A cylinder would allow all geodesics, but then it would still have two 90 degree angles and two 270 degree angles so still not a square. I think it would be a trapezoid/trapezium, and might be a parallelogram depending on what definition you use.
There might be some crazy custom shape that makes the angles on the more complete circle segment actually 90 degrees but I don’t think there’s a common easy-to-conceive shape that works.
still have two 90 degree angles and two 270 degree angles
But you just said internal vs. external angles was a distraction that people shouldn’t get hung up on.
To be clear, apart from that one bit, I agree with you completely. I don’t even necessarily disagree with what you said back there per se. I just don’t think it was useful to bring it up because even if it isn’t explicitly in the definition of a square, it is an implicit assumption that when talking about the angles of a shape, you’re always talking about all internal angles (or, equivalently, all external angles, just no mixing), so getting “hung up on” internal vs. external angles is not a bad thing.
A cylinder would allow all geodesics, but then it would still have two 90 degree angles and two 270 degree angles so still not a square. I think it would be a trapezoid/trapezium, and might be a parallelogram depending on what definition you use.
There might be some crazy custom shape that makes the angles on the more complete circle segment actually 90 degrees but I don’t think there’s a common easy-to-conceive shape that works.
But you just said internal vs. external angles was a distraction that people shouldn’t get hung up on.
To be clear, apart from that one bit, I agree with you completely. I don’t even necessarily disagree with what you said back there per se. I just don’t think it was useful to bring it up because even if it isn’t explicitly in the definition of a square, it is an implicit assumption that when talking about the angles of a shape, you’re always talking about all internal angles (or, equivalently, all external angles, just no mixing), so getting “hung up on” internal vs. external angles is not a bad thing.