A curve dividing a square in a given ratio
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What does it mean for a curve to divide a square in a given ratio? Does it necessarily mean it has to intersect it at two points. Can it be that we have a circle of the given area inside it, thereby dividing it in the given ratio?
geometry
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What does it mean for a curve to divide a square in a given ratio? Does it necessarily mean it has to intersect it at two points. Can it be that we have a circle of the given area inside it, thereby dividing it in the given ratio?
geometry
Depends on the context. If closed curves are allowed, the circle would be fine.
â Jens
Aug 26 at 13:02
@Jens In what context, must it mean that it has to intersect it at two points.
â user330477
Aug 26 at 13:04
1
It would be easier if you could provide the context of your question. Is there any reason to think a closed curve is not allowed?
â Jens
Aug 26 at 13:23
Presumably the area of the square is divided in the prescribed ratio (as opposed to the perimeter). The curve should unambiguously split the square in two regions. Whether these must be connected or simply connected is unsure. This must be stated.
â Yves Daoust
Aug 26 at 14:06
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What does it mean for a curve to divide a square in a given ratio? Does it necessarily mean it has to intersect it at two points. Can it be that we have a circle of the given area inside it, thereby dividing it in the given ratio?
geometry
What does it mean for a curve to divide a square in a given ratio? Does it necessarily mean it has to intersect it at two points. Can it be that we have a circle of the given area inside it, thereby dividing it in the given ratio?
geometry
asked Aug 26 at 12:49
user330477
7911
7911
Depends on the context. If closed curves are allowed, the circle would be fine.
â Jens
Aug 26 at 13:02
@Jens In what context, must it mean that it has to intersect it at two points.
â user330477
Aug 26 at 13:04
1
It would be easier if you could provide the context of your question. Is there any reason to think a closed curve is not allowed?
â Jens
Aug 26 at 13:23
Presumably the area of the square is divided in the prescribed ratio (as opposed to the perimeter). The curve should unambiguously split the square in two regions. Whether these must be connected or simply connected is unsure. This must be stated.
â Yves Daoust
Aug 26 at 14:06
add a comment |Â
Depends on the context. If closed curves are allowed, the circle would be fine.
â Jens
Aug 26 at 13:02
@Jens In what context, must it mean that it has to intersect it at two points.
â user330477
Aug 26 at 13:04
1
It would be easier if you could provide the context of your question. Is there any reason to think a closed curve is not allowed?
â Jens
Aug 26 at 13:23
Presumably the area of the square is divided in the prescribed ratio (as opposed to the perimeter). The curve should unambiguously split the square in two regions. Whether these must be connected or simply connected is unsure. This must be stated.
â Yves Daoust
Aug 26 at 14:06
Depends on the context. If closed curves are allowed, the circle would be fine.
â Jens
Aug 26 at 13:02
Depends on the context. If closed curves are allowed, the circle would be fine.
â Jens
Aug 26 at 13:02
@Jens In what context, must it mean that it has to intersect it at two points.
â user330477
Aug 26 at 13:04
@Jens In what context, must it mean that it has to intersect it at two points.
â user330477
Aug 26 at 13:04
1
1
It would be easier if you could provide the context of your question. Is there any reason to think a closed curve is not allowed?
â Jens
Aug 26 at 13:23
It would be easier if you could provide the context of your question. Is there any reason to think a closed curve is not allowed?
â Jens
Aug 26 at 13:23
Presumably the area of the square is divided in the prescribed ratio (as opposed to the perimeter). The curve should unambiguously split the square in two regions. Whether these must be connected or simply connected is unsure. This must be stated.
â Yves Daoust
Aug 26 at 14:06
Presumably the area of the square is divided in the prescribed ratio (as opposed to the perimeter). The curve should unambiguously split the square in two regions. Whether these must be connected or simply connected is unsure. This must be stated.
â Yves Daoust
Aug 26 at 14:06
add a comment |Â
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Depends on the context. If closed curves are allowed, the circle would be fine.
â Jens
Aug 26 at 13:02
@Jens In what context, must it mean that it has to intersect it at two points.
â user330477
Aug 26 at 13:04
1
It would be easier if you could provide the context of your question. Is there any reason to think a closed curve is not allowed?
â Jens
Aug 26 at 13:23
Presumably the area of the square is divided in the prescribed ratio (as opposed to the perimeter). The curve should unambiguously split the square in two regions. Whether these must be connected or simply connected is unsure. This must be stated.
â Yves Daoust
Aug 26 at 14:06