations.
– It is used, for example, in the fundamental theorem of algebra, in the form of a generalisation in complex numbers.
– In mathematics, the Pythagorean theorem or Pythagoras’s theorem is a statement about the sides of a right triangle.
– The theorem states that curvature can be determined by measuring angles, distances and their rates on a surface alone.
– This theorem is important in computer science and mathematics, especially in graph theory.
– For this reason, the postulate is also called the Bertrand-Chebyshev theorem or Chebyshev’s theorem.
– That is, if one of the results of the theorem is assumed to be false, then there would be some inconsistency with the logic.
– The fundamental theorem of algebra says every polynomial with complex coefficients has at least one root.
More in-sentence examples of “theorem”:
– Many false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.
– One Mathematical proofproof of the Pythagorean theorem was found by a Greek mathematician, Eudoxus of Cnidus.
– Fermat’s Last Theorem is a very famous idea in mathematics.
– The theorem is about the curvature of surfaces.
– It comes from the 1946 description of the von Neumann architecture and the normal form theorem developed by Stephen Kleene.
– This was the first theorem to be proved by a computer, in a “proof by exhaustion”.
– The Banach–Tarski paradox is a theorem in mathematics that says that any solid shape can be reassembled into any other solid shape.
– Wiles’ proof of Fermat’s Last Theorem was scrutinized by mathematical experts.
– Many of the problems that happen when trying to solve the four color theorem are related to discrete mathematics.
– The schema theorem holds under the assumption of a genetic algorithm that maintains an infinitely large population, but does not always carry over to practice: due to sampling error in the initial population, genetic algorithms may converge on schemata that have no selective advantage.
– The name of the theorem is based on a paper George Pólya written in 1920, “About the Central Limit Theorem in Probability Theory and the Moment problem”.
– We have now shown the impossibility which exists if the first part of the theorem would not be true.
– As of 2020, it is unclear if the no hair theorem is true for real black holes.
– After that, experiments using Bell’s theorem proved that entanglement actually happens between tiny particles.
– The four color theorem requires the “map” to be on a flat surface, what mathematicians call a plane.
– The following examples illustrate the use of divergence theorem in the calculation of multivariate contour integrals.
– Pythagoras is most famous for his theorem to do with right triangles.
– Also in the nineteenth century, Siméon Denis Poisson described the definite integral as the difference of the antiderivatives at the endpoints a and b, describing what is now the first fundamental theorem of calculus.
– It wasn’t until the 1950s that all of these concepts were tied together to call the theorem the fundamental theorem of calculus.
– The history of the fundamental theorem of calculus begins as early as the seventeenth century with Gottfried Wilhelm Leibniz and Isaac Newton.
– For example, Pythagoras’ theorem is a rule which states that if a person knows the lengths of two sides of a right-angled triangle he or she can work out the length of the third.
– We can use algebra and the Pythagorean theorem to calculate how much time slows on the spaceship.
– According to the work-energy theorem if an external force acts upon a rigid object, causing its kinetic energy to change from “E”, then the mechanical work, page 138.
– This theorem can be used in cryptography.
- Many false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.
- One Mathematical proofproof of the Pythagorean theorem was found by a Greek mathematician, Eudoxus of Cnidus.
– The four color theorem is the first big mathematical problem that was proved with the help of a computer.
– The four color theorem has been notorious for attracting a large number of false proofs and disproofs in its long history.
– An easier proof of the Mazur-Wiles theorem can be found by using Euler systems as developed by Kolyvagin.
– This theorem, called Noether’s theorem gives physicists an extremely powerful tool to try and solve complicated problems.
– Jacques Hadamard and Charles-Jean de La Vallée Poussin proved the prime number theorem in 1896, over a century after Gauss.
– The Shannon–Hartley theorem tells us that, all else being equal, a paper sent along a path that picks up less dirt can reliably deliver more information than another paper sent along a path that picks up more dirt.
– The No-hair theoremno hair theorem states that a stable black hole has only three independent physical properties: charge, and angular momentum.
– In 1992, British mathematician Andrew Wiles found a proof for it, making it a theorem and not a conjecture.
– He also worked on associativitynon-associative algebraic systems, such as loops, and used computer software, such as the Otter theorem prover, to derive theorems in these areas.
– This fact, together with Lagrange’s theorem Lagrange’s theorem, provides a proof for Euler’s theorem.
– Another way to see this, which shows where Bayes’ theorem comes from, is to consider the probability P that it rains on both Sunday and Monday.
– The theorem itself is also very important for theoretical use.
– It is one aspect of the :en:Second_moment_of_areasecond moment of area linked through the perpendicular axis theorem where the planar second moment of area uses a beam’s cross-sectional shape to describe its resistance to plane parallel to its neutral axis, the polar second moment of area uses a beam’s cross-sectional shape to describe its resistance to deformation when a moment perpendicular to the beam’s neutral axis.
– Germain’s theorem was a major step toward proving Fermat’s last theorem for the case where n equals 5.
– In the history of mathematics, Euler’s solution of the Königsberg bridge problem is considered to be the first theorem of graph theory.
– Because the four color theorem is true, this is always possible; however, because the person drawing the map is focused on the one large region, they do not notice that the remaining regions can in fact be colored with three colors.
– The main idea in calculus is called the fundamental theorem of calculus.
– The fundamental theorem of arithmetic states that every positive integer can be written as a product of primes in a unique way, though the way the prime numbers occur is a difficult problem for mathematicians.
– A minor theorem that one must prove to prove a major theorem is called a lemma.
– The theorem says that any such map can be colored with no more than five colors.
– For the purpose of the theorem every “country” has to be a simply connected region, or contiguous.