equation: theta = t * 360 * 10 ,
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Cartesian coordinates
theta = t * 360 * 2.2
Cartesian coordinate system
cylindrical coordinate
equation: x = 50 * t
b = 8
9. double arc Epicycloid
pictures about this subject as follows: 23.jpg
a = 4
18.Rhodonea curve
y = 25 + (10-6) * sin (theta) -6 * sin ((10/6-1) * theta)
equation: l = 2.5
y = (exp (x) + exp (0-x)) / 2
equation: a = 5
equation: rho = 8 * t
mathematical equation: r * r = a * a * theta
cylindrical coordinates
30. logarithmic spiral
phi = t * 360 * 20
theta = t * 380
cylindrical coordinates
y = 4 * sin (t * (5 * 360))
equation: x = 4 * cos (t * (5 * 360))
y = (3 * t) + (5 * t ^ 2)
b = 1
a = 1
equation: r = 5
32.tan curve
b = sin (theta)
pictures about this subject as follows: 8.jpg
y = a * (2 * sin (t * 360)-sin (2 * t * 360))
x = 6 * t-3
r = a * theta
pictures about this subject as follows: 29.jpg
x = 3 * a * t / (1 + (t ^ 3))
z = t * 3
pictures about this subject as follows: 6.jpg
equation: theta = t * 360
pictures about this subject as follows: 14.jpg
x = a * (cos (t * 360)) ^ 3
pictures about this subject as follows: 3.jpg
23. Lissajous curve
y0 = s * sin (ang)
Cartesian coordinate system
35. hyperbolic tangent
Y = 3 * b * sin (t * 360) + l * sin (3 * t * 360)
using Cartesian coordinates
z = 0
pictures about this subject as follows: 31.jpg
2. shaped line.
cylindrical coordinates
z = 0
z = 2 * sin (6 * theta)
33. hyperbolic cosine
pictures about this subject as follows: 12.jpg
Seoul
pictures about this subject as follows: 9.jpg
y = (exp (x)-exp (0-x)) / (exp (x) + exp (0-x))
4. Butterfly curve
equation: a = 1
7. on the number of curves
Cartesian coordinates
r = a * (1 + cos (theta))
y = (a * a-2 * f + f * f * c * c) * sin (theta) / b
equation 1: theta = 360 * t * 5
22. Epicycloid
Seoul
phi = -360 * t * 8
theta = t * 3600
z = 10 * t
y = y0-s * cos (ang)
y = t * 100-50
a = 10
pictures about this subject as follows: 25.jpg
x = t * 10-5
a = 0.005
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equation: rho = 4
r = a * sqrt (theta * 180/pi)
y = (a + b) * sin (theta)-c * sin ((a / b +1) * theta)
pictures about this subject as follows: 15.jpg
c = 2.2
equation: a = 5
y = 10 * sin (t * 360)
16.Talbot curve
pictures about this subject as follows: 5.jpg
z = (cos (theta-90)) +24 * t
a = 4
equation: a = 10
pictures about this subject as follows: 22.jpg
a = 1.1
27. probability curve!
