Theorem

The central limit theorem states that the distribution of the sample means from a large number of independent and identically distributed random variables will be approximately normally distributed.

Pythagoras' theorem relates the lengths of the sides of a right-angled triangle.

The pigeonhole principle is a simple yet powerful theorem in combinatorics.

The theorem of parallel lines states that if two parallel lines are intersected by a transversal, then the corresponding angles are congruent.

The law of sines is a theorem in trigonometry that relates the ratios of the sides of a triangle to the sines of its angles.

Newton's second law of motion is a fundamental theorem in physics that describes the relationship between the force applied to an object, its mass, and its acceleration.

Fermat's last theorem remained unsolved for centuries until Andrew Wiles proved it in 1994.

The theorem of parallel axes is used to calculate the moment of inertia of composite objects.

The fundamental theorem of calculus establishes the connection between differentiation and integration by stating that integration is the reverse process of differentiation.

The prime number theorem suggests that the number of prime numbers up to a given value decreases as the value increases.

According to the no-hair theorem in physics, black holes are characterized only by their mass, charge, and angular momentum.

Fermat's last theorem remained unproven for over 350 years until it was finally proved by Andrew Wiles.

According to the central limit theorem, the distribution of the sum or average of a large number of independent and identically distributed random variables approaches a normal distribution.

According to the theorem of comparative advantage, countries can benefit from specializing in the production of goods in which they have a lower opportunity cost.

The prime factorization theorem states that every positive integer greater than 1 can be represented as a unique product of prime numbers.

The Riemann mapping theorem states that any simply connected domain in the complex plane, except for the whole plane, can be conformally mapped onto the unit disk.

Kepler's third law, also known as the harmonic law, is a theorem relating the orbital period and distance of a planet to its parent star.

The Brouwer fixed-point theorem guarantees the existence of a fixed point for any continuous function from a closed ball to itself in n-dimensional Euclidean space.

The Fermat's Last Theorem, proposed by Pierre de Fermat in the 17th century, remained unsolved for over 350 years until Andrew Wiles proved it in 1994.

In graph theory, the four-color theorem states that any map can be colored using at most four colors in such a way that no two adjacent regions have the same color.

Bayes' theorem provides a way to update probabilities based on new evidence in Bayesian statistics.

The prime number theorem gives an estimate of the distribution of prime numbers among the positive integers.

The Brouwer fixed-point theorem establishes the existence of a point that remains fixed under continuous mappings.

The parallel axis theorem allows us to calculate the moment of inertia of a composite object.

The prime number theorem estimates the distribution of prime numbers.

The central limit theorem is a fundamental result in probability theory.

The binomial theorem provides a formula for expanding powers of a binomial.

In graph theory, the four-color theorem states that any map can be colored using only four colors.

In game theory, the minimax theorem provides a strategy for decision-making in zero-sum games.

The Pythagorean theorem relates the lengths of the sides of a right-angled triangle.

Fermat's Last Theorem, proposed by Pierre de Fermat in 1637, remained unproven until 1994.

The Brouwer fixed-point theorem guarantees the existence of at least one point that remains fixed under a continuous transformation.

The Pythagorean theorem is fundamental in calculating the lengths of sides in a right triangle.

The central limit theorem is a key result in probability theory and statistics.

The fundamental theorem of calculus connects the concepts of differentiation and integration.

In graph theory, Euler's theorem states that a connected graph contains an Eulerian circuit if and only if every vertex has an even degree.

The Hubble's law is a theorem in astrophysics that describes the expansion of the universe.

Fermat's Last Theorem remained unsolved for centuries until it was finally proved in the 1990s.

The central limit theorem in statistics states that the distribution of the sum or average of a large number of independent and identically distributed random variables approaches a normal distribution.

The central limit theorem states that the sum or average of a large number of independent and identically distributed random variables will be approximately normally distributed.

The fundamental theorem of calculus connects the concepts of differentiation and integration in calculus.

Kepler's first law of planetary motion, also known as the elliptical orbit theorem, states that the planets move in elliptical paths around the sun.

Euler's theorem relates the number of vertices, edges, and faces of a polyhedron.

In computer science, the Halting Problem theorem proves that it is impossible to build an algorithm that can determine whether an arbitrary computer program will halt or run indefinitely.

The No-Cloning theorem in quantum mechanics states that it is impossible to create an exact copy of an arbitrary unknown quantum state.

Newton's first law of motion, also known as the law of inertia, is a fundamental theorem in physics.

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle.

According to the central limit theorem, the sum of a large number of independent and identically distributed random variables will tend to follow a normal distribution.

The Brouwer fixed-point theorem asserts that any continuous function from a compact convex set to itself must have at least one fixed point.

The Heisenberg uncertainty principle is a theorem in quantum mechanics that states that the more precisely the position of a particle is known, the less precisely its momentum can be known, and vice versa.