## rLogo puzzle

rLogo is a Java based implementation of the Logo programming language. I used a simple ‘starter’ in a recent Maths lesson where students had to learn about the exterior and interior angles of a polygon and learn to solve problems along the lines of ‘can a regular polygon have an interior angle of 125 degrees?’.

• Imagine you are on a golden beach in the Med. You are facing East and as it is early in the morning, the Sun is rising.
• Walk 100 paces forward. Turn right through 90 degrees. Walk another 100 paces forward. Turn right through 90 degrees. Walk another 100 paces forward. Turn right through 90 degrees. Walk another 100 paces forward. Turn right through 90 degrees again.
• What shape have your footsteps traced in the sand?
• Which direction are you facing in?
• How many degrees have you turned through?

Challenges included

• How would you change the instructions to draw a regular hexagon?

After some pairs work and some ‘walking through’ solutions (a rare use of ‘kinetic intelligence’ in Maths) I introduced the Logo primitives for forward and right turn, and used the rLogo tutorial page on a projector to draw solutions. I mentioned the ‘repeat 4 [fd 100 rt 90] approach as well. Finally, I suggested that crop circles might be drawn the same way…

It all seems to have stuck but it will come as no suprise that people had problems setting up and solving the equation to show that a regular polygon can’t have an interior angle of 125 degrees…