2D shapes and their properties
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problemExplain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other. -
problemLOGO challenge 10 - circles
In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.
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problemLOGO challenge 6 - triangles and stars
Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.
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problemLOGO challenge 2 - diamonds are forever
The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.
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problemLOGO challenge 8 - rhombi
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
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problemCircles in circles
This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them. -
problemOverlapping circles
What shaped overlaps can you make with two circles which are the same size?
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problemPentagonal
Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon? -
problemCentral distance
Weekly Problem 1 - 2006
The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles? -
problemFirst forward into Logo 4: circles
Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?