extended to finding the radius of curvature of curves expressed in these coordinates. The actual term polar coordinates has been attributed to Gregorio Fontana...

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...

point, then the polar is the percussion line of action as described in planar screw theory. Dual polygon Dual polyhedron Polar curve Brokard's theorem...

Polar cone Polar coordinate system, uses a central point and angles Polar curve (a point and a curve), a generalization of a point and a line Polar set...

rhodonea curve is a sinusoid specified by either the cosine or sine functions with no phase angle that is plotted in polar coordinates. Rose curves or "rhodonea"...

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...

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...

depicted by a polar curve. 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...

curve at P. Similarly, let N now be the point where the normal to the curve intersects the line. Then OT and ON are, respectively, called the polar subtangent...

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...

smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose...

required is an airspeed indicator and a variometer. The pilot will use the polar curve information for the particular glider to derive the exact speeds to fly...

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...

a surface obtained by revolving around the y-axis is similar. For a polar curve r = f ( θ ) {\displaystyle r=f(\theta )} where α ≤ θ ≤ β {\displaystyle...

covered in this course include mathematical induction, complex number, polar curve and conic sections, differential equations, recurrence relations, matrices...

drag curves. Speed is shown increasing from left to right. The lift/drag ratio is given by the slope from the origin to some point on the curve and so...

\mathbf {C} (t)=(r(t),\theta (t))} be a curve expressed in polar coordinates. The mapping that transforms from polar coordinates to rectangular coordinates...

or, in polar coordinates, r = 2 b cos ⁡ θ 3 {\displaystyle r=2b\cos {\theta \over 3}} making it a member of the rose family of curves. This curve is a trisectrix...

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 −...

Watt's pioneering work on the steam engine. The equation of the curve can be given in polar coordinates as r 2 = b 2 − [ a sin ⁡ θ ± c 2 − a 2 cos 2 ⁡ θ...

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...

spiral galaxies and architectural volutes. As a plane curve, a hyperbolic spiral can be described in polar coordinates ( r , φ ) {\displaystyle (r,\varphi )}...

The butterfly curve is a transcendental plane curve discovered by Temple H. Fay of University of Southern Mississippi in 1989. The curve is given by the...

is constant. Curvature The curvature κ {\displaystyle \kappa } of a curve with polar equation r = r ( φ ) {\displaystyle r=r(\varphi )} is κ = r 2 + 2 (...

result of diligent experimentation. Another advantage was that, while the polar curve for thin profile wings typically had a relatively restricted range of...

The Keeling Curve is a graph of the annual variation and overall accumulation of carbon dioxide in the Earth's atmosphere based on continuous measurements...

L; Cochran, Lyle; Gilett, Bernard; Schulz, Eric. "11 Parametric and Polar Curves". Calculus for Scientists and Engineers – Early Transcendentals. Pearson...

denotes the polar tangential angle, then ψ = φ − θ, where φ is as above and θ is, as usual, the polar angle. If the curve is defined in polar coordinates...