SOME BEAUTIFUL 2D CURVES AND THEIR EQUATIONS

  •  THE LOVE EQUATION
`x^2+{(y-x^{2/3})}^2=1`





  • THE POLAR ROSE
General Equation:  `r=a\sin(k\theta)`  or  `r=a\cos(k\theta)`

For positive integral values of k, the rose will have 2k petals if k is even, and k petals if k is odd.
(For k = 1, it will simply be a circle).

  
`r=\sin(4\theta)`



`r=\sin(5\theta)`



For non-integral value of k, we get beautiful graphs like :


`r=\sin(2.5\theta)`



`r=\sin\left(\pi\theta\right)`




  • THE ARCHIMEDIAN SPIRAL
General Equation:  `r=a\theta`   ('a' is a constant)

`r=\theta`




  • THE LOGARITHMIC SPIRAL
General Equation:  `r=ae^{b\theta}` 

`r=e^{0.5\theta}`




  • THE BRACELET
x = cos t
y = sin t + 0.1 cos 6.2t




  • THE LEMNISCATE OF BERNOULLI
General Equation:  `\left(x^2+y^2\right)^2=2c^2\left(x^2-y^2\right)`


`\left(x^2+y^2\right)^2=2\left(x^2-y^2\right)`




  • THE BATMAN LOGO



























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