Math Circle Meeting: October 15th, 2016

Agenda: Mathematics and the Presidential Election

Facilitated by: Kim Moore

Voting Methods

Mathematics and the Presidential Election Student Guide

mam

Candy Simulation

  • Popular Vote

  • Representative Vote

  • Modified Electoral College

  • Electoral College

Which method do you think is the most fair?

Which is the best way to decide?

Can you think of a way to make the system even better?

electoral-map

Are the number of electoral votes allotted to each state directly proportional to the population of the state?

  • Run-off Methods

Challenge

What is the smallest percent of popular vote you could win and still win the electoral vote?

button

Electoral College and Population Reference Sheet

Other Interesting Resources:

Math Circle Meeting: September 10th, 2016

Agenda: Irregular Polygons

Presenters: Aubrey Rhoden and Kim Moore

Irregular Polygons Practice Problems 

Irregular Polygons Practice Problems Solutions

MATHCOUNTS Minis

  • How can you use similarity to solve irregular polygon problems?

  • How can you use the Shoelace Method to solve irregular polygon problems?

Explanation of Shoelace Method

A Million Dollar Problem

imbedded-square

Four Challenge Questions

  • Does every taxi loop have an inscribed square?

  • Does every loop have more than one inscribed square?

  • Does every taxi cab loop have an inscribed square if diagonals are allowed?

  • What is the link between this problem and the 1911 inscribed square problems of Toeplitz?

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