Math Is Fun Forum

Depends how you think about it, if you define a circular object as either a shape whose sides are negligible, or with ∞ tangents. You can state that two tangent lines are parallel, but that is because we only assume that there is a point on the circumference such that a straight line is existent. But if we think about a circle as having ∞ sides, then you *could* say that there is a point, ∞/2, which lies between two of the infinitesimal sides, but if we define this as a limit then we say that this is going to approach infinity. So what are we really saying when we say a circle can have ∞ tangents?

The concept is an interesting one, but as for the topic, you could say that a circle has either no parallel lines or ∞ parallel lines. Some people say that a circle has an infinite number of sides is just another proof that 0 ∙ (±∞) is an indetermination and not only 0.