polar curven.

Brit.

/ˌpəʊlə ˈkəːv/, U.S.

/ˌpoʊlər ˈkərv/

Origin: Formed within English, by compounding. Etymons: polar adj., curve n.

Etymology: < polar adj. + curve n.

Mathematics.

1. A curve whose equation is expressed in polar coordinates, esp. one whose equation is usually so expressed, such as a spiral or a limaçon.

ΚΠ

1831 J. Hind Princ. Differential Calculus 262 If r be the radius vector of a polar curve, and θ be the angle which it makes with a fixed axis.

1880 Analyst 7 19 The differential area of a polar curve is ½ρ²dθ.

1955 Math. Mag. 28 270 Any polar point (r, θ) has generalized coordinates (−1)ⁿr, θ + nπ.... To determine all the points of intersection of two polar curves, except the pole, it is only necessary to solve simultaneously the equations of the two curves.

1997 College Math. Jrnl. 28 55 Plot the polar curves r = cos (nt) and r = sin (nt) for n = 1, 2,..,5.

2. A curve defined with reference to a given plane curve and a given point, being a curve that is of one degree less than the given curve and meets it at the points of contact of the tangents to the given curve from the given point.

ΚΠ

1848 G. Salmon Treat. Conic Sections xiv. 243 When we speak of polar curves, we intend the reader to understand polars with regard to a circle.

1878 Philos. Trans. 1877 (Royal Soc.) 167 374 The polar curve of this point of the (n − m)th degree, with respect to U, is [etc.]... This equation contains the variables in the degree n − m.

1904 Amer. Jrnl. Math. 26 164 Since the question belongs to metric geometry, it will be convenient to first derive the equations for polar curves in rectangular, instead of the usual homogeneous coordinates.

1989 Proc. Amer. Math. Soc. 106 380 V(γ_f,s) is the polar curve of f with respect to the coordinate s.

This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022).

单词	polar curve
释义	polar curven. Brit. /ˌpəʊlə ˈkəːv/, U.S. /ˌpoʊlər ˈkərv/ Origin: Formed within English, by compounding. Etymons: polar adj., curve n. Etymology: < polar adj. + curve n. Mathematics. 1. A curve whose equation is expressed in polar coordinates, esp. one whose equation is usually so expressed, such as a spiral or a limaçon. ΚΠ 1831 J. Hind Princ. Differential Calculus 262 If r be the radius vector of a polar curve, and θ be the angle which it makes with a fixed axis. 1880 Analyst 7 19 The differential area of a polar curve is ½ρ²dθ. 1955 Math. Mag. 28 270 Any polar point (r, θ) has generalized coordinates (−1)ⁿr, θ + nπ.... To determine all the points of intersection of two polar curves, except the pole, it is only necessary to solve simultaneously the equations of the two curves. 1997 College Math. Jrnl. 28 55 Plot the polar curves r = cos (nt) and r = sin (nt) for n = 1, 2,..,5. 2. A curve defined with reference to a given plane curve and a given point, being a curve that is of one degree less than the given curve and meets it at the points of contact of the tangents to the given curve from the given point. ΚΠ 1848 G. Salmon Treat. Conic Sections xiv. 243 When we speak of polar curves, we intend the reader to understand polars with regard to a circle. 1878 Philos. Trans. 1877 (Royal Soc.) 167 374 The polar curve of this point of the (n − m)th degree, with respect to U, is [etc.]... This equation contains the variables in the degree n − m. 1904 Amer. Jrnl. Math. 26 164 Since the question belongs to metric geometry, it will be convenient to first derive the equations for polar curves in rectangular, instead of the usual homogeneous coordinates. 1989 Proc. Amer. Math. Soc. 106 380 V(γ_f,s) is the polar curve of f with respect to the coordinate s. This entry has been updated (OED Third Edition, September 2006; most recently modified version published online March 2022). < n.1831
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