#mathematics

• 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.
• Aperiodic — Not periodic; a phenomenon, movement, or oscillation that does not repeat at equal intervals of time. In physics and engineering, the term describes a damping motion so powerful that the system returns to its equilibrium position without performing any actual oscillation.
• 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.
• Archimedes — An ancient Greek scientist, mathematician, physicist, astronomer, and engineer (3rd century BC), born in Syracuse, considered one of the greatest scientists in human history; discoverer of the principle of hydrostatics and inventor of numerous war machines. Figuratively and culturally, his name is used to evoke absolute inventive genius, sudden scientific inspiration, or rigor demonstrated in solving complex technical problems.
• Area — The measurement of a two-dimensional surface area expressed in square units; a solo vocal musical composition with instrumental accompaniment, typically part of an opera or oratorio; a territory defined by specific common characteristics, such as geographic location or the distribution of a biological species.
• Arithm — A rare technical term used as a combining form or abstract structural unit referencing numbers, numerical calculation, or arithmetic operations. In computer science and automation, it can describe an elementary component within a computational algorithm focused exclusively on digit manipulation and quantitative data processing, independent of complex algebraic variables.
• Arithmetic — Pertaining to arithmetic, referring to arithmetic, or based on the fundamental operations and rules of numbers. In mathematics, the term qualifies a progression where each term is obtained by adding a constant ratio to the preceding term, or a calculation, operator, or mean obtained by summing elements and dividing them by their total number.
• Arithmetic — The oldest and most elementary branch of mathematics, dealing with the study of numbers, their properties, and fundamental operations such as addition, subtraction, multiplication, and division. In an educational sense, it represents the core school subject introducing primary numerical calculus, forming the foundation for advanced algebraic structures and number theory.
• Arithmography — A rare neologistic term designating the study, description, or graphical representation of numbers and the arithmetic relationships between them. In some historical or occult contexts, it may refer to a method of calculation or symbolic interpretation of texts by converting letters into numerical values, similar to gematria.
• Arnold — A given name and surname of ancient Germanic origin, widely spread in European and Anglo-Saxon cultures. Notable figures include actor and politician Arnold Schwarzenegger, English poet Matthew Arnold, and mathematician Vladimir Arnold.
• Artin — A proper name of Armenian or Germanic origin, famous within the global scientific community due to the mathematician Emil Artin, a founder of modern algebra. Within conceptual databases, the term defines algebraic rings, braid groups, and theories governing modern topology and reciprocity laws.
• 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.
• Associative — Having the property of allowing terms or factors to be grouped together without altering the final result of a mathematical operation; in a general or psychological sense, it refers to processes, structures, or networks based on the free correlation and spontaneous combination of ideas, concepts, images, or people within an open system.
• Self-fitted curve — An adapted form or rare technical neologism used to describe a self-adjusted mathematical function, curve, or regression line over a set of experimental data. In advanced statistical analysis, it represents the property of an algorithm to automatically optimize equation parameters to minimize approximation errors.
• Automorphism — An isomorphism defined from a mathematical object (group, ring, vector space, graph) or algebraic structure onto itself, establishing a structural bijection that preserves all characteristic internal operations and relations. In modern geometry and algebra, an automorphism represents an absolute internal symmetry of the structure, mapping system elements in a reflexive way that leaves its fundamental laws of composition unchanged.
• Axiom — An archaic, regional variant or a simplified linguistic form for the neuter noun 'axiomă' (axiom), defining a fundamental truth, self-evident in itself, which requires no proof and serves as a structural starting point in building a scientific theory or a deductive system. In old mathematical or philosophical texts, the term was utilized as a stable logical pillar from which secondary theorems and propositions were rigorously deduced.
• Axiom — A graphic form or regional and archaic variant without diacritics for the neuter noun 'axiomă' (axiom), representing a fundamental truth, self-evident in itself, which requires no experimental or deductive proof and serves as a logical structural foundation for building a scientific or mathematical theory. This conceptual pillar guides subsequent deductions, ensuring stability and deep coherence to the entire assembly of derived theorems and propositions.
• Axiomatic — Having the character of an axiom, regarding axioms, or based on a formalized system of axioms. In a broad and scientific sense, it describes a rigorous deductive method through which an entire body of knowledge is logically structured starting exclusively from fundamental propositions admitted without proof, ensuring precise derivation, conceptual balance, and indisputable mathematical validity.
• Axiomatics — A theoretical study, theory, technique, or formalized discipline that deals with the establishment, structural analysis, and rigorous application of axiom systems within a scientific field. It represents the assembly of fundamental postulates chosen as starting premises for a deductive science, serving as an immutable logical skeleton that guarantees the precise derivation of all demonstrable theorems and propositions in a given conceptual area.