How much should a globe be cut up to render it into flat squares? (math question)

[imp_fireball]

I was watching this video, and it made me think how I would be able to do this in order to devise a realistic world map of a planet?

[waldronate]

All mappings from a sphere or spheroid to a plane have distortions. What kind of distortion you get (shape and size) depends on the projection you use. If you were trying to approximate the globe via many near-square facets tangent to the globe, then the number of facets would depend on the maximum amount of distortion that you're willing to tolerate.

When you ask about projecting the globe to a flat map, how much and what kind of errors are you willing tolerate? In other words, what constitutes "realistic" to you?

[Falconius]

I don't understand why the guy didn't just cut along the seams if he wanted it to lay flat.

That said, he is correct, this is what cartographers have been struggling with since forever. But the truth is as long as you know what the particular distortion of a projection it is, distortion doesn't actually matter that much, since as long as one know one can deal with it. The key feature is to do what you want with as few steps as possible, and so you choose the most appropriate projection for that task. And indeed for many tasks the distortion is relatively irrelevant. Which is why for some maps, notably subway maps, size and distance are totally ignored, in favour of station order and intersects.

[Azélor]

If for you a realistic map is a map without distortion:

Either use a sphere or a globe to draw the map on.
Use a 3d software and map it directly on the sphere.
Chose a compromise projection that will overall distortions in general like Robinson or Winkel tripel.

As Falconius said, distortions don't really make a map unrealistic as long as you understand what these distortions are.

[Redrobes]

Depends on the material its printed on and basically how much it will stretch. Printed vinyl can be wrapped onto cars and vans now and they have curvy bits to them. Whether you compensate the image for the stretch / shrink depends on the errors like Waldronate says. Its about how much error your prepared to tolerate.