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I’m trying to determine the equation for a heart starting from the unit circle. I figured a way to do it is to go from progressively closer shapes. What is the equation for shapes A-D? The very first equation I started from was the bottom half of the unit circle, which is $y=-\sqrt{1-x^2}$, however I didn’t know how to proceed from there to derive the following shapes.

enter image description here

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    $\begingroup$ You might find this useful: en.wikipedia.org/wiki/Cardioid $\endgroup$
    – Akiva Weinberger
    Commented Dec 14, 2020 at 5:29
  • $\begingroup$ (and a good online graphing calculator: desmos.com/calculator) $\endgroup$
    – Akiva Weinberger
    Commented Dec 14, 2020 at 5:30
  • $\begingroup$ Why reinvent the wheel? I find something like $(x^2+y^2-1)^3 - x^2y^3 = 0$ is close enough to the traditional heart symbol. See mathworld's entry on heart curve for other choices. $\endgroup$
    – achille hui
    Commented Dec 14, 2020 at 6:43
  • $\begingroup$ I see the graphs for the final heart, but are there equations for graphs A-D? $\endgroup$
    – 000
    Commented Dec 14, 2020 at 19:07

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