LOGO challenge - tiling with equilateral triangles
Try making patterns with equilateral triangles
Age
11 to 14
Challenge level
Problem
At a maths conference someone said that - "not much can be done when tiling the plane with equilateral triangles."
Below are just four tilings that grabbed my attention.
Try replicating them in LOGO.
Can you extend this catalogue of tilings?
Using ONLY equilateral triangles what other tilings can YOU devise?
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Teachers' Resources
Let's start to experiment:
Here is a procedure for an equilateral triangle:
to equi :s
repeat 3[fd :s rt 120]
end
Now I think that I might be able to tile the plan by putting enough triangles together as a basic unit turning a bit and repeating myself so let's see:
to Pat1 :r :p :s
repeat :r [repeat :p[ equi :s rt 60]]
fd :s
end
Well Pat1 10 4 20 just gives a hexagon - so would Pat1 6 4 20 of course.
I might experiment a little more with the variables but perhaps just turning right 60 after every triangle is a bit predictable. How about:
to Pat2 :r :p :s
repeat :r [repeat :p[ equi :s rt 60 fd :s] repeat :p [equi :s lt 60 fd :s]]
end
That is slightly more interesting but a bit ad hoc. Hope you are getting an idea though ...