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?

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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

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Math Circles Meeting: April 4th, 2015

The 4th meeting of the Islander Math Circles, Spring 2015

FacilitatorDr. Frank Sottile

hyperbolicballpic

Agenda: Hyperbolic Soccer Ball

Hyperbolic Soccer Ball Instructions

Template for Center of Ball   Template for Side of Ball

Variations on the Hyperbolic Soccer Ball

  • What are the properties of parallel lines in hyperbolic geometry?

triangle

  • What are the properties of triangles in hyperbolic geometry?

Math Circles Meeting: January 31st, 2015

The 2nd meeting of the Islander Math Circles, Spring 2015

FacilitatorsDr. Aubrey Rhoden, Kim Moore

dracula

AgendaThe Human Vampire Conflict

I.  Do Vampires Exist?

  • Assumption One: Every time a vampire sucks the blood out of a human, that human becomes a vampire.

  • Assumption Two: It takes a vampire exactly one week to suck the blood out of a human.

  • How long would it take for the entire human population to turn into vampires?

  • What is the limit of the human population in this model?

  • What is the limit of the vampire population?

 

II. Mathematics of the Human-Vampire Conflict: a few more considerations…

  • Do humans have any defense against vampires?

  • Can vampires mate?

  • Can vampires be destroyed?

  • Are humans dying of any other causes?

  • Are human babies being born?

  • Do vampire have preferences for certain blood types?

twilight

Math Circles Meeting: January 10th, 2015

The 1st meeting of the Islander Math Circles, Spring 2015

FacilitatorsDr. Aubrey Rhoden

AgendaLarge Numbers

I. How big do numbers get?

 

II. Paper Folding

III. Calculating the Volume of the Universe

IV. Computer Memory Storage

 

Math Circles Meeting: May 10th, 2014

The 6th meeting of the Islander Math Circles, Spring 2014

Facilitators: Dr. Philip Yaskin

Agenda: Polygon Differencing

Problem

Put 4 integers on the corners of a square. At the midpoint of each side put the positive difference of the numbers at the corners. Connect the midpoints to form a new square. Repeat this process until it terminates. What do you notice? Do you think this happens no matter what numbers you put on the 4 corners? Repeat this process with a triangle. Now what do you think about your conjecture about the square? Repeat this process for an N-gon (a polygon with N sides). For which N’s does the process behave like a square? For which does it behave like the triangle? Prove your conjectures.

Survey from National Association of Math Circles