How Many Angles are in a Circle?
I don't quite recall what the specific question was started the conversation but at one point the question was asked do circles have zero angles or do they have an infinite amount of angles. These students were allowed to think about it and then discuss it. Following basic rules of discussion. I found this question fascinating and again. I don't remember where it came from it. Just it was brought up in the natural flow of this conversation now. I do want to specify that by angles We can also call it points as well. Of course a point would be where two lines intersect at any. You know degree. Well i think Like specifically of definitely. What you mean is like because an angled gingras between the three points or the intersection between two lines. Right cry and point is just where they intersect. So you could see every point on the circle as having an angle. Because there's a line going into and out of that now it was cool is is again. This conversation was with middle school students. And we're not grading for mathematical rigor or even necessarily correctness for just grading on pursue on participation. The discussion followed. Like so you can start off with a single point. And then you can add another point with which you can make a line between the two points. You can add a third point and you'd get a triangle. A fourth point would create a square. And you can keep adding points in this general shape and again. I realize we discussed this on previous episodes. But it's worth bringing up again you. Can you know add eight points and create an octagon essentially you can add n points and create an n cited shape that that that essentially approaches a circle. So the argument could be made that a circle has infinite angles infinite