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.

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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.

Quote from The_Ace_of_Rogues >>

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.

 I see what you're trying for but a circle and a square of the same size cover the same surface area. A circle with radius r Pi and a square with side length s = r Square Root of Pi of R cover the exact same total surface area pi r^2. Idk how to make those symbols on my phone but google it to see it the formula. The "partially covered" squares of the sphere are curved so they actually cover half the square. It shows it in the picture in the DMG but in the hex grid instead of the square one so I get the confusion but should have the same surface areas.

I’m not following your math. If a circle’s diameter is equal to a square’s radius, then they objectively do not have the same area because the circle will sit inside the square and leave space at the corners exposed. If the square’s sides are equal to the radius, then by definition the circle’s area must be over 3 times as large since the square’s area is x squared while the circle’s is pi times x squared.

Quote from heydanseegil >>

Quote from The_Ace_of_Rogues >>

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.

 I see what you're trying for but a circle and a square of the same size cover the same surface area. A circle with radius r Pi and a square with side length s = r Square Root of Pi of R cover the exact same total surface area pi r^2. Idk how to make those symbols on my phone but google it to see it the formula. The "partially covered" squares of the sphere are curved so they actually cover half the square. It shows it in the picture in the DMG but in the hex grid instead of the square one so I get the confusion but should have the same surface areas.

What we're talking about comparing is a circle of radius 10 feet, and a square with side 20 feet, which both extend two 5-ft squares out from a central point in each direction. These definitely do not have the same area, and the four grid squares in the corners are not more than half covered by the circle.

Quote from heydanseegil >>

 I see what you're trying for but a circle and a square of the same size cover the same surface area. A circle with radius r Pi and a square with side length s = r Square Root of Pi of R cover the exact same total surface area pi r^2. Idk how to make those symbols on my phone but google it to see it the formula. The "partially covered" squares of the sphere are curved so they actually cover half the square. It shows it in the picture in the DMG but in the hex grid instead of the square one so I get the confusion but should have the same surface areas.

Depends what you mean by 'size'. A 100 square foot circle (radius = sqrt( 100/pi ) or about 5.64 feet) has the same area as a 100 square foot cube, sure, but there are exactly zero circles defined in the rules by the area they cover.

Quote from wagnarokkr >>

Quote from heydanseegil >>

Quote from The_Ace_of_Rogues >>

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.

 I see what you're trying for but a circle and a square of the same size cover the same surface area. A circle with radius r Pi and a square with side length s = r Square Root of Pi of R cover the exact same total surface area pi r^2. Idk how to make those symbols on my phone but google it to see it the formula. The "partially covered" squares of the sphere are curved so they actually cover half the square. It shows it in the picture in the DMG but in the hex grid instead of the square one so I get the confusion but should have the same surface areas.

What we're talking about comparing is a circle of radius 10 feet, and a square with side 20 feet, which both extend two 5-ft squares out from a central point in each direction. These definitely do not have the same area, and the four grid squares in the corners are not more than half covered by the circle.

I don't know man. I went to school for music. I just googled that and looked it up in the DMG.

Quote from heydanseegil >>

Quote from wagnarokkr >>

Quote from heydanseegil >>

Quote from The_Ace_of_Rogues >>

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.

 I see what you're trying for but a circle and a square of the same size cover the same surface area. A circle with radius r Pi and a square with side length s = r Square Root of Pi of R cover the exact same total surface area pi r^2. Idk how to make those symbols on my phone but google it to see it the formula. The "partially covered" squares of the sphere are curved so they actually cover half the square. It shows it in the picture in the DMG but in the hex grid instead of the square one so I get the confusion but should have the same surface areas.

What we're talking about comparing is a circle of radius 10 feet, and a square with side 20 feet, which both extend two 5-ft squares out from a central point in each direction. These definitely do not have the same area, and the four grid squares in the corners are not more than half covered by the circle.

I don't know man. I went to school for music. I just googled that and looked it up in the DMG.

 
Then perhaps don’t copy/paste something an LLM spat out that you don’t understand.

Touché