This article is about a concept in algebraic geometry. For concept in aviation that goes by that name, see Polar curve (aviation). For curves given in polar coordinates, see Polar coordinate system § Polar equation of a curve.
The elliptic curve E : 4Y2Z = X3 − XZ2 in blue, and its polar curve (E) : 4Y2 = 2.7X2 − 2XZ − 0.9Z2 for the point Q = (0.9, 0) in red. The black lines show the tangents to E at the intersection points of E and its first polar with respect to Q meeting at Q.
In algebraic geometry, the first polar, or simply polar of an algebraic plane curve C of degree n with respect to a point Q is an algebraic curve of degree n−1 which contains every point of C whose tangent line passes through Q. It is used to investigate the relationship between the curve and its dual, for example in the derivation of the Plücker formulas.
geometry, the first polar, or simply polar of an algebraic plane curve C of degree n with respect to a point Q is an algebraic curve of degree n−1 which...
The drag curve or drag polar is the relationship between the drag on an aircraft and other variables, such as lift, the coefficient of lift, angle-of-attack...
extended to finding the radius of curvature of curves expressed in these coordinates. The actual term polar coordinates has been attributed to Gregorio Fontana...
Polar cone Polar coordinate system, uses a central point and angles Polarcurve (a point and a curve), a generalization of a point and a line Polar set...
Spherical coordinate system, the three-dimensional form of a polar response curve In sailing, a Polar diagram is a graph that shows a sailing boats potential...
point, then the polar is the percussion line of action as described in planar screw theory. Dual polygon Dual polyhedron Polarcurve Johnson RA (1960)...
depicted by a polarcurve. These curves show the airspeed where minimum sink can be achieved and the airspeed with the best L/D ratio. The curve is an inverted...
of curves. Orthogonal coordinates: coordinate surfaces meet at right angles Skew coordinates: coordinate surfaces are not orthogonal The log-polar coordinate...
required is an airspeed indicator and a variometer. The pilot will use the polarcurve information for the particular glider to derive the exact speeds to fly...
The polar bear (Ursus maritimus) is a large bear native to the Arctic and nearby areas. It is closely related to the brown bear, and the two species can...
smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose...
curve of a given curve results from the orthogonal projection of a fixed point on the tangent lines of this curve. More precisely, for a plane curve C...
Cartesian coordinates Three-leaved clover in polar coordinates The ampersand curve is a quartic plane curve given by the equation: ( y 2 − x 2 ) ( x −...
spiral galaxies and architectural volutes. As a plane curve, a hyperbolic spiral can be described in polar coordinates ( r , φ ) {\displaystyle (r,\varphi )}...
a surface obtained by revolving around the y-axis is similar. For a polarcurve r = f ( θ ) {\displaystyle r=f(\theta )} where α ≤ θ ≤ β {\displaystyle...
curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve...
dual curve of a given plane curve C is a curve in the dual projective plane consisting of the set of lines tangent to C. There is a map from a curve to...
is a helix. The curve shown in red is a conical spiral. A two-dimensional, or plane, spiral may be described most easily using polar coordinates, where...
covered in this course include mathematical induction, complex number, polarcurve and conic sections, differential equations, recurrence relations, matrices...
In inversive geometry, an inverse curve of a given curve C is the result of applying an inverse operation to C. Specifically, with respect to a fixed circle...
approximately as linear. If a curve is defined in polar coordinates by the radius expressed as a function of the polar angle, that is r is a function...
In geometry, a cardioid (from Greek καρδιά (kardiá) 'heart') is a plane curve traced by a point on the perimeter of a circle that is rolling around a...
The Keeling Curve is a graph of the accumulation of carbon dioxide in the Earth's atmosphere based on continuous measurements taken at the Mauna Loa Observatory...
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical...
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