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In geometry, a strophoid is a curve generated from a given curve C and points A (the fixed point) and O (the pole) as follows: Let L be a variable line passing through O and intersecting C at K. Now let P1 and P2 be the two points on L ...
Jesse Russell, Ronald Cohn, 2012
This book examines the shape of curves and their mathematical relationships.
3
CRC Concise Encyclopedia of Mathematics, Second Edition
Right Strophoid Inverse Curve The right strophoid has CURVATURE 4(1 + 3<2)
and TANGENTIAL ANGLE cj>(t) = -2 tan'1 t- (5) (6) The right strophoid first
appears in work by Isaac Barrow in 1670, although Torricelli describes the curve
in his ...
4
A Catalog of Special Plane Curves
J. Dennis Lawrence. a sinzt sec t r = tan 6 = tan t m = %-tan t seczt (1 + 2 coszt)
tan w = Sln t co; t 1 + cos t - 3 p = _ a $1n t 2 v1 + 3 cos t 3/2 p = %-a sin t sec4t [1
+ 3 coszt] u = - %-a sinzt sec4t (1 + 5 coszt) 6 = g-a tan t 4.6. Right Strophoid ...
5
Handbook of Conformal Mapping with Computer-Aided Visualization
1.10.11 The strophoid The infinite curve defined by the polar equation p — sec (p
— 2 cos (p or where — 7r/2 < (p < n/2 is called the strophoid. The strophoid is not
a Jordan curve, it has the self-intersection point at the origin (as (p = ±7r/4).
Valentin I. Ivanov, Michael K. Trubetskov, 1994
6
Foundations of Fluid Mechanics with Applications: Problem ...
71) Eliminating the angle 3 from equations (6.4.70) and (6.4.71). we obtain the
equation for the shock polar' 8: The equation of shock polar (6.4.72) describes in
the hodograph plane u2,v2 a curve. which is a strophoid (see Fig. 6.35). It can be
...
Sergey P. Kiselev, Evgenii Vorozhtsov, Vasily M. Fomin, 1999
7
Modern Differential Geometry of Curves and Surfaces with ...
ti — strophoid[a] [t] is the parametrized curve whose implicit equation is strophoid[
a_] [t_J:ti (a*<t~2 - l)/(t~2 + 1), t*a*(t"2 - l)/(t"2 + 1)} t->atrophoid[m, a] [t] is the
parametrized curve whose implicit equation is y2(o — x) = I2(am -f i). The case m-
0 ...
8
A Differential Approach to Geometry: Geometric Trilogy III
It seems that the study of the right strophoid began during the 17th century, with
Roberval and Torricelli. The origin of the name is not clear: it is perhaps a
reference to a strophos, the Latin name for a belt with a twist used to hold a sword
.
9
Calculus of a Single Variable
If the planes must keep a separation of at least 3 miles, is the requirement met? .
Strophoid The curve given by the parametric equations z(l I t2) 1 + l2 x(t)I1T 1 + t2
and y(t) I is called a strophoid. (a) Find a rectangular equation of the strophoid.
Ron Larson, Bruce Edwards, 2013
10
Practical Handbook of Spreadsheet Curves and Geometric ...
Deane Arganbright. 3 2 1 0 -1 . -2 -3 -5 -4-3-2-10 1 2 3 Figure 33. Strophoid (
Base: Circle). Activities 1. Examine the effects of changes in the locations of the
fixed point and the pole. Figures 3.4 and 3.5 illustrate two new strophoids that are
...
WIADOMOŚCI, KTÓRE ZAWIERAJĄ SŁOWO «STROPHOID»
Sprawdź, o czym dyskutuje się w prasie krajowej i zagranicznej oraz jak jest stosowane słowo
strophoid w wiadomościach.
What the $*@&#! is the Nephroid of Freeth?
Specifically, one T.J. Freeth, an English mathematician who died in 1904. He was pretty into strophoids, plane curves that are shaped like "a belt with a twist. «Boing Boing, Lis 09»
