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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.

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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?

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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

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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?

Diamonds are forever.

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