A Recursive Process | A Recursive Process

Chaos Game v2

March 19, 2014, 12:00 am

I prepared a small demonstration of the Chaos game for some math teachers. First we used transparencies, markers, dice, and rulers, but humans are mistake-prone and slow.

To The Computer!

I decided to experiment with the rules of the game to see where it’d go.

Human Error

What happens wh...

Buffon’s Needles simulation in Processing

March 14, 2014, 12:00 am

Buffon’s Needle is a famous way to (slowly) estimate $\pi$ .
Here’s a processing.org program to calculate $\tau$ (to keep the math-hipster hatred of $\pi$ -day at a critical point and concave up).

Link to live simulation and code. All variables are easy to change, size of window, length of needle, spacin...

Power Series on Desmos

March 5, 2014, 12:00 am

This is a crosspost from my Photo 180 blog.

Power Series work in AP Calculus BC.

$\sum_{n=0}^{\infty}(-1)^{n}\frac{x^{2n+1}}{(2n+1)!}=\frac{x}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}-...$

Process: Since it’s a infinite series, look at partial sums to get an idea what this graph looks like.
So look at
$y_1=\frac{x}{1!}$
$y_2=\frac{x}{1!}-\frac{x^3}{3!}$
$y_2=\frac{x}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}$
…
Perfect time to use technology.

Texas Instruments Method

Go to y1. Enter in $y=x$ .
Gra...

Brian Greene’s take on teachers.

February 5, 2014, 12:00 am

My best teachers were not the ones who knew all the answers, but those who were deeply excited by questions they couldn’t answer.

— Brian Greene (@bgreene) February 5, 2014

Fantastic.

Two James Tanton Questions

January 28, 2014, 12:00 am

It’s midterm week at school, and James Tanton threw out two interesting questions in two days. I spent a little time programming “solutions” to these problems (not solutions, just verifications for an infinitesimally small portion of the natural numbers).

Problem One:

Start with a prime, s...

Prime Matrix – Processing

January 16, 2014, 12:00 am

Saw this tweet yesterday:

All prime numbers between 2 and 2073600 mapped as pixels ARE THE MATRIX http://t.co/5skoRMc0gh

— Kyle Hill (@Sci_Phile) January 14, 2014

Pretty cool. Josh Giesbrecht also did some great work with Mathematica to replicate the image.

Thought that primes-look...

Four and Five – Cartalk Puzzler

January 4, 2014, 12:00 am

From cartalk.

Ray: Get a piece of paper and write the number four, leave a little space, and write the number five. What common mathematical symbol, when placed between the numbers four and five, will result in a number that is greater than four but less than six?

Tom: It has to be a mathem...

Pebbling a Checkerboard Game (Or Chessboard)

December 20, 2013, 12:00 am

I happened upon this tweet when I got to work this morning:

Freeing imprisoned clones: finally a use for geometric series that isn't about computing interest http://t.co/FpJWxO73xI @numberphile #math

— Matt Caicco (@MatthewJCaicco) December 20, 2013

So I watched the fantastic numb...

Super Ball

December 6, 2013, 12:00 am

From Wikipedia’s entry on Super Balls.

Wham-O Executive Vice-president Richard P. Kerr said, “Each Super Ball bounce is 92% as high as the last.

Will it ever stop bouncing?

Geometric sequences and series anybody?

edit:
Amazon review of a superball:

What’s the bounce return rate?

Why I Blog (Nowak requested post)

November 12, 2013, 12:00 am

Fellow Empire State rep Kate Nowak requested answers to the following in her post: Tell Me Why You Blog.

1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation?

I got...