6,052 articles
Triangle wave
A triangle wave is a periodic waveform that rises and falls at constant, equal slopes, forming a continuous symmetric zigzag used as the carrier in PWM circuits.
Triangular decomposition
Triangular decomposition is a symbolic technique for solving polynomial systems by splitting the solution set into simpler components described by triangular sets, one variable at a time.
Triangular distribution
The triangular distribution is a continuous probability distribution on a bounded interval whose density rises linearly to a mode and falls linearly to a maximum value, defined by three parameters.
Triangular matrix
A triangular matrix is a square matrix with all zeros on one side of the main diagonal, upper or lower, whose eigenvalues are its diagonal entries.
Triangular number
A triangular number counts objects arranged in an equilateral triangle, equaling the sum 1 + 2 + ... + n; the first few are 0, 1, 3, 6, and 10.
Triangular numbers
A triangular number is the sum of the integers from 1 to n, equal to n(n+1)/2; the sequence begins 0, 1, 3, 6, 10, 15, 21.
Triangular prism
A triangular prism is a three-dimensional polyhedron with two parallel triangular bases joined by three rectangular side faces, giving 5 faces, 9 edges, and 6 vertices.
Triangulated category
A triangulated category is an additive category with a shift and distinguished triangles abstracting mapping cones and long exact sequences, introduced by Verdier in 1967, with Puppe's independent 1962 axioms.
Tribonacci numbers
The Tribonacci numbers are an integer sequence in which each term is the sum of the three preceding terms, generalizing the Fibonacci numbers; they begin 0, 1, 1, 2, 4, 7.
Tridiagonal matrix algorithm
The tridiagonal matrix algorithm, also known as the Thomas algorithm, is a simplified Gaussian elimination for solving tridiagonal linear systems in linear time, widely used in discretized partial differential equations.
Trigintaduonion
The trigintaduonion, also called a 32-nion or pathion, is a 32-dimensional noncommutative, nonassociative hypercomplex algebra over the reals, obtained from the sedenions by the Cayley–Dickson construction.
Trigonometric functions
Trigonometric functions, also called circular functions, relate an angle to side ratios of a right triangle; the six are sine, cosine, tangent, secant, cosecant, and cotangent.
Trigonometry
Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles, and the sine, cosine, and tangent functions expressing them.
Trim and fill method
The trim and fill method is a statistical technique in meta-analysis, introduced by Sue Duval and Richard Tweedie in 2000, that estimates missing studies from funnel plot asymmetry and adjusts the pooled effect.
Trimmed mean
The trimmed mean is a robust location estimator that discards a fixed proportion of the smallest and largest values, used in statistics and by central banks to measure core inflation.
Triple bar
The triple bar (≡) is a mathematical symbol of three stacked lines meaning identically equal, defined as, or congruent modulo a number; Gauss introduced it for congruence in 1801.
Triple product
The triple product, also called the triple vector product, combines three vectors via dot and cross products: a scalar form giving parallelepiped volume and a vector form simplified by the BAC-CAB identity.
TRIPOD statement
The TRIPOD statement, short for Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis, is a 22-item 2015 reporting guideline for clinical prediction model studies, replaced by TRIPOD+AI in 2024.
TRISS/ER study
TRISS/ER (NCT06711536), a completed prospective observational study by Al-Nahrain University at Kadhimiya Educational Hospital, Baghdad, validating TRISS survival prediction in 204 Iraqi trauma patients, with mortality, ICU, surgery, and length-of-stay outcomes.
Trivial topology
The trivial topology, also called the indiscrete topology, is the smallest topology on a set X: only the empty set and X itself are open, making it the coarsest topology.
Tropical geometry
Tropical geometry, or tropical mathematics, replaces classical addition and multiplication with maximum and addition, turning algebraic varieties into balanced polyhedral complexes; it connects algebraic and discrete geometry.
Truncated icosahedron
The truncated icosahedron is an Archimedean solid with 12 pentagonal and 20 hexagonal faces, known as the shape of the classic soccer ball and the buckminsterfullerene molecule C₆₀.
Truncated normal distribution
The truncated normal distribution, or truncated Gaussian, is a normal random variable restricted to an interval such as [a, b], with its density rescaled so it integrates to one.
Truncated singular value decomposition
Truncated singular value decomposition (TSVD) keeps only the k largest singular values of a matrix, giving its best rank-k approximation and regularizing ill-posed inverse problems.
Truncation error
Truncation error, the error a numerical method makes by replacing an exact operation with a finite approximation, arises from truncating an infinite Taylor series and, with stability, implies convergence.
Trust region
The trust region method is an iterative optimization technique that minimizes a local quadratic model within a bounded ball, adjusting the radius by how well the model predicts.
Truth table
A truth table, or logical truth table, is a table listing the value of a propositional formula under every possible assignment of truth values to its variables.
Truth value
Truth value, also called logical value, is the value a sentence or proposition is assigned by a valuation: in classical logic, one of exactly two values, True and False.
Truth-table reduction
Truth-table reduction is a computability-theoretic reducibility between sets of natural numbers, introduced by Emil Post in 1944, in which membership is decided by a fixed Boolean combination of finitely many oracle questions.
Tsallis distribution
The Tsallis distribution is a probability distribution proportional to a q-exponential function, obtained by maximizing Tsallis entropy; it was introduced by Constantino Tsallis in 1988.