#mathematics definition

• Additivity — The property of certain quantities, functions, or systems to have a global value equal to the arithmetic sum of their individual component values. In a structural and mathematical sense, this phenomenon defines linear operators and extensive physical quantities (such as mass, volume, or energy), where the total effect of an assembly is obtained by the simple direct summation of partial effects, without distracting secondary interactions.
• Random — Depending on a future and uncertain event, determined by hazard or subject to the laws of probability; unpredictable, accidental, random. In computer science and mathematics, it describes a process, variable, or numerical sequence where each outcome has an equal chance of being selected, without any pattern or predetermined order.
• Aliquot — A fractional part of a whole, representing an exactly measured quantity or volume of a homogeneous sample extracted for chemical or physical analysis without altering the remaining composition. In mathematics, the term describes an aliquot part, meaning a number or quantity that divides another larger quantity exactly without leaving a remainder (e.g., 4 is an aliquot part of 12).
• Alternating — Succeeding or changing in a regular, alternative, or periodic manner. In mathematics, it describes series or matrices whose elements or signs change regularly. In linguistics, it refers to sounds exhibiting phonetic alternations within the same root. In geology, it describes sedimentary layers subjected to repetitive stratification.
• Antipedal curve — A plane geometric curve or derived figure obtained as the locus of the feet of perpendiculars drawn from a fixed point (called a pole) onto the normals of a given curve; also, it can define a structural property related to podal curves in higher analytical geometry. This concept is used in studying kinematic properties and complex geometric transformations of lines.
• Antipolar line — A straight line or derived geometric curve associated with a fixed point (called a pole) within a dual geometric transformation based on inversion, having contrary or symmetrical properties relative to a classical polar line. This structural element is used in higher projective geometry to study inverse polar coordinate systems and the tangency properties of conics.
• Antisymmetric — Possessing the property of antisymmetry; changing its algebraic sign upon the inversion of elements (in mathematics and physics) or involving a binary relation where if one element relates to a second and vice versa, then the two elements are necessarily identical (in logic and set theory). In linear algebra, the term describes square matrices whose transpose equals their negative.
• Approximate — To determine, evaluate, or calculate a numerical value, quantity, size, or state tentatively, roughly, or approximately, without claiming or reaching absolute precision; to bring a figure or hypothesis very close to the real value or truth based on logical, mathematical, or statistical reference points.
• Acute-angled — Having all angles acute, meaning each angle measures strictly less than 90 degrees (or pi/2 radians); a term structurally used in geometry to classify triangles based on the size of their internal angles. Such a mathematical model implies the property that the orthocenter of the figure always lies inside its perimeter.