### Is the Earth flat?

Well, the shape of the Earth is quite an interesting topic. In science and physics, it’s never shameful to start with approximations. We can start with some working hypothesis and improve our ideas along the way. As long as we keep a working and playful spirit, we will continue to learn and improve. Wasn’t it the same gentleman who wrote “E=mc²”, who also wrote: “Once you stop learning, you start dying”? So let’s all try to follow Einstein’s advice, keep learning, and not die too soon.

### Flat

Determining the shape of the Earth was quite a challenge for the human brain. It started in very ancient times. As long as you stand on your own two feet and watch around from the solid ground, an argument can be made that the Earth is flat. A farmer plowing his field would say so with absolute certainty. And that would definitely work as a first approximation.

### Spherical

However, the best way to figure it out would be to watch it from far above. We would then easily find and decide: does the Earth look rather flat (like a fried egg), or spherical (like a hard boiled egg)? Look:

A 21st century picture of the Earth, from above (curved)

Unfortunately, the means to watch the Earth from a distance were not that common back in the day. Rockets and satellites didn’t exist. Aria(d)ne was a figure in Greek mythology, not a wonderful piece of technology. The race to space between the Americans and the Soviets wasn’t yet as boiling hot as it was during the Cold War. And Space-X was not yet invented (neither was PayPal nor Zip2). So you had to be very inventive to produce a lot of science with little means (which we love). So who were the candidates to solve this existential question? Plato and Aristotle were already convinced that the Earth was spherical. But the first gentleman who really kicked off the global geodesy contest was a Greek traveller by the name of Eratosthenes. This very creative man figured out the circumference of the Earth with an astonishing precision (1.7%), using barely more than a stick. This fascinating story deserves an article in its own right (which we will certainly write in the future!).

### Ellipsoidal

So let’s review our successive approximations. Our first approximation is flat. Our second approximation has more depth to it: spherical. With a minimal number of characters, that would translate to: “x²+y²+c²=r²”. Since we also found out that the Earth was spinning around its axis, we later came to a third (and better) approximation: ellipsoidal. In more efficient and abstract wording: “(x/a)²+(y/a)²+(z/c)²=1”. That makes interesting improvements to our first hypothesis, one step at a time.

### The geoid

So, flat, spherical, ellipsoidal, what’s the next step? Well, the next step would be to describe all the details and irregularities of the Earth: mountains, volcanoes, craters, islands, oceanic trenches, and so on. That’s the physical shape, or “topography”. This is easy to understand. But we could also use something more etheric, some sort of “sensitive shape”, like… wait for it: an equipotential of the Earth gravity field. You’ll be forgiven if you didn’t guess that. You cannot invent it if you’re not working in the field. But let’s continue and to tease your curiosity: if you calculate the gravity potential of the Earth, and if you link all the points which have a same common given value, you also get a shape. We call it the “geoid”. Here’s a picture of the geoid smiling at you.

**The geoid**

### Conclusion

So, from flat to spherical to ellipsoidal, now you get to the finest approximation of Earth’s shape: “the geoid”. We’ll talk about the geoid in more details in our next articles. Conclusion: Is the Earth flat? Let’s put it this way: it depends on the error margin you tolerate. Today, we’d say the answer is a definitive no. Rather, it is a sphere, or an ellipsoid, or some sort of potatoid called the geoid. In future articles, you’ll get to know a lot lot more about the geoid, and also about the men and women who made the scientific advances and fascinating discoveries on this topic. Stay tuned for more!