If I sail a ship to the far far seas, continue on, and on, and on and– well, you got the point. Where will I find myself? Well, if I travel in a more-or-less straight line (ignoring weather or geography, or time constraints, or my pending homework) I will end up right where I started. Why? Because the Earth is round. Duh.

Today we have a lot of sophisticated (and simple) methods of calculating the curvature and size of the earth. But how did humanity figure this out in the first place? I mean.. it’s so easy, without the help of satellites, airplanes and Jules Verne, to look at the flat horizon and mistake the earth for a flat table top. How could anyone figure out not only that the world is not flat, but also calculate the size of its radius?

Well, when in doubt, try it out. Hey.. I think I like that motto. It’s rhyming, and rhymes are usually true. Just ask Dr Seuss.

Plus.. it works!

[youtube_video id=”56K1sj70X24″]

So, a long time ago, people believed the earth was flat, and that if someone was to go away off to the horizon, he (or she) would fall off the end of it.

We look at this ancient concept as ridiculous today. We al know that the flatness of the horizon is an illusion. We have more than enough proof today to see absolutely that the world is definitely curved, but it is for the ingenuity of people like Erastosthenes of Cyrene that humanity knew about this so long ago.

Eratosthenes was a greek scholar that lived in 275-194 B.C. in Alexandria (Egypt). Some even say he was the curator of the library of Alexandria. One day, he had a bright idea. Actully, it wasn’t just any day, it was the summer solstice, and it wasn’t just any idea, it was a brilliant experiment. But, let’s not dwell on the tiny details. He was very smart and he acted on it.

He received word that on that summer solstice day the sun is reflected perfectly in a deep well in Syene. But at the same time and same day, in Alexandria, the sun wasn’t reflected perfectly in the same type of well. Why?

It occured to him that the only way that could have happened is if the earth was not flat. Using simple trigonometry, he managed to calculate the radius and diameter of the earth. In this experiment, we do the same, only we use a Pummelo. Because it’s easier. And tastier.

Materials Needed for the Experiment:

  • Any type of round, big, (preferably tasty) fruit. I used a Red Pummelo, but a Watermelon will work too.
  • Small sticks to simulate Eratosthenes’ big sticks.
  • One bright and focused lamp.
  • A ruler.
  • A sharpie.

The pummelo represents the earth. Nevermind it isn’t perfectly round – the earth isn’t either, and we are only trying to see the method, not actually calculate the radius of the fruit.

Error Margin

Wow, there’s a lot of reasons to have that, but they are less important than you would have thought. If our goal was to accurately calculate the circumference of the earth (or the fruit) then our method is not perfect at all.

The fruit was far from being spherical. It was almost cubic at some pionts, flat at others, and had lots of bumps on it. The radius on one small section of it is not necessarily the radius on another point on it. So, error margin in that matter is quite obvious.

But Eratosthenes’ method is important not necessarily because of the numerical result, but for its significance in discovering the world is a sphere. Remember, Galileo Galilei almost lost his head over this idea (among others), and that was about 2000 years after Eratosthenes.

Not to mention many of us learned the (sadly, very common) misconception that Christopher Columbus is the explorer who discovered the world is round.


Humanity was Smarter Than That a long time ago, and Eratosthenes’ ingenious way of estimating the circumference verifies it completely.



Earth Radius:

Trigonometry Reminder:

Flat Earth (not!):

Red Pummelo is good for you:


  1. Loved the experiment and will use something similar for my classes for the new school Term in the UK. You are right, Science should be fun and you should be able to take away deep learning from it. Well done and if you have the qualifications, I will get you a job in a tough but nice school in the UK.

