Plane curve constructed from a given curve and fixed point
In Euclidean geometry, for a plane curve C and a given fixed point O, the pedal equation of the curve is a relation between r and p where r is the distance from O to a point on C and p is the perpendicular distance from O to the tangent line to C at the point. The point O is called the pedal point and the values r and p are sometimes called the pedal coordinates of a point relative to the curve and the pedal point. It is also useful to measure the distance of O to the normal pc (the contrapedal coordinate) even though it is not an independent quantity and it relates to (r, p) as
Some curves have particularly simple pedal equations and knowing the pedal equation of a curve may simplify the calculation of certain of its properties such as curvature. These coordinates are also well suited for solving certain type of force problems in classical mechanics and celestial mechanics.
Euclidean geometry, for a plane curve C and a given fixed point O, the pedalequation of the curve is a relation between r and p where r is the distance from...
polar equation of the pedal is r = a cos 2 θ 2 . {\displaystyle r=a\cos ^{2}{\theta \over 2}.} The pedalequations of a curve and its pedal are closely...
\end{aligned}}} The pedalequation with respect to the origin is r 2 = a 2 − 3 p 2 , {\displaystyle r^{2}=a^{2}-3p^{2},} the Whewell equation is s = 3 a 4 cos...
A bicycle, also called a pedal cycle, bike, push-bike or cycle, is a human-powered or motor-assisted, pedal-driven, single-track vehicle, with two wheels...
) , f > 0 , {\displaystyle F=(0,f),\ f>0,} and the directrix has the equation y = − f {\displaystyle y=-f} , one obtains for a point P = ( x , y ) {\displaystyle...
revolutions per minute, the above equation gives power in foot pounds-force per minute. The horsepower form of the equation is then derived by applying the...
the lower extremity. Certain drugs (for example, amlodipine) can cause pedal edema. Cerebral edema is extracellular fluid accumulation in the brain....
semi-major axis and semi-minor axis, and symmetry about them, but defined by an equation that allows for various shapes between a rectangle and an ellipse. In two...
mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation F ( x , y , z ) = 0 {\displaystyle F(x,y,z)=0} applied to homogeneous coordinates...
{\displaystyle k} are points of a cardioid. Hence a cardioid is a special pedal curve of a circle. In a Cartesian coordinate system circle k {\displaystyle...
other words, the Simson line of a triangle ABC and a point P is just the pedal triangle of ABC and P that has degenerated into a straight line and this...
A fish curve is an ellipse negative pedal curve that is shaped like a fish. In a fish curve, the pedal point is at the focus for the special case of the...
Rutherford and William Bragg. In his 1913 thesis, he derived the Fokker–Planck equation along with Max Planck. After his military service during World War I he...
capstan equation. Most cars and trucks with a manual transmission use a dry clutch, which is operated by the driver using the left-most pedal. The motion...
analysis in formulating the equations in terms of concepts which are reasonably familiar. Applying an impulse via the rudder pedals should induce Dutch roll...
hilly road. The question is, how should the driver press the accelerator pedal in order to minimize the total traveling time? In this example, the term...
geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates r n = a n cos ( n θ ) {\displaystyle r^{n}=a^{n}\cos(n\theta...
with large wheels and pedals, the term is now used in relation to powered self-balancing scooters with smaller wheels and no pedals such as the Segway PT...
'game play parameters'.[citation needed] When a system is modeled by equations, the values that describe the system are called parameters. For example...
rock, post rock, and alternative rock. Their fifth studio album, The Only Equation, was released on 16 June 2023. Suns of the Tundra began as a collaboration...
acoustically similar to closed conical pipes with some deviations (see pedal tones and false tones). Like strings, vibrating air columns in ideal cylindrical...
x = a 2 {\displaystyle x={a \over 2}} relative to the origin. It is the pedal with respect to the origin of the parabola y 2 = 2 a ( x − 3 2 a ) . {\displaystyle...
deviation from equal temperament is called the Railsback curve. The following equation gives the frequency f (Hz) of the nth key on the idealized standard piano...
first used in a simple balance scale. In ancient Egypt c. 4400 BC, a foot pedal was used for the earliest horizontal frame loom. In Mesopotamia (modern...
the vehicle's regenerative braking distance. This is referred to as One Pedal Driving. Current regenerative brakes do not immobilize a stationary vehicle;...
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