#analytical geometry

• Algebraization — The act of algebraizing and its result; the process of transposing, reformulating, or expressing concepts, problems, or scientific branches within the language, structures, and equations of algebra. Historically, algebraization represents a crucial stage of abstract formalization.
• Analytic — Based on analysis, utilizing analysis as its primary research method, or pertaining to it. In mathematics, it refers to branches that employ algebraic methods and differential calculus (analytic geometry) or to functions that can be expanded into power series. In linguistics, it describes languages in which grammatical relationships are expressed through separate helper words (prepositions, articles, auxiliary verbs) and word order, as opposed to synthetic languages based on inflection.
• 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.
• Astroid — A remarkable plane curve with four sharp cusps, resembling a four-pointed star, generated by the trajectory of a fixed point on the circumference of a circle that rolls without slipping inside another fixed circle with a radius four times larger (a particular hypocycloid). Algebraically, its implicit Cartesian equation is x^(2/3) + y^(2/3) = a^(2/3), being extensively studied in analytical geometry due to its remarkable properties related to the envelope of a line segment of constant length.