There are so many negative numbers and statistics flying around at the moment,it's a little overwhelming.

So let metell you an inspiringstory about numbers: it willbea relief to think about something else for a few minutes.

## Travel back in time

About 2,250 years ago, there was a man called Eratosthenes.

He wasone of those ancient Greeks who changed the world.

He was a polymath,someone with expert knowledge of a range of topics.

A mathematician, geographer, astronomer, philosopher, poet, and music theorist.

He'sfamous for being the first person known to have measured the earth's circumference.

How did he do it?

It's surprisingly simple.You just need some basic geometry.

Watch the short clip below of the great Carl Sagan to see how it was done.

I've set it to play from the 4 min 11 sec mark, because that's where Sagan explains the calculations. But the few minutes before thatpoint are also wonderful.

In case you couldn't watch or hear the video, I'll explain the story quickly.

Around 245 BC, when Eratosthenes was in his 30s, he was working as a librarian in the famous Library of Alexandria in Egypt.

It was there where he read about a water well in the city of Syene(modern-day Aswan in southern Egypt).

At midday every summer solstice,the sun would shine directly down into the well, illuminating the waterat the bottom - but casting no shadow on the walls of the well.

Itmeant the sun sat directly above Syene at that exact moment.

So Eratosthenes wondered, if he stuck a pole in the ground in Alexandria at thatsame moment, would it cast a shadow?

And it turns out it did.

## What did it prove?

His little experiment demonstrated that the surface of the earth was curved like a sphere.

Why? Because his pole in Alexandria was sticking straight into the airbut the curvature of the earth made it face slightly away from the sun, causingthe pole to throw a small shadow onto the ground.

And that allowed him to do something else.

Since he knew the height of the pole, and the length of the shadow it cast, it meant he knew the lengths of two sides of a right-angled triangle.

That meant he could figure out the length of the third side of the triangle, and hecould also figure out theangle at the top of the pole, between the sunbeam and the pole itself.

It was 7.2 degrees.

Therefore, he knew the sun was hittingAlexandria at an angle of 7.2 degrees precisely at midday on the summer solstice.

## When a fraction goes a long way

And that left him with one final measurement.

To figure out the circumference of the earth, heneeded to somehow measure the distance between Alexandria and Syene.

So he asked someone (or a team of people) to walk it.

Those people were called "bematists", professional surveyors who weretrained to measure vast distances extremely accurately by pacing the distance.

They estimated the distance between the two cities was roughly 5,000 stadia (or 800 kilometres).

And that was everything Eratosthenes needed.

He had all the ingredients to calculate the circumference of the earth.

## A few assumptions help

Let's go.

Assume the earth is a perfectsphere (it's not, but it's not a problem for thesecalculations).

We know there are 360 degrees in a circle.

If you cut the earth in half, theearth's great circle will obviously have360 degrees, and the circumference of that circle (i.e. the total length of its perimeter) could be divided up into equal bits of whatever length.

Eratosthenes knew that the distance between Syene and Alexandriawas 7.2 degrees along the surface of the earth.

So howmany of those distances would he need to stretch around the entire 360 degree circumference of the earth?

He divided 360 by 7.2, which gave a neat 50.

Nice.

That meant, given the distancebetween Alexandria and Syene was 800 kilometres, all he hadto do was multiply800 by 50, which came to 40,000.

And that was it.

Thecircumference of the earth was 40,000 kilometres, according to Eratosthenes' calculations.

## Was he correct?

He was *incredibly *close.

As it turns out, themeridional circumference of Earth (from pole to pole) is roughly 40,008 km, and theequatorial circumference is about 40,075 km (it's bigger at the equator because Earth slightly bulges in its middle).

Not bad for someone with such rudimentary tools.

Eratosthenes used his new knowledgeto revolutionise map making.

He drew amap of the known worldwith parallels and meridians, makingit possible to estimate real distances between objects, and plotted the names and locations of hundreds of cities over the grid.

It was the beginning of modern geography.

Anyway, I hope that's been a pleasant escape from reality.

When so much attention is focused on the maths of hospitalisations and vaccinations and contagion, it'seasy to forget that maths can also be a source of innocent joy.

Take care this week.

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