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

Math Circles Meeting: April 18th, 2015

The 5th meeting of the Islander Math Circles, Spring 2015

FacilitatorAubrey Rhoden and Kim Moore

AgendaStochasticity and Coin Flipping

Let’s Do an Experiment!

Coin Flipping

 A Close Look at the Results

  • What is the largest number of heads you had in a row?

  • What is the largest number of tails you had in a row?

//www.radiolab.org/widgets/ondemand_player/radiolab/#file=%2Faudio%2Fxspf%2F91684%2F

Exploring Probabilities

Exploring Coin Flipping

  • What is the probability of getting 2 heads in a row?

  • What is the probability of getting 3 heads in a row?

  • What is the probability of getting 4 heads in a row?

  • What is the probability of getting a string of 7 heads or 7 tails if you flip a coin 100 times?

Pascals

Pascal’s Triangle and Coin Flipping

More Patterns in Pascal’s Triangle

Fibonacci n-step Number Sequences