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If you've ever used Twitter you'll know that you're only allowed to write 140 characters in any one tweet. The team at Twilgo used this idea, combined it with a programming language (Logo) and set up a site for us where you can write instructions to design a mathematical picture, but only using 127 characters!
If you want to just get going, follow the link here and come back to this page later to see what our challenges are for this month.
For example, let's say you wanted to mark out a square which has sides 10 units long.
The first instruction will be to move forward 10 units. In Twilgo we write this as FD 10.
Then we have to turn through 90 degrees before we draw the next side. In Twilgo we write this as RT 90.
We need to do this four times to get back to the beginning so we could write:
FD 10 RT 90 FD 10 RT 90 FD 10 RT 90 FD 10 RT 90
However, that uses a lot of characters so we can make it shorter by writing:
REPEAT 4 [FD 10 RT 90]
That's the general idea so now go to NRICHTWILGO and explore! Everything you need to know is in the HELP tab.
a regular hexagon
a dodecagon
a circle.
Challenge 2. Design a pattern which uses:
five squares
six hexagons
three dodecagons
four circles.
Challenge 3. Make a design based on spirals.
Challenge 4. Can you find instructions that would result in this design? Can you find a shorter set?
Challenge 5a. Can you come up with a program that covers the Twilgo window with a tiling? Challenge 5b. Can you think of a way of making an algorithm that would tile the whole plane (not just the Twilgo window) if left to run forever? This is hard and it may be impossible.
Want more? There are more challenges here.
Introducing NRICH TWILGO
Age 5 to 18
Challenge Level 
If you've ever used Twitter you'll know that you're only allowed to write 140 characters in any one tweet. The team at Twilgo used this idea, combined it with a programming language (Logo) and set up a site for us where you can write instructions to design a mathematical picture, but only using 127 characters!
If you want to just get going, follow the link here and come back to this page later to see what our challenges are for this month.
Starting to use TWILGO
For example, let's say you wanted to mark out a square which has sides 10 units long.
The first instruction will be to move forward 10 units. In Twilgo we write this as FD 10.
Then we have to turn through 90 degrees before we draw the next side. In Twilgo we write this as RT 90.
We need to do this four times to get back to the beginning so we could write:
FD 10 RT 90 FD 10 RT 90 FD 10 RT 90 FD 10 RT 90
However, that uses a lot of characters so we can make it shorter by writing:
REPEAT 4 [FD 10 RT 90]
That's the general idea so now go to NRICHTWILGO and explore! Everything you need to know is in the HELP tab.
This month's challenges:
If you would like to let us know how you got on with these, you can either
join Twitter and upload your designs into the gallery
or
take a screen shot of your design and upload under the 'submit a solution' tab here
Challenge 1. Write instructions for:
an equilateral trianglea regular hexagon
a dodecagon
a circle.
Challenge 2. Design a pattern which uses:
five squares
six hexagons
three dodecagons
four circles.
Challenge 3. Make a design based on spirals.
Challenge 4. Can you find instructions that would result in this design? Can you find a shorter set?
Challenge 5a. Can you come up with a program that covers the Twilgo window with a tiling? Challenge 5b. Can you think of a way of making an algorithm that would tile the whole plane (not just the Twilgo window) if left to run forever? This is hard and it may be impossible.
Want more? There are more challenges here.
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Geoboards
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