  2. Good stuff – we have competition!

    Ed Booth
    Series Producer
    BBC Bang Goes The Theory

    1. @Ed Booth, huge compliment, thank you! Unfortunately, I can’t watch the show from the USA on the site. I’ll have to look for the DVD. In any case, thank you for possibly one of the coolest comments I got here 🙂

  3. That video is amazing even though i am
    13, i discovered something my science teacher has perhaps been trying to explain to me
    for like ages because my class and i are learning about the the earth-if the earth is circling around the
    sun or if the sun is circling around earth, and to find out if the earth is flat or round-but this
    helped me alot to understand that that the earth is round.

    so now i can show this to my class and too my teacher and to prove to them
    that the earth is ROUND-thank you

    P.S-my class will probly still have a debate about this.lol

  4. Krunal Dedhiya

    It is difficult for me to believe that earth is round. I strongly believe that earth is disc-like or coin-like shape but not ball like shape.

  5. Bruce Atwood

    Eratosthenes assumed that the Sun was very far away.

    An alternative conclusion would have been that the Earth is flat and that the Sun is 4,000 miles away.

    Of course, we can measure the curvature directly on ice or water on a big lake or bay.

  6. This (and the other page about the Earth being flat:http://new.smarterthanthat.com/astronomy/top-10-ways-to-know-the-earth-is-not-flat/ ) are pretty awesome. Thanks very much!
    I did want to point out that in order for this sort of discourse to affect the opinions of people like

    It is very hard to convince someone who doesn’t have a grounding in Science and/or doesn’t trust Science. That’s unfortunate but I imagine Eratosthenes probably had people who thought he was an idiot because the Earth is obviously a disk or a coin…


  7. DeanMatthewIzzard

    Hold on, am I missing something … IF the Earth was flat, two sticks in different locations would still produce different length shadows.
    Also, your equations assume that the Sun is in 2 different locations, and only a single beam of light is coming from each, and these two beams are parallel. The Sun has a diameter, which means that light would be travelling to the stick over several different trajectories. Sunlight hitting the stick from different angles to those you’ve assumed would change the calculated arc length. There seems to be a lot of assumptions required for this to apply to the real example of our Earth and the Sun.
    Basically, I like this experiment as a method of showing students how to approximate the “circumference” of Earth in a certain plane (remembering that it isn’t exactly spherical), but it doesn’t seem to be a PROOF that the Earth is NOT flat. Am I missing something or was Eratosthenes? As far as I can tell, the only way the Sun could be reflected in two different wells (assuming the wells are perpendicular to the tangent of the curvature of the Earth) in two separate places, is if the Earth was concave to the Sun. A flat Earth AND a spherical Earth could both explain the result of this experiment … Couldn’t they? Help me out if I am missing something.

  8. if the earth was round and sun 93 m m away youd never see the morning rays pointing in a fan like direction-secondly if the sunn was 93 m m away wed have one tempuratre  here- the equator is about 6,ooo m from either poles that 6,000 miles represents .000004 of the distance to sun- youd never have temperature fluxuations in that small of distance

  9. also if the round earth is spinning at 1000 miles an hr once a plane left the ground hed find that the runway was running away  secondly all land masses would conglomerate to the equator on a spinning earth- when you see a ship going over the horizon then ‘blam its gone but not because of earth curvature- just break out the binoculars–on clear days people can see Chicago across lake mich- that’s 60 miles- at 25,000 circumfrance thas roughly 8 inch drop per mile or you wouldn’t be able to see anything under 40 feet- and that’s just not so!  – if some body held a real big rubber ball and you stood on the top then tried to walk around it guess what ?  uyou’d be upside down if you could stand upside down and your pen fellmm out of your pocket which way would it go?- gravity is a manmade word- it doesn’t exist- theirs only air density-anything I let go from my hand will fall because its heavier than airpp speaking of such things- even if a spacecraft, made mostly out of aluminum could get to space in its 2,0000 degree vaccumm- it would melt- secondly if you were on the moon in a spaceship youd never be able to take off-  the thrusters push against the ground ,for a few seconds and then guess what?- yup your right then the thrusters push against the atmosphere- their is no at mosphere on the moon  all long tunnels-railroad tracks bridges airplane trajectorys are never built with a predetermind curvature-always on the straight!- why are the constellatioms always fixed and predictable? theirs only one answer folks and that’s the flat earth– by the way- the bible says the earth is flat  also

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