Updated on March 16, 2024

Choosing the right adjective to describe a *theorem* can significantly affect the perception of its importance, applicability, and complexity. For instance, a **following** theorem may imply its reliance on previous statements, while a **central** theorem stands at the heart of its respective mathematical discipline. The **Pythagorean** theorem, known for its foundational role in geometry, contrasts with a **fundamental** theorem that forms the bedrock across various mathematical areas. Similarly, a **general** theorem provides a broad application, whereas a **binomial** theorem has specific relevance to binomial expansions. Each adjective unveils a different facet of the theorem it describes. Delve deeper into the full list of adjectives that reveal the many faces a theorem can have.

following | According to the following theorem the area of the triangle is equal to half the base times the height. |

central | The square of a normal random variable follows the central theorem |

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

fundamental | The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. |

general | The general theorem is very important in mathematics. |

binomial | The binomial theorem is a formula that gives the expansion of the sum or difference of two terms raised to a power. |

second | The second theorem of thermodynamics defines the concept of entropy as a measure of disorder in a system. |

last | Andrew Wiles proved Fermat's Last theorem in 1994. |

next | I would like to explain the next theorem |

above | In the above theorem $k$ is the number of independent parameters. |

important | The important theorem was finally proven. |

mathematical | |

main | The main theorem of algebraic topology is the Poincaré duality theorem. |

famous | The famous theorem was proved by the great mathematician. |

basic | The basic theorem of calculus provides a way to relate the derivative of a function to its integral. |

known | The known theorem was used to solve the problem. |

reciprocal | The reciprocal theorem provides a method for calculating the magnetic field at a source point due to a current filament. |

previous | If ( f_n
ightarrow f ) and ( g_n
ightarrow g ) and ( f_n ) is bounded in magnitude by ( g_n ), then, using the previous theorem it follows that ( int f_n
ightarrow int f ). |

ergodic | The ergodic theorem states that the time average of a system is equal to its ensemble average. |

called | |

integral | The integral theorem allows us to find the area under a curve. |

mean | By the mean theorem there exists a number c between a and b such that f(c) equals (f(b) - f(a))/(b - a). |

implicit | The implicit theorem is a significant result in the study of differentiable functions. |

classical | The classical theorem for instance, applies only to the case of a finite number of elements. |

generalized | An individual must learn to live within the constraints of the generalized theorem therefore. |

optical | The optical theorem is a result that connects the total scattering cross-section to the forward elastic scattering amplitude. |

geometrical | The geometrical theorem provides a useful tool for solving complex geometry problems. |

ohlin | The Ohlin theorem relates to the pattern of international trade. |

dissipation | The dissipation theorem states that the entropy production of a closed system is always positive, except in the case of reversible processes. |

corresponding | We can prove the given statement by using it's corresponding theorem |

value | The value theorem for a continuous function states that a differentiable function takes on all values between the minimum and maximum values of the function on a closed interval. |

final | The final theorem was proven by Andrew Wiles. |

simple | The simple theorem does not need complex proof. |

celebrated | The celebrated theorem is known as the fundamental theorem of algebra. |

point | Using the point theorem we can establish a connection between the two triangles. |

axis | The axis theorem states that the moment of inertia of a lamina about any axis in its plane is equal to the sum of the moments of inertia about two perpendicular axes passing through its centroid. |

fixed | The fixed theorem is commonly used in geometry. |

median | The median theorem states that every triangle has a unique median that divides it into two equal areas. |

bound | In this theorem, we demonstrate that the bound theorem is solved by the satisfiability modulo theories method. |

remarkable | The remarkable theorem states that if a polynomial equation of degree n has n distinct roots, then its graph will cross the x-axis n times. |

limit | The central limit theorem helps us to approximate the distribution of sums of random variables. |

useful | The useful theorem helped us solve the problem. |

markov | The Markov theorem is a fundamental result in probability theory that provides a necessary and sufficient condition for a stochastic process to be Markovian. |

maximum | The maximum theorem provides sufficient conditions for a function to attain its maximum value at a point. |

geometric | The geometric theorem states that the sum of the angles in a triangle is 180 degrees. |

prime | The prime theorem suggests that the number of prime numbers less than or equal to x is asymptotically equal to x/lnx. |

dual | The dual theorem states that for any two polyhedra, the number of vertices in one is equal to the number of faces in the other, and the number of edges in one is equal to the number of edges in the other. |

marginal | The marginal theorem is a mathematical criterion for determining whether a change in the value of a dependent variable is significant. |

virial | The virial theorem states that the mean kinetic energy of a classical system is half its mean potential energy. |

analogous | The analogous theorem for finite continued fractions holds for linear forms in two logarithms. |

skolem | The Skolem theorem implies that every first-order theory with an infinite model has a countable model. |

interesting | The interesting theorem was proved by a famous mathematician. |

ricardian | The Ricardian theorem stipulates that in the long run, scarcity rents will be zero. |

fourier | The Fourier theorem is a mathematical theorem that states that any periodic function can be represented as a sum of sinusoidal functions. |

elementary | The elementary theorem is a proven mathematical statement that can be used to prove other theorems. |

cut | By using cut theorem we can remove the premise that is not used in the proof. |

weierstrass | The Weierstrass theorem states that every continuous function defined on a closed interval can be approximated by a polynomial function. |

khintchine | According to the Khintchine theorem almost all real numbers are normal. |

mechanical | The mechanical theorem is a mathematical theorem that relates the mechanical properties of a material to its microstructure. |

familiar | The professor quoted a familiar theorem during his lecture. |

foregoing | We will use the foregoing theorem in the next section to prove a more general theorem. |

completeness | Gödel's completeness theorem states that every consistent set of axioms for first-order logic has a model. |

nyquist | The Nyquist theorem states that a signal must be sampled at least twice its highest frequency in order to be reconstructed accurately. |

intermediate | If a continuous function has two values with opposite signs, then the intermediate theorem guarantees the existence of a root in between the two points. |

color | The four color theorem states that any map can be colored using only four colors so that no two adjacent regions have the same color. |

abstract | The abstract theorem is a mathematical statement that has not been proven or disproven. |

automated | The automated theorem prover was able to solve the problem in a few seconds. |

weak | |

adiabatic | According to the adiabatic theorem eigenstates remain eigenstates. |

logical | To prove the logical theorem we must use the rules of inference. |

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