Squares
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articleStart with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens? -
articlePeg and pin boards
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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problemFitting in
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ -
problemFirst forward into Logo 1: square five
A Short introduction to using Logo. This is the first in a twelve part series.
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problemLOGO challenge 5 - patch
Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
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problemLOGO challenge 7 - more stars and squares
Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.
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problemLOGO challenge - the humble square
Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.
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problemSquares, squares and more squares
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares? -
problemTrig rules OK
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
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problemLOGO challenge 3 - star square
Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles