Math fail or out of the box answer.

[Jersey #10]

^Do you know how to find the circumference of a circle ? If you really do, you wouldn't be arguing about the limit of regular polygon -> circle as number of sides go to infinity either. And stop embarrassing yourself man, that 0.999 =1 has been done to death. If you don't believe us, go ask a math prof at your university.

exactly, limit of regular polygon -> circle as number of sides go to infinity but it does not equal to a circle. It can only get very close to it. Same argument. with the 0.999... =1. I am done here but I'll leave you with some good info,

Here is the simple answer: no, a circle is not a polygon. A polygon is composed of a finite set of straight line segments, and a circle is not. But you can make a polygon that is as close to a circle as you want; the more sides you give it, the more it will look like a circle. In fact, the other day a student asked if we could show him what a "googolgon" looks like (a polygon with a "googol" of sides, meaning 10 to the 100th power!). I said I can't make one, but if he looks at a circle he will see what a googolgon looks like as accurately as I could draw one! The sides of a googolgon would be smaller than atoms, so if I tried to draw it, it would look no different from a circle. That is what we mean when we say that a circle is in some sense an "infinite polygon" or "the limit of a sequence of polygons": it is not a polygon, but you cannot tell the difference between a circle and a sufficiently big polygon. And where mathematicians might disagree is simply in their willingness to talk about infinity as if it were a real number, and to leave out careful words like "limit." - Doctor Peterson Talking about infinity is always tricky. There's a way in which what your teacher said is true, and a way in which it isn't. Here's a useful idea that comes up in mathematics you'll learn in HS and college. It's the idea of a limit. Say you can't calculate something about x, but you can calculate it for other numbers besides x. Well, choose a number y that's close to x and calculate it. Then calculate the thing for y. Try letting y get a little closer to x, and calculate it again. Keep going. See if the things you're calculating seem to be "homing in" on something - that is, they get closer and closer, but never quite reach it. This is a useful way to talk about infinity because if your x is infinity, there's nothing you can calculate about x directly, but you can calculate for y and let y get larger and larger - that is, "closer" to infinity. Then see if the values seem to be homing in on something. Why don't you try doing