cylindrical coordinates
using spherical coordinate system
21. trefoil line
y = log (10 * t +0.0001)
34. hyperbolic sine
x = (a * a + f * f * c * c) * cos (theta) / a
pictures about this subject as follows: 26.jpg
n = 3
theta = t * 360
pictures about this subject as follows: 35.jpg
b = 3
y = 8 * a ^ 3 / (x ^ 2 +4 * a ^ 2)
Equation 2: theta = 360 * t * 5
29. Archimedean spiral
pictures about this subject as follows: 10.jpg
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r = DB / 2
theta = t * 360 * B * tan (beta) * cos (alpha) / (pi * DB)
z = t * B
r = 10 +10 * sin (6 * theta)
y = tan (x * 20)
x ^ 3 = y ^ 2 * (2 * a-x)
using Cartesian coordinates
pictures about this subject as follows: 21.jpg
cylindrical coordinates
spherical coordinates
pictures about this subject as follows: 28.jpg
x = a * sin (n * theta + c)
x = 6 * t-3
a = 1
y = (exp (x)-exp (0-x)) / 2
equation: a = 10
3. Spiral (Helical curve)
Kadir coordinates
pictures about this subject as follows: 2.jpg
28. Kei Tongue
Seoul
c = 100
ang = 360 * t
for x
equation: theta = t * 360
x = 10 * t
Kadir coordinates
Cartesian coordinates
1. disc spring
a = 10
b = 0.666
equation: theta = t * 720 * 5
19. Parabola
equation: r = t
pictures about this subject as follows: 34.jpg
10. star line line
pictures about this subject as follows: 24.jpg
c = sin (theta)
theta = 360 * t * 4
pictures about this subject as follows: 19.jpg
r = exp (a * theta)
pictures about this subject as follows: 4.jpg
pictures about this subject as follows: 32.jpg
r =- a * sqrt (theta * 180/pi)
theta = t * 360
f = 1
Cartesian coordinates
x = -5 + t * 10
equation:
6. helix.
pictures about this subject as follows: 20.jpg
y = a * (sin (t * 360)) ^ 3
8. spherical helix
pictures about this subject as follows: 17.jpg
Cartesian coordinates
z = 0
z = (sin (3.5 * theta-90)) +24 * t
y = (a-b) * sin (theta)-c * sin ((a/b-1) * theta)
17.4 leaf line (an equation do not copy)
25. length of the pieces of the roller outside the circle line
b = 2.5
theta = t * 1800
z = 0
pictures about this subject as follows: 7.jpg
31. Man-Ye line
12. circle spiral
x = t * 8.5 -4.25
pictures about this subject as follows: 18.jpg
Cartesian coordinate system
pictures about this subject as follows: 16.jpg
14. the sun line (it used to do other curves, the results wrong,
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b = 7
x0 = s * cos (ang)
y = (a + b) * sin (theta)-b * sin ((a / b +1) * theta)
c = 5
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x = (a-b) * cos (theta) + c * cos ((a/b-1) * theta)
a = 100
Cartesian coordinate system
y = 3 * a * (t ^ 2) / (1 + (t ^ 3))
theta = 360 * t * 10
x = (a + b) * cos (theta)-c * cos ((a / b +1) * theta)
cylindrical coordinates
theta = t * 400
s = 2 * pi * r * t
20. spiral line
pictures about this subject as follows: 33.jpg
cylindrical coordinates (cylindrical)
solve
Cartesian coordinate system
equation: theta = t * 360 * 4
a = 5
x = 25 + (10-6) * cos (theta) +10 * cos ((10/6-1) * theta)
Cartesian coordinates
y = exp (0-x ^ 2)
by column coordinates
x = 3 * b * cos (t * 360) + l * cos (3 * t * 360)
x = x0 + s * sin (ang)
5. involute
theta = 10 + t * (20 * 360)
x = (a + b) * cos (theta)-b * cos ((a / b +1) * theta)
x = a * (2 * cos (t * 360) + cos (2 * t * 360))
13. sine curve
pictures about this subject as follows: 1.jpg
Cartesian coordinates
r = a * cos (theta) * (4 * b * b-1)
equation: r = 5
15. Fermat curve (a bit like a thread line)
equation: x = (4 * t)
a = 5
equation: r = 1
26. tricuspid line
y = b * sin (theta)
24. length of the pieces of the roller circle line
pictures about this subject as follows: 30.jpg
x = 6 * t-3
theta = t * 180
Cartesian coordinates
11. cardioid
pictures about this subject as follows: 13.jpg
Pro / E a collection of various curve equation
pictures about this subject as follows: 27.jpg
equation: z = 0
pictures about this subject as follows: 11.jpg