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| image: commons.wikimedia.org |
In honor of Valentine’s Day, we wanted our throwback fact of
the week to be heart themed. What in math looks like a heart? A cardioid, of
course!
The cardioid was named in 1741 by Italian mathematician
Giovanni Salvemini de Castillon, though it was already a studied shape. It is a
degenerate case (with no internal pedals) of the limaçon, a figure formed when
a circle rolls around the outside of a circle
of equal radius.
How does one generate the cardioid? This Wolfram Mathworldpage gives us the equations.
What makes a cardioid relevant today? Aside from its
importance in geometry, cardioids are a shape seen in acoustics. The cardioid
microphone is nam
ed so not because the microphone is shaped like a heart, but
because the sound pick-up pattern is heart shaped. The shape allows a
microphone to be used in a loud setting, because the microphone will pick up
only sounds very close to it within the cardioid spread. For more detail on
this topic, click here.
Possibly the most important application of the cardioid for
this week, however, is that they produce beautiful looking, heart-shaped
curves. You can see a few members of the Center’s attempts to draw hearts
below. Although perhaps we should leave the heart-shaped curves to geometrically precise cardioids.
In the image above, Tori drew out a few sample heart curves with some imprecise geometrical backing. Then Zach, Adam, Ruairi and Tori all drew heart curves their own way.
We hope you have a good weekend, whether you celebrate Valentine's day or not! Have you had a chance to watch our new video on the Monty Hall problem? See it here:
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