Mathematical Figures


Home Page Last Updated: 2002-6/25, 2004-4/12, 2007-9/10 


Mathematics : theta=omega*t

      #20  azlissajours.htm Lissajours
              x=c*sin(a*theta)
              y=d*sin(b*theta)

      #24 azspiral.htm Archimedes Spiral
              r=2*theta
              x=r*cos(theta)
              y=r*sin(theta)
      #25 azcardioid.htm Cardioid: Limason: special fig of r=a*cos(theta)+b 
              r=a*(1+cos(theta))
              x=r*cos(theta)
              y=r*sin(theta)
      #26 az3leaf.htm Leaves(2 to n):Lemniscate
              r=a*cos(b*theta) 
              x=r*cos(theta)
              y=r*sin(theta)
      #27 azinvolute.htm Involute
              x=a*(cos(theta)+theta*sin(theta))
              y=a*(sin(theta)-theta*cos(theta))
      #28 azasteroid.htm Asteroid
              x=a*cos(theta)*cos(theta)*cos(theta)
              y=a*sin(theta)*sin(theta)*sin(theta)
      #29 azcycloid.htm Cycloid(b=1)ATrocoid(b‚1)
              x=a*(theta-b*sin(theta))
              y=a*(1-b*cos(theta))
      #30 azzukei01.htm Triangular Function(2D)
              rr=r0+sin(c*theta)
              xn1=r*rr*cos(a*theta-posi)
              yn1=r*rr*sin(b*theta-posi)

      #32 azclothoid.htm Clothoid:Curvature of Highway
              x=çcos(u*u)du,  y=Integral(sin(u*u))du
              xn1=xn+(cos(a*a))*b
              yn1=yn+(sin(a*a))*b

      #66 azcatenary.htm Catenary
              y=(a/2)*(exp(x/a)+exp(-x/a))                             

      #99 azeq08.htm Runge kutta vs Euler

  Return Home


AZure  All rights reserved. Hajime Satoh, 2002, 2007