Robots, Coins, Patterns, and a Prism. Math Circle 2.0 Oct 10 2015

Robots

Last week we re-programed the robot so that it could backwards.

Now, the robot not only understands North and West, but also South and East.

Furthermore, now instead of giving one instruction at a time, we give the robot all commands. To do so, first we write out the steps, then have the robot read the steps, and then see what the robot does 

Can we get the robot back from the NW to SE?

Coin Algebra

How many pennies in a nickel? How many in two nickels?

What is a dime worth in terms of pennies? In terms of nickels?

Started with a dime, a nickel, and a penny

trade nickel for five pennies. How many pennies?

Trade dime for ten pennies, how many pennies?

How many nickles can we get

Patterns

Lego chains

Drawing zigzags

1. What is the core pattern? How many times can we repeat this pattern given the pile of legos below?

Draw Triangle, circle square, and repeat. 

Experiments 

Split light into colors with a prism

What color is sunlight? Where do the colors of the rainbow come from?

If we split into ROYGBIV, where do brown, grey, and black come from? Why is the table brown, but we only get ROYGBIV from the prism?

And look at the Sun. How has the shadow changed in 3 weeks since solstice?

Homework 

Continue the patterns: