Islander Math Circle Meeting on May 7th, 2016

Agenda: The Mathematics of Spot it!

Presenters: Aubrey Rhoden and Kim Moore

Analyze the Spot It Deck Student Hand-out

spot it

Analyze the Spot It deck

  • How many cards are there?

  • How many different pictures are there?

spot it cards

Analyze the Spot It deck with three pictures, four pictures, five pictures

  • Can you create a deck with two pictures on each card? three? four? five?

  • How many different pictures would there be?

  • How many total cards?

  • How many total pairings?

  • How many pairing on each card?

  • Draw the deck

Is there an algorithm that can determine the number of cards you would need for  n pictures per card?

Useful Resources for Understanding the Mathematics of Spot-It

seven

Math Circles Meeting on December 5th, 2015

Agenda: Fractal Dimensions

Presenters: Aubrey Rhoden and Kim Moore

Understanding Fractal Dimensions

More Fractal Dimensions

Exploring Fractal Dimensions Student Worksheet

Sierpinski Triangle

  • 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?

Sierpinski Carpet

  • 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?

Koch Snowflake

How do you describe the dimensions of a Koch Snowflake?

tetrahedronHow do you describe the dimension of a Sierpinski Tetrahedron?

Menger Sponge

How do you describe the dimensions of a Menger Sponge?

Making the Tree

Koch Snowflake Template

Sierpinski Tetrahedron Template

Menger Sponge Template

fractal Christmas tree

 

 

Math Circle Meeting on November 7th, 2015

Agenda: Platonic Solids and Origami

Presenters: Aubrey Rhoden and Kim Moore

Platonic Solids

Platonic Solids

characteristics

Euler’s Formula

Euler’s Characteristic

  • What is the relationship between the edges, faces, and vertices in the five platonic solids?

  • What three dimensional shapes follow Euler’s formula?

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

non examples

cubo

Origami

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)