What does algebraic geometry mean?
Definitions for algebraic geometry
al·ge·bra·ic ge·om·e·t·ry
This dictionary definitions page includes all the possible meanings, example usage and translations of the word algebraic geometry.
Wiktionary
algebraic geometrynoun
a branch of mathematics that studies solutions of systems of algebraic equations using both algebra and geometry.
Wikidata
Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and quartic curves like lemniscates, and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology of the curve and relations between the curves given by different equations. Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory. Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.
Numerology
Chaldean Numerology
The numerical value of algebraic geometry in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of algebraic geometry in Pythagorean Numerology is: 4
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"algebraic geometry." Definitions.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.definitions.net/definition/algebraic+geometry>.
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