The Best Square

How would you judge a competition to draw a freehand square?

Trig-trig

Explore the properties of combinations of trig functions in this open investigation.

Chance of That

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

Investigating Twilgo

Stage: 4 and 5 Challenge Level:

Twilgo is a cool combination of Twitter and Logo. The basic idea is this: what images can you create using at most 140 characters and the commands from the Logo coding system? You can simply have fun making images or you can think about the possibilities in more detail -- this investigation is both open and endless!

First, experiment with http://twilgo.com and draw some images.

You can then start to get more thoughtful with these two explorations:

1. Think of an interesting and relatively simple shape, such as a Christmas tree or a star. What is the shortest set of instructions that you can create to make such a shape? Can you PROVE that there is no shorter set of instructions which would generate such a shape?

2. Think of a very complicated but mathematically exactly-defined shape, such as a Koch snowflake, a Mandelbrot set or a Sierpinski gasket. Consider how these could be approximated using Twilgo. Is it possible to redefine such shapes in a mathematically exact manner as a piece of Logo code?