analytical geometry

Definitions

  • WordNet 3.6
    • n analytical geometry the use of algebra to study geometric properties; operates on symbols defined in a coordinate system
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Webster's Revised Unabridged Dictionary
    • Analytical geometry that branch of mathematical analysis which has for its object the analytical investigation of the relations and properties of geometrical magnitudes.
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Chambers's Twentieth Century Dictionary
    • Analytical geometry geometry treated by means of ordinary algebra, with a reference, direct or indirect, to a system of co-ordinates
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Etymology

Chambers's Twentieth Century Dictionary
Gr. analysis, analy-ein, to unloose, ana, up, ly-ein, to loose.

Usage

In literature:

He smiled to think that any one should presume to become a parson without having at least mastered analytical geometry.
"Where the Blue Begins" by Christopher Morley
He told me that he was working at analytical geometry.
"The Life of the Fly" by J. Henri Fabre
Just as little is any principle of pure geometry analytical.
"The Critique of Pure Reason" by Immanuel Kant
Analytic geometry aided in making good lenses for eyeglasses.
"Our Legal Heritage, 5th Ed." by S. A. Reilly
When I was younger I had studied logic, analytical geometry, and algebra.
"The Worlds Greatest Books, Volume XIII." by Various
J. F. HEATHER 2/- Analytical Geometry.
"French Polishing and Enamelling" by Richard Bitmead
Examples of Analytical Geometry of Three Dimensions.
"The Works of William Shakespeare [Cambridge Edition] [9 vols.]" by William Shakespeare
Analytical geometry originated with his investigation of the nature and origin of curves.
"Library of the World's Best Literature, Ancient and Modern — Volume 11" by Various
Of these the most indubitable is the creation of analytical geometry, the starting-point of modern mathematics.
"History of Modern Philosophy" by Alfred William Benn
Mathematics was all right; in fact, he had done very well in analytic geometry.
"The Song of Songs" by Hermann Sudermann
Elements of Analytical Geometry.
"Rob of the Bowl, Vol. I (of 2)" by John P. Kennedy
Analytical geometry was stimulated by the algebra of invariants, a subject much developed by A. Cayley, G. Salmon, S.H.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
From this springs the modern analytic geometry, a subject that has revolutionized the methods of all mathematics.
"The Teaching of Geometry" by David Eugene Smith
The new problems presented by the analytical geometry and natural philosophy of the 17th century led to new limiting processes.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5" by Various
Analytical Geometry: Guldberg's text.
"The School System of Norway" by David Allen Anderson
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In news:

Among them were 72 letters by René Descartes , the founding genius of modern philosophy and analytic geometry.
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In science:

In the classical commutative setting those results allow the application of complex-analytic, Hodge-theoretic, and K¨ahler geometric, methods to complex pro jective varieties, and conversely the methods of algebraic geometry apply to appropriate complex manifolds.
Noncommutative complex differential geometry
Hironaka, Flattening theorem in complex-analytic geometry, Amer. J.
A new series of compact minitwistor spaces and Moishezon twistor spaces over them
For most problems, the details of the geometry of the body make these matrices impossible to calculate analytically.
The hydrodynamics of swimming microorganisms
This interplay between topology and analytic geometry provides one of the deepest, richest, and most powerful avenues for mathematics.
A Simple Introduction to Particle Physics Part II
We will find that such analytic relationships provide a profound gateway between topology and geometry, and will be a primary tool in more advanced topics, especially string theory.
A Simple Introduction to Particle Physics Part II
To infer the D3d in the corona, they created an analytical flare geometry model.
The correlation of fractal structures in the photospheric and the coronal magnetic field
In [KoSo1] we used two motivic versions of this notion: one developed by Denef and Loeser and another one (in the framework of nonarchimedean analytic geometry) developed by Nicaise and Sebag.
Motivic Donaldson-Thomas invariants: summary of results
The version of the motivic Milnor fiber defined by means of non-archimedean analytic geometry in [NiSe] agrees with the formula of Denef and Loeser.
Motivic Donaldson-Thomas invariants: summary of results
If the tangential velocity profile is known, the coupling term between matter and geometry can be obtained explicitly in an analytical form.
Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry
Example [CT, 3.1.1] used valuations that correspond to analytic but non-rigid points, so it could be naturally interpreted in the analytic (but not rigid) geometry.
Pr\"ufer algebraic spaces
Subsequently, test ideals have also found application far beyond their original scope to questions arising in complex analytic geometry.
A survey of test ideals
They may additionally find sections 3 and 8 useful. (iii) Readers with a background in complex analytic and algebraic geometry working on notions related to the multiplier ideal or the minimal model program who wish to learn about characteristic p > 0 methods.
A survey of test ideals
In this section we explain the connection between the test ideal and the multiplier ideal, a construction which first appeared in complex analytic geometry.
A survey of test ideals
His model is an ‘analytic’ one (in the sense of analytic geometry): it is based on the field obtained from the number 1 by closing under +, −, ×, ÷, and x 7→ √1 + x2 .
Numbers
Since the minimum energy state for a given total magnetic helicity is a linear force-free field, the geometry of the field lines can be described analytically given the boundary conditions at the stellar surface.
Searching for star-planet magnetic interaction in CoRoT observations
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