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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Introducing NRICH TWILGO

### Starting to use TWILGO

### This month's challenges:

#### If you would like to let us know how you got on with these, you can *either*

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Age 5 to 18

Challenge Level

If you've ever used X (Twitter) you'll know that you're allowed a maximum number of 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.

join X (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 triangle

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.

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.