Symmetry. Round table v square table

​Evgeny’s point is that symmetry = all the transformations that leave an object unchanged.

So you compare objects by how many transformations keep them the same.

Round table

If you rotate a perfect circle around its center by any angle, it looks identical.

That means it has infinitely many rotational symmetries.

This is exactly the idea of a graphable function describing a circle (all directions look the same):

Because every direction from the center satisfies the same equation, rotating doesn’t change anything.

Square table

A square only matches itself after specific rotations:

• 0°
• 90°
• 180°
• 270°
• 360°

So it has 4 rotational symmetries, not infinitely many.

Why the round table is “more symmetrical”

• Square → 4 rotations that keep it unchanged
• Circle → infinitely many rotations that keep it unchanged

Since the circle has more symmetry transformations, mathematicians say it’s more symmetrical.

This leads to a deeper idea:

• Square symmetry = discrete (separate angles)
• Circle symmetry = continuous (every angle)

That’s why the round table wins.