Code For Producing An Euler Spiral
The following Sage code produces the second graph above. The first four lines express the Euler spiral component. Fresnel functions could not be found. Instead, the integrals of two expanded Taylor series are adopted. The remaining code expresses respectively the tangent and the circle, including the computation for the center coordinates.
var('L') p = integral(taylor(cos(L^2), L, 0, 12), L) q = integral(taylor(sin(L^2), L, 0, 12), L) r1 = parametric_plot(, (L, 0, 1), color = 'red') r2 = line(, rgbcolor = 'blue') x1 = p.subs(L = 1) y1 = q.subs(L = 1) R = 0.5 x2 = x1 - R*sin(1.0) y2 = y1 + R*cos(1.0) r3 = circle((x2, y2), R, rgbcolor = 'green') show(r1 + r2 + r3, aspect_ratio = 1, axes=false)The following is Mathematica code for the Euler spiral component (it works directly in wolframalpha.com):
ParametricPlot[ {FresnelC] t]/Sqrt], FresnelS] t]/Sqrt]}, {t, -10, 10}]Read more about this topic: Euler Spiral
Famous quotes containing the words code for, code, producing and/or spiral:
“Many people will say to working mothers, in effect, I dont think you can have it all. The phrase for have it all is code for have your cake and eat it too. What these people really mean is that achievement in the workplace has always come at a priceusually a significant personal price; conversely, women who stayed home with their children were seen as having sacrificed a great deal of their own ambition for their families.”
—Anne C. Weisberg (20th century)
“Acknowledge your will and speak to us all, This alone is what I will to be! Hang your own penal code up above you: we want to be its enforcers!”
—Friedrich Nietzsche (18441900)
“The man whose whole activity is diverted to inner meditation becomes insensible to all his surroundings. If he loves, it is not to give himself, to blend in fecund union with another being, but to meditate on his love. His passions are mere appearances, being sterile. They are dissipated in futile imaginings, producing nothing external to themselves.”
—Emile Durkheim (18581917)
“What is art,
But life upon the larger scale, the higher,
When, graduating up in a spiral line
Of still expanding and ascending gyres,
It pushes toward the intense significance
Of all things, hungry for the Infinite?
Arts life,and where we live, we suffer and toil.”
—Elizabeth Barrett Browning (18061861)