Math Circle Meeting on October 17th

Agenda: Creating a Cardioid

Presenters: Aubrey Rhoden and Kim Moore

Problem: How can we create a cardioid with a radius of 10 feet on the beach?

Solution: Let there be 36 points labeled 0 to 35 equally spaced on a circle. Connect nth point to Mod [2 n,36] th point. These lines are tangents to a cardioid.

cardiod diagram

  1. Use a stake and rope to create the circle. The stake goes in the middle of the circle.
  2. Calculate the circumference of the circle. The circumference would be 62.8 feet or 753 inches.
  3. Divide the circumference into 36 equal parts. The stakes need to be 20.9 inches apart.Cardioid


Creating cardioids and other curves

Formula for a cardioid:

X= a cos t (1 – cos t)

Y= a sin t (1- cos t)


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