Imagine you have a very long rope that goes all the way around the equator of the perfectly spherical earth. Then you cut the rope and insert an extra metre. Will it make any difference?

Intuition might tell you that this is not the case, since our planet is so much larger in comparison. However, by using mathematics rather than intuition, it turns out that just one extra metre would allow the rope to be lifted around 17 centimetres above the ground.

The circumference of a circle – in our case, the distance you would travel around the equator – is found by multiplying pi by the earth’s diameter (the distance when cutting straight through the earth’s core). Playing around with this simple formula shows that the new circumference of the rope is completely independent of length, and the same result would happen if we wrapped a circular rope around the entire Milky Way.

A crucial benefit of mathematics is providing an objective way to scale up thought experiments beyond dimensions we cannot imagine. Key is to make the right assumptions. Is the earth actually perfectly round? Yet again, the situation is not as simple as we might think.

Measuring the earth’s diameter across the equator, we find that this is 44 km longer than the diameter across the poles. Rather than being a perfect sphere, our planet is squished into a shape known as oblate spheroid.

This is due to the rotation around its axis: looking at the equator as a disk, the earth has a much larger diameter there than a slice near the poles. The so-called centripetal force, which results from rotation, is therefore larger at the equator and stretches the earth out more.

There are many more intricacies underlying the earth’s geometry, but always remember to check your intuition with maths.