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ELI5 Yahaaa

Eratosthenes, about 240 BC

How We Measured the Earth With a Stick

Two shadows, one long walk, and the size of the planet — without leaving Egypt.

Noon at Syene A stick casts noshadow at allNoon at Alexandria The same stick castsa short one
The whole measurement is the difference between these two.

  1. Step 1 of 5

    It started with a well that had no shadow.

    1 Midsummer noon2 Sunlight reachesthe bottom of awell3=The Sun isexactly overhead

    At noon on midsummer's day in Syene, the Sun shone straight down a deep well and lit the water at the bottom. Directly overhead means a vertical stick casts no shadow at all. That is an odd enough fact to remember.

  2. Step 2 of 5

    On the same day, a stick in Alexandria did cast one.

    If the Earth were flat Both sticks:identical shadowsWhat was actually seen One stick: no shadow.The other: 7°

    Five hundred miles north, the same Sun at the same moment was not overhead — it was about seven degrees off. On a flat Earth that is impossible: the Sun is far enough away that its rays arrive parallel, so a flat ground would give both sticks the same shadow.

  3. Step 3 of 5

    Seven degrees is one fiftieth of a circle.

    7.2° between the twoshadows360° in a full circle7.2 goes into 360fifty timesSo the gap is afiftieth of Earth
    No instruments beyond a stick. The rest of it is long division.

    A full circle is 360 degrees, and 7.2 goes into it exactly fifty times. So the distance between the two cities must be one fiftieth of the way round the whole planet. That is the entire trick.

  4. Step 4 of 5

    Then someone had to walk it.

    1 Pacers walkbetween thecities2 About 5,000stadia3×Multiply by504 The wholeplanet

    The distance between the cities was measured by professional pacers — men trained to walk with an even stride and count. They made it about 5,000 stadia. Multiply by fifty and you have the circumference of the Earth.

  5. Step 5 of 5

    He was within a few per cent.

    Eratosthenes' answerroughly39,000–46,000 kmThe true circumference40,075 km

    The real answer is 40,075 kilometres. Depending on which stadion he was using, Eratosthenes got somewhere between 39,000 and 46,000 — with two sticks, a well, and some arithmetic, two thousand years before anyone could check.

    He never travelled to Syene. He read about the well in a library, which is where he worked.

The short version

7.2 degrees goes into a full circle exactly fifty times, so the walk between two Egyptian cities was one fiftieth of the planet — and professional pacers walked it. Eratosthenes landed between 39,000 and 46,000 kilometres against a true 40,075, two thousand years before anyone could check.

Try it yourself

On any sunny day, get a friend far north or south of you to measure their noon shadow at the same moment as yours. The lengths will not match.

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