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Love curve

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Submitted by Marianne on 26 February, 2015

If you feel in need of some love this cold, dark February, then our images of the week might be just what you need. These hearts, created by Hamid Naderi Yeganeh, aren't drawn by hand, but defined by mathematical equations.

Image by Hamid Naderi Yeganeh.

Image by Hamid Naderi Yeganeh.

The first curve consists of points in the plane whose coordinates $(x,y)$ satisfy

  \[ x=\frac{48}{25}\sin (5t)+\frac{40}{25}\sin (6t) \]    
  \[ y=\frac{48}{25}\cos (4t)+\frac{40}{25}\cos (5t) \]    

for $\Theta \leq t \leq 2\pi -\Theta ,$ where $\Theta \approx 2.32.$ ($\Theta $ is a zero of $\frac{48}{25}\sin (5t)+\frac{40}{25}\sin (6t)$.)

The second curve consists of points in the plane whose coordinates $(x,y)$ satisfy

  \[ x=-(\sin (3t))^{3} \]    
  \[ y=\sin \left(4t+\frac{7\pi }{36}\right)-\frac{\sin \left(\frac{7\pi }{36}\right)-\sin \left(\frac{103\pi }{36}\right)}{2}(\cos (\frac{3t}{2}))^{5} \]    

for $0 \leq t \leq \frac{2\pi }{3}$.

You can see more of Hamid's images on this website, in The Guardian and on the American Mathematical Society website.

Click here to see previous images of the week.

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