Click here to register for the 2023 GLOBAL MATHS AND SCIENCE LESSON ON TUESDAY 10 OCTOBER. See below for links to lesson resources.

### 4. If you repeated the experiment for a very large square field making an outer ‘string-fence’ again exactly one metre longer than the perimeter of the field, would path between the field and the fence be wide enough for a cow to walk along it? Would a mouse be able to run along the path?

Follow-up 1  NOT-SO-SQUARE FENCE

A fence is built around a square field. Suppose another fence is built exactly one metre longer, so the path between the two fences is the same width all the way round including at the corners of the field.

How wide would this path be?

Would a mouse be able to run along it?

Could a farmer drive his cows along the path between the two fences?

Follow-up 2 BELT AROUND THE EARTH

A wire belt is tied tightly around the Earth at the Equator. (Let’s assume the Earth is perfectly spherical and we have no worries about oceans and mountains interfering with our ability to conduct this task!)

Now suppose the belt is made exactly one metre longer and held around the Earth at the Equator so that it is the same distance away from the Earth everywhere. Would a mouse be able to crawl under the new belt? How do you know?

Would a cat be able to crawl under?

Would the answer be the same for the moon?

What assumptions do you need to make to answer this question?