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'Path to Where?' printed from http://nrich.maths.org/

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Yesterday morning, I went for a walk.
Here is a picture which shows the path that I took, looking from above:

straight path

Can you describe the shape of the path I took?
Can you imagine where I could have been to walk like this?

In the afternoon I walked a different route. This is what it looked like from above:

street path

Can you tell a story of where I could have been this time?

At the weekend I went for another walk.
This picture shows the path, again looking from above:

curved path

What is the shape of the path this time?
Where could I have been for my path to look like this?