## Exploring Mathematical Patterns with LOGO

Julianne Hammink

LOGO is a simple yet powerful programming language designed to be used with kids. The commands are simple, and for this project you’ll need to know only three.

• RT 90 turns the ‘turtle’ 90º to the right
• LT 90 turns the ‘turtle’ 90º to the left
• FD # moves the turtle forward. You must specify the distance by replacing # with a number.

In this project, we’ll look for the patterns and designs hidden in the multiplication tables.

1. Choose a number. List the multiples of this number, up to 10 or 11. You may use the table at the bottom of the page to write down the numbers. I used the multiples of four.

### E.g.: 4812162024283236404448

1. Add the digits of each number, until you have a string of single digit numbers. Can you see a pattern?

### E.g. 483726159483

1. Add a zero to the end of each number in your pattern.

### E.g. 408030702060105090408030

1. Open MSW LOGO. Double click on the icon on your desktop. You’re going to draw the number pattern you just found.

Move the turtle forward by typing FD, and then the first number in your pattern (FD 40) Press ENTER.

1. Turn your turtle by typing either LT 90 or RT 90. Always turn your turtle the same way each time.

1. Move your turtle forward again, using the second number in your pattern (FD 80), then turn your turtle again. Continue moving your turtle forward according to your number pattern and turning it. What do you see on your screen?

1. You may have to repeat your number pattern three or four times for your complete spiral to appear.

1. Every number makes a different spiral. Try drawing another spiral over the first one. (Change pen color by going to ‘Set’ then clicking on ‘Pen Color’) Do the spirals fit together? Can you find two numbers whose spirals do fit together?

Use this table to work out your number pattern.