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Thursday, February 12, 2015

Throwback Fact: Cardioids

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 lima├žon, 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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