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?  How do you describe the dimension of a Sierpinski Tetrahedron? Making the Tree

Menger Sponge Template Math Circle Meeting on November 7th, 2015

Agenda: Platonic Solids and Origami

Presenters: Aubrey Rhoden and Kim Moore

Platonic Solids Euler’s Formula

Euler’s Characteristic

• Are there shapes that do not follow Euler’s formula?  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

Math Circle Meeting on September 26th

Agenda: Tiling the Plane

Presenter: Kim Moore

New Pentagonal Tiling

Tilings on NPR The First Fourteen Pentagonal Tilings

What is a Rep-tile? Right Trapezoid Template       Sphinx Template        L Shaped Template

Special Rep-tilings

Meeting on September 12th, 2015

Agenda: Golden Spiral 