### Darts and Kites

A rhombus PQRS has an angle of 72 degrees. OQ = OR = OS = 1 unit. Find all the angles, show that POR is a straight line and that the side of the rhombus is equal to the Golden Ratio.

### Roaming Rhombus

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point D?

### Center Path

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of the point X and prove your assertion.

# LOGO Challenge 2 - Diamonds Are Forever

## LOGO Challenge 2 - Diamonds Are Forever

It is useful to feel comfortable using procedures, though if you have not met procedures before- this might help you feel why they might be useful. More about procedures can be found in FIRST FORWARD 6 and in the next challenges.

The challenge is to produce elegant solutions to the problem. Elegance here implies simplicity. The focus is on rhombi. Or:

REPEAT 2 [ FD 40 RT 60 FD 40 RT 120]

The design below is part of tile seen in a shop - sadly now closed, at King's Cross in London. Can you generate it in as elegant a fashion as possible?

You can download some excellent free LOGO software from the internet atÂ http://fmslogo.sourceforge.net/.

There are many ways to tackle the challenge.

You might like to consider returning to this challenge when you have found out about procedures. For now you might like to see how you might use the REPEAT command.

Here are some ideas:
• Can you draw one rhombus?
• Can you write a single line of code that draws the two rhombi joined together?
You can change the pencolour by using the command SETPC followed by a number between 0 and 15.

Try drawing pairs of rhombi in different colours and in different arrangements. For example, what does the following line of code produce?:

RT 60 FD 40 RT 60 FD 40 RT 120 FD 60 LT 120 FD 20 LT 60 FD 20 LT 120 FD 60

Now, how are they connected?
What part does the colour play?
Could you repeat this pattern forever?

Would it be useful to be able to store some commands to re-use? If so you need to learn about procedures.