Almost everyone knows and accepts that Earth is not a flat disk but instead a slightly squished-at-the-poles sphere – after all, the ancient Greeks proved this over 2,300 years ago. But in recent years flat-Earthers have been empowered by both the number of "celebrities" lending their status to the cause, and the Internet allowing keyboard warriors to spread their views across a global stage.
Some flat-Earthers are going to quite the expense to prove their theories correct; one guy took an airplane flight, costing around $200, so he could use a level to prove himself correct. Another is building an actual rocket, costing in the realms of $20,000, to launch to space and prove it.
There are many ways to challenge their beliefs. We can discuss how the Sun would not set on a flat world. We can ask them how volcanoes and earthquakes would happen on this wafer-thin planet. Or maybe discuss if an asteroid impact could even flip it like a pancake.
But, if you are looking for a way to disprove it on a budget and without any maths, this is the list for you.
The Fault Is Not In Our Stars But In Ourselves
The simplest, cheapest way to show that the Earth is not flat is to look at the night sky. At any given time, certain stars and constellations will have a certain height on the horizon. Depending on your relative position on Earth you won’t be able to see some of them when others can. The classic example is that you can’t see Polaris, the North Star, from the Southern hemisphere.
As you move anywhere on Earth in a North-South direction you’d be able to see constellations moving up and or down in the sky, new stars appearing and old stars disappearing. There is no way for this effect to happen on a flat disk.
Stick It To The Man
The next step up in the scale of complexity (or if you don’t like to be out late at night) is to use sticks and shadows. To do this, you need two people at different distances from the equator and two sticks with the same length. You place the sticks in the ground and measure the length of the shadows at the same time. If the Earth is flat, the shadow will be the same. But since it’s not, the shadow length will be different.
This is not only a very straightforward way to prove the roundness of our planet. It can also allow you to measure just how big the planet is. This method, done with water wells rather than sticks, was used by Eratosthenes to calculate the circumference of the Earth back in the 3rd century BCE.