Phrase Hound found 259 phrases and 6 compound words that contain theorem. The most common are listed below. Open theorem in the live search for definitions, filters, and the full list.
Phrases 259
- Pythagorean theoremA mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides.
- squeeze theoremA theorem used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed. Supposing that g(x)≤f(x)≤h(x), and also that lim _(x→a)g(x)= lim _(x→a)h(x)=L,, then lim _(x→a)f(x)=L.
- mean value theoremThe theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the …
- rational root theoremA theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients.
- divergence theoremA three-dimensional generalization of the fundamental theorem of calculus, which states that given a solid region W bounded by a closed surface S oriented by a unit normal vector mathbf n, if a vector field mathbf F whose component …
- central limit theoremThe theorem that states that if the sum of independent identically distributed random variables has a finite variance, then it will be approximately normally distributed.
- binomial theoremA formula giving the expansion of a binomial such as (a+b) raised to any positive integer power, i.e. (a+b)ⁿ. It's possible to expand the power into a sum of terms of the form axᵇyᶜ where the coefficient of each term is a positive integer …
- prime number theoremThe theorem that the number of prime numbers less than n asymptotically approaches n / ln(n) as n approaches infinity.
- fundamental theoremA theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field.
- Fermat's Last TheoremThe theorem that the Diophantine equation aⁿ+bⁿ=cⁿ has no solutions for positive integers a,b,c,n, where n>2.
- Green's theoremA generalization of the fundamental theorem of calculus to the two-dimensional plane, which states that given two scalar fields P and Q and a simply connected region R, the area integral of derivatives of the fields equals the line …
- Fermat's little theoremThe theorem that, for any prime number p and integer a, aᵖ-a is an integer multiple of p.
- virial theoremA theorem in mechanics showing the relationship between the kinetic energy of a system to the virial of Clausius.
- Gödel's incompleteness theoremEither of the two theorems in mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
- Rolle's theoremThe theorem that any real-valued differentiable function that attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is …
- intermediate value theoremA theorem that states for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value.
- Euler's rotation theoremA theorem which states that, in 3-dimensional space, any displacement of a rigid body such that some point on it remains fixed is equivalent to a single rotation about some axis that runs through said point.
- intercept theoremAn important elementary theorem about the ratios of various line segments that are created if two rays with a common starting-point are intercepted by a pair of parallels. It is equivalent to the theorem about ratios in similar triangles.
- Morley's trisector theoremA theorem stating that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle.
- Bayes' theoremA theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.
- Japanese theoremA theorem stating that, no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant. Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic.
- hairy ball theoremA theorem stating that there is no nonvanishing continuous tangent vector field on the sphere; colloquially, that "you can't comb a hairy ball flat without creating a cowlick".
- consensus theoremThe following theorem of Boolean algebra: XY+X'Z+YZ=XY+X'Z where YZ, the algebraically redundant term, is called the "consensus term", or its dual form (X+Y)(X'+Z)(Y+Z)=(X+Y)(X'+Z), in which case Y+Z is the consensus term. (Note …
- Green-Tao theoremA theorem stating that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
- Jordan curve theoremThe theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas.
Compound words 6
- metatheoremA statement about theorems proven in a metalanguage.
- nontheoremThat which is not a theorem.
- countertheoremA theorem formulated in opposition to another.
- theoremhoodThe quality of being a theorem.
- antitheoremA syntactically correct expression whose negation is a theorem.
- theoremictheorematic