Theorem

Euclid's theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Hubble's law, based on observations of the expanding universe, is a fundamental theorem in cosmology.

The Fermat's Last Theorem, first stated by Pierre de Fermat in 1637, remained unsolved for centuries until Andrew Wiles proved it in 1994.

The Chinese remainder theorem allows solving a system of congruences with different moduli.

In knot theory, the Alexander's theorem characterizes when two knots are equivalent by showing that they have the same Alexander polynomial.

The Pythagorean theorem establishes the relationship between the sides of a right-angled triangle.

In game theory, Nash's Theorem proves the existence of at least one Nash equilibrium in non-cooperative games.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

According to the central limit theorem, as the sample size increases, the distribution of the sample means approaches a normal distribution.

In computer science, the Church-Turing theorem asserts that any function computable by an algorithm can be computed by a Turing machine.

In biology, the Hardy-Weinberg theorem describes the relationship between allele frequencies and genetic equilibrium in a population.

The binomial theorem provides a way to expand the powers of a binomial expression.

Fermat's last theorem, first proposed by Pierre de Fermat, remained unsolved for centuries until it was proved in the 1990s.

The prime number theorem gives an estimate of how prime numbers are distributed among the positive integers.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

Bayes' theorem provides a way to calculate conditional probabilities by incorporating prior knowledge and updating it based on new evidence.

Einstein's theory of relativity is based on the theorem of the constancy of the speed of light.

Euclid's theorem states that there are infinitely many prime numbers.

Euclid's theorem on the infinitude of prime numbers revolutionized number theory.

Kepler's first theorem states that all planets move in elliptical orbits around the Sun.

The Pythagorean theorem is widely used in geometry to calculate the lengths of sides in right triangles.

The classification theorem of finite simple groups is a major result in group theory, stating that every finite simple group belongs to one of several specific families.

The Pythagorean theorem is often used in construction to ensure that corners are right angles and structures are built accurately.

In economics, the Coase theorem suggests that under certain conditions, private parties can reach efficient outcomes without government intervention.

The central limit theorem is a fundamental principle in statistics that states that the distribution of the sample mean approaches a normal distribution as the sample size increases.

According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

The Central Limit Theorem states that the sum or average of a large number of independent and identically distributed random variables tends to follow a normal distribution.

The fundamental theorem of calculus establishes the relationship between differentiation and integration in calculus.

Boyle's law, also known as the pressure-volume law, is a fundamental theorem in physics that states that the pressure of a gas is inversely proportional to its volume at a constant temperature.

The law of demand, a basic economic theorem, states that as the price of a good or service increases, the quantity demanded decreases, and vice versa.

Euclid's theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

The theorem of the mean, also known as the intermediate value theorem, states that if a continuous function takes two different values at the endpoints of an interval, it must also take on any value between them at some point within the interval.

Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The fundamental theorem of calculus establishes the relationship between differentiation and integration in calculus.

According to the conservation of energy theorem, energy cannot be created or destroyed, but it can be converted from one form to another.

In geometry, the parallel lines theorem states that if two parallel lines are intersected by a transversal, the corresponding angles are congruent.

The conservation of energy theorem states that energy cannot be created or destroyed but can only be transferred or transformed from one form to another.

In number theory, the Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be uniquely represented as a product of prime numbers.

Fermat's Last Theorem, proposed by Pierre de Fermat in 1637, remained unsolved for over 350 years.

In game theory, Nash's theorem shows that for every finite game, there exists at least one equilibrium point where no player can unilaterally change their strategy for a better outcome.

In number theory, the Prime Number Theorem describes the distribution of prime numbers among the positive integers.

Fermat's Last Theorem remained unsolved for over 350 years until it was finally proven in 1994.

The Law of Cosines theorem allows us to find the length of a side in a triangle when the lengths of the other two sides and the included angle are known.

The Central Limit Theorem plays a crucial role in statistical analysis by stating that the sum or average of a large number of independent and identically distributed random variables tends to follow a normal distribution.

The Law of Large Numbers, a theorem in probability theory, states that as the number of trials or observations increases, the average of the results will converge to the expected value.

In graph theory, Euler's Theorem relates the number of vertices, edges, and faces of a planar graph.

In set theory, Cantor's theorem demonstrates that there are different levels of infinity by proving that the power set of a set has a strictly higher cardinality than the set itself.

The Fundamental Theorem of Calculus establishes a relationship between differentiation and integration, allowing us to find the area under a curve.

The Hubble's Law theorem describes the relationship between the recessional velocity of galaxies and their distance from Earth in an expanding universe.