What is it?

The supercomputer in control of the Aperture Science corporation and your primary frenemy throughout the game. When you finally encounter Glados, it doesn’t seem to be circular until you get up close. It’s actually composed of three spheres and makes one of the strongest arguments for the widely accepted but ultimately not provable spheres to awesomeness correlation hypothesis.

But could it be rounder?

No, it’s pretty round. Oh, except for those bars sticking out of the back of the spheres. Who the heck thought that would be a good idea? Here’s a picture:

Above: Through any three points, not all on the same line, there lies a unique circle

Runner-up: Companion Cube

Err… so close.

What is it?

It’s like a real barrel, but it’s a barrel in Donkey Kong. Don’t be get tricked by imposters.

But could it be rounder?

These barrels appear to be almost perfectly spherical when rolling down ramps, but if you’ve studied even rudimentary cooperage, you’ll know that their profile can frequently be misleading. A trained eye will notice the barrels are actually cylindrical.

Take a look at Donkey Kong’s stockpile at the top of the structure (exhibit A) and as each barrel falls to the next level down (exhibit B). They get points for being circular from a side view, but ultimately, these receptacles could be rounder.

Above: Circles are simple closed curves which divide the plane into two regions

Runner-up: Oil drum

Presumably, the flaming oil barrel is round on top.

What is it?

They’re the most feared of all red spherical demons, with horns and one green eye in the center of their grinning faces. They can spit lightning, have teeth the size of fists and bite pretty hard. They have 400 HP.

Above: The contours and plane sections of the sphere are circles

But could it be rounder?

Horns and intimidating molars may be helpful when trying to destroy unnamed space marines, but they won’t win you any sphere contests. However, after doing some experimental game design, we can see why the ancient nerds who made Doom decided to include facial features.

Runner-up: Blood explosion

This puff of blood is pretty round if you squint your eyes and kinda turn your head to the side a little.