# Math Circles Meeting on December 5th, 2015

## Agenda: Fractal Dimensions

Presenters: Aubrey Rhoden and Kim Moore

### Exploring Fractal Dimensions Student Worksheet

• What patterns are there in the Sierpinski Triangle?
• What is the rule for the number of shaded triangles in n iterations?
• What is the rule for the number of unshaded triangles in n iterations?
• What fraction of the triangles are shaded in n iterations?
• How do you describe the dimension of a Sierpinski Triangle?

• What patterns are there in the Sierpinski Carpet?
• What is the rule for the number of shaded squares in n iterations?
• What is the rule for the number of unshaded squares in n iterations?
• What fraction of the squares are shaded in n iterations?
• How do you describe the dimension of a Sierpinski Carpet?

# Math Circle Meeting on November 7th, 2015

## Agenda: Platonic Solids and Origami

Presenters: Aubrey Rhoden and Kim Moore

## Euler’s Formula

Euler’s Characteristic

# 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.

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.

Creating cardioids and other curves