The Whewell equation of a plane curve is an equation that relates the tangential angle (φ) with arc length (s), where the tangential angle is the angle between the tangent to the curve at some point and the x-axis, and the arc length is the distance along the curve from a fixed point. These quantities do not depend on the coordinate system used except for the choice of the direction of the x-axis, so this is an intrinsic equation of the curve, or, less precisely, the intrinsic equation. If one curve is obtained from another curve by translation then their Whewell equations will be the same.
When the relation is a function, so that tangential angle is given as a function of arc length, certain properties become easy to manipulate. In particular, the derivative of the tangential angle with respect to arc length is equal to the curvature. Thus, taking the derivative of the Whewell equation yields a Cesàro equation for the same curve.
The concept is named after William Whewell, who introduced it in 1849, in a paper in the Cambridge Philosophical Transactions. In his conception, the angle used is the deviation from the direction of the curve at some fixed starting point, and this convention is sometimes used by other authors as well. This is equivalent to the definition given here by the addition of a constant to the angle or by rotating the curve.
The Whewellequation of a plane curve is an equation that relates the tangential angle (φ) with arc length (s), where the tangential angle is the angle...
\tau } . Specifically: The natural equation is the curve given by its curvature and torsion. The Whewellequation is obtained as a relation between arc...
sermons and theological tracts. In mathematics, Whewell introduced what is now called the Whewellequation, defining the shape of a curve without reference...
\end{aligned}}} The pedal equation with respect to the origin is r 2 = a 2 − 3 p 2 , {\displaystyle r^{2}=a^{2}-3p^{2},} the Whewellequation is s = 3 a 4 cos...
curves Whewellequation Subtangent Weisstein, Eric W. "Natural Equation". MathWorld. For example: Whewell, W. (1849). "Of the Intrinsic Equation of a Curve...
Tangential angle Torsion of curves Trajectory Transcendental curve W-curve Whewellequation World line Curve List of curves List of differential geometry topics...
coordinates, using intrinsic equations that use invariant quantities such as curvature and arc length. These include: The Whewellequation relates arc length and...
The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident...
the parameter a is equivalent to a uniform scaling of the curve. The Whewellequation for the catenary is tan φ = s a , {\displaystyle \tan \varphi ={\frac...
This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References...
given electric field strength. The term dielectric was coined by William Whewell (from dia + electric) in response to a request from Michael Faraday. A...
the Mathematics. J. Salusbury.) Barrow, Isaac (1860). "Lecture XXIV". In Whewell, William (ed.). The mathematical works of Isaac Barrow (in Latin). Harvard...
technical fields and titles. The term physicist was coined by William Whewell (also the originator of the term "scientist") in his 1840 book The Philosophy...
representation".) The term "Laplace's coefficients" was employed by William Whewell to describe the particular system of solutions introduced along these lines...
by William Whewell, proved troublesome. Whewell had George Biddell Airy write on it in his 1826 Tracts, but the solution of the equation appeared unmotivated...
of Newtonian mechanics especially in topics other than gravity. William Whewell (1837). History of the inductive sciences: from the earliest to the present...
five times the common rate. In the 19th century Whewell and Jevons re-expressed the estimate as an equation. The estimate raises several questions. To whom...
William Whewell, who allegedly became his lifelong friend. From Peacock, he derived an interest in the renovation of algebra, and from Whewell, an interest...
reliable tide tables around British shores, and with his friend William Whewell, expanded weather record-keeping at 200 British coast guard stations. Robert...
weeks, Ramanujan moved out of Neville's house and took up residence on Whewell's Court, a five-minute walk from Hardy's room. Hardy and Littlewood began...
published posthumously in 1886 by Karl Pearson. A biographical work on William Whewell was published in 1876, in addition to many original papers in scientific...
William Whewell found enumerative induction not nearly as convincing, and, despite the dominance of inductivism, formulated "superinduction". Whewell argued...
February 2016. (quoting from Aristotle's Treatise on Sound and Hearing) Whewell, William, 1794–1866. History of the inductive sciences : from the earliest...
science as a profession; the term scientist was coined in 1833 by William Whewell, which soon replaced the older term of natural philosopher. Among the most...
Global Information