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Cornu Spiral -- from Wolfram MathWorld
Cornu Spiral -- from Wolfram MathWorld
The Cornu spiral is a plot in the complex plane of the points B(t)=S(t)+iC(t), (1) where S(t) and C(t) are the Fresnel integrals (von Seggern 2007, p. 210; Gray 1997, p. 65). The Cornu spiral is also known as the clothoid or Euler's spiral. It was probably first studied by Johann Bernoulli around 1696 (Bernoulli 1967, pp. 1084-1086). A Cornu spiral describes diffraction from the edge of a half-plane. The quantities C(t)/S(t) and S(t)/C(t) are plotted above. The slope of the curve's...
·mathworld.wolfram.com·
Cornu Spiral -- from Wolfram MathWorld
Clarisse_2016.pdf
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Helix -- from Wolfram MathWorld
Helix -- from Wolfram MathWorld
A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides, flattening it out, and noting that a straight line connecting the points becomes helical upon re-wrapping (Steinhaus 1999, p. 229). It is for this reason that squirrels chasing one another up and...
·mathworld.wolfram.com·
Helix -- from Wolfram MathWorld
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