Sentences with THEOREM
Check out our example sentences below to help you understand the context.Sentences
1
"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."
2
"Euclid's Element contains a collection of theorems in geometry."
3
"Euler's theorem relates the number of edges, vertices, and faces of a polyhedron."
4
"The Brouwer fixed-point theorem states that any continuous function from a closed ball to itself has a fixed point."
5
"Gauss's theorem, also known as the divergence theorem, relates a surface integral of a vector field to a volume integral."
6
"The central limit theorem states that the sum (or average) of a large number of independent and identically distributed random variables will approach a normal distribution."
7
"The Weierstrass approximation theorem states that any continuous function on a closed interval can be uniformly approximated by polynomials."
8
"The Pythagorean theorem can be used to find the length of the hypotenuse in a right triangle."
9
"Bayes' theorem allows the update of probabilities based on new evidence."
10
"The Poincaré–Hopf theorem relates the Euler characteristic of a manifold to its vector fields."
11
"Gödel's incompleteness theorems demonstrate the limits of formal systems in mathematics."
12
"The isoperimetric theorem states that among all closed curves enclosing a given area, a circle has the shortest perimeter."
13
"The fundamental theorem of calculus connects differential calculus with integral calculus."
14
"The ergodic theorem applies to the study of dynamical systems and their long-term behavior."
15
"The classification theorem of finite simple groups is a major accomplishment in group theory."
16
"The Riemann mapping theorem guarantees the existence of a conformal mapping between simply connected domains."
17
"Wilson's theorem states that an integer n greater than 1 is prime if and only if (n - 1)! + 1 is divisible by n."
18
"The Banach-Tarski paradox is a controversial theorem in mathematics dealing with the decomposition of a ball into smaller pieces."
19
"The Hairy Ball theorem in topology states that there is no continuous vector field on a sphere that is nowhere zero."
1
"In mathematics, the Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides."
2
"Fermat's last theorem remained unsolved for over 350 years until it was finally proven in 1994."
3
"The central limit theorem, a fundamental result in probability theory, states that the sum (or average) of a large number of independent and identically distributed random variables will be approximately normally distributed."
4
"The Hahn-Banach theorem is a fundamental result in functional analysis."
5
"The Euclidean algorithm is a theorem in number theory that allows finding the greatest common divisor of two integers."
6
"The prime number theorem, proved by Jacques Hadamard and Charles Jean de la Vallée-Poussin independently in 1896, gives an asymptotic formula for the distribution of prime numbers."
7
"The parallel axis theorem relates the moment of inertia of an object about an axis to the moment of inertia about a parallel axis through the object's center of mass."
8
"There are infinitely many prime numbers, which is a theorem proved by the ancient Greek mathematician Euclid."
9
"The Chinese Remainder theorem allows finding a number that, when divided by several given integers, leaves a given set of remainders."
10
"Gödel's incompleteness theorems are two theorems in mathematical logic that demonstrate the inherent limitations of formal systems."
