2024 rules, Difference between Sphere and Cube

I know i use templates and overlay, all i'm saying is as written a Sphere of 10 feet/2 squares radius in all direction include diagonals. But perfect circle have 1 square radius in diagonal meaning not in all direction have the same radius when translated in square contrary to text. Similarly in Theater of the Mind, if a creature is within 10 feet of a Sphere's radius point of origin extending 10 feet in all direction, you'd say it's affected being within 10 feet of it. It's non-euclidean in grid play IIRC is commonly referred as "circle are squares". 

The mention that if an area of effect covers at least half a square, the entire square is affected can be useful to cover situation like this but also where the DM doesn't snap to grid and an area of effect like Cloud Daggers overlap two squares to some degree.

Quote from heydanseegil >>

Quote from The_Ace_of_Rogues >>

Areas of Effect

An area of effect must be translated onto squares or hexes to determine which potential targets are in the area. If the area has a point of origin, choose an intersection of squares or hexes to be the point of origin, then follow its rules as normal. If an area of effect covers at least half a square or hex, the entire square or hex is affected.

Straight from the 2024 DMG

I was about to say the sphere still covers those partial squares. It is really just for description and to accommodate hex based maps. Not everyone is a square. Pun intended.

 
It touches those squares, but it does not necessarily meet the criteria for them to be included in the AoE.