Tiling the Plane

sarlaur

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Question: Which of the following shapes can be used to tile the entire plane?

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I believe that all of these shapes could be used. Is that correct?
 

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Question: Which of the following shapes can be used to tile the entire plane?
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I believe that all of these shapes could be used. Is that correct?

Your graphic was broken and did not come through.
 
By what basis have you determined that each of these five shapes can tile an entire plane? I'm not necessarily saying you're wrong, but if your class is anything like every math class I've ever had, you'll only get a few points for the right answer. The majority of the points come from justifying your answer.
 
By what basis have you determined that each of these five shapes can tile an entire plane? I'm not necessarily saying you're wrong, but if your class is anything like every math class I've ever had, you'll only get a few points for the right answer. The majority of the points come from justifying your answer.

I think it would work because each of the shapes, when duplicated, can create symmetrical figures. As long as the pattern is symmetrical, you can use it to infinitely tile?
 
I think it would work because each of the shapes, when duplicated, can create symmetrical figures. As long as the pattern is symmetrical, you can use it to infinitely tile?
So... circles can entirely fill the plane, with no overlap? ;)
 
Question: Which of the following shapes can be used to tile the entire plane?

attachment.php


I believe that all of these shapes could be used. Is that correct?

Tiling has a specific definition in Mathematics (geometry). Are you supposed to use that definition?
 
So... circles can entirely fill the plane, with no overlap? ;)

Hmm, I see what you mean. I suppose symmetry isn't the right standard here. I learned that squares, triangles, and hexagons are the only shapes which can perfectly tile an entire plane. So then, it is only the first two (the square and the triangle) which are correct?
 
I learned that squares, triangles, and hexagons are the only shapes which can perfectly tile an entire plane.
No; squares, equilateral triangles, and regular convex hexagons are the only regular convex polygons which tile the plane. There are many, many other "shapes" which can tile the plane, such as the rectangular ceramic wood-look tiles that some people are using for flooring (example). ;)
 
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