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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 51N: Analytic and descriptive geometry

Introduction

Mostly this area includes topics related to ordinary analytic geometry as studied in secondary school.

History

Applications and related fields

Subfields

• 51N05: Descriptive geometry, See also 65D17, 68U07
• 51N10: Affine analytic geometry
• 51N15: Projective analytic geometry
• 51N20: Euclidean analytic geometry
• 51N25: Analytic geometry with other transformation groups
• 51N30: Geometry of classical groups, See also 20Gxx, 14L35
• 51N35: Questions of classical algebraic geometry, See also 14Nxx
• 51N99: None of the above but in this section

Parent field: 51: Geometry

Browse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

Software and tables

A compendium of plane curves

Other web sites with this focus

Selected topics at this site

• Using projective geometry to perform a construction meeting incidence conditions.
• A little analytic geometry (finding the intersection of two cones.)
• Computing intersection of two ellipses with elementary elimination
• Computing intersection of a torus and a circle in R^3
• More general curves and surfaces too, in this case ruled surfaces.
• How many points determine a torus?
• Need a parameterization of the set of orthogonal matrices
• Angles between three vectors determine location of the vector in their "center".
• Parameterizations of unitary operators on a Hilbert space (and thus parameterization of the unitary and orthogonal groups).
• Formula for the equation of a curve formed by rotating the graph of a function
• Effect of rotation on the graph of a function
• What's the distance between a point and a parabola? (This is essentially an elimination-theoretic description of an envelope of the parabola.)
• Lagrange multipliers: nearest point on an ellipsoid to a given point
• What is a porism? (Poncelet's, Steiner's)
• Poncelet's Porism: Which nested pairs of circles are in- and circumscribed circles for a triangle? How many triangles?
• Many ways to compute the area of a circle given 3 points on it
• Kepler's equation and cycloids
• Converting pitch and roll to Euler rotations