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)

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s