A girl in my class and I are always arguing about infinity, and while doing so I came up with this theory. Roughly half the people I suggest it to agree with me. Do you?
So...
> Maybe it breaks the rule of the circle by not having a curvature.
> Maybe the circle's lines meet, but we will never find out.
> The because the length of the radius can never be determined, the line is still always equidistant from the centre.
> A straight line has a curvature of 0. Curvature is defined by 1/r, so if r = ∞, then the equation will be correct.
> Yes I know I'm not the first person to come up with this lol.
> What would a sector of this circle look like? A perpendicular line?
> What would a segment look like? A parallel line?
So...
> Maybe it breaks the rule of the circle by not having a curvature.
> Maybe the circle's lines meet, but we will never find out.
> The because the length of the radius can never be determined, the line is still always equidistant from the centre.
> A straight line has a curvature of 0. Curvature is defined by 1/r, so if r = ∞, then the equation will be correct.
> Yes I know I'm not the first person to come up with this lol.
> What would a sector of this circle look like? A perpendicular line?
> What would a segment look like? A parallel line?
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Yes you are correct. Using calculus, the limit of 1/r as r approaches infinity = 0. Of course, the entire concept of limits is that it will never actually reach infinity, and the line will never actually be straight or it wouldn't be a circle, but for all intents and purposes an infinitely large circle will have a curvature of 0 and will be a straight line.
A sector of the circle would look like perpendicular lines have been drawn, creating a paradoxical shape of a triangle with two right angles, but again, this is theoretical. A segment would look like two parallel lines assuming that the curvature is 0, you are again correct.
Whereas your classmate is correct in stating that in reality, a circle can never have a curvature of 0, you are correct that theoretically a circle with an infinite radius would be a straight line.
A sector of the circle would look like perpendicular lines have been drawn, creating a paradoxical shape of a triangle with two right angles, but again, this is theoretical. A segment would look like two parallel lines assuming that the curvature is 0, you are again correct.
Whereas your classmate is correct in stating that in reality, a circle can never have a curvature of 0, you are correct that theoretically a circle with an infinite radius would be a straight line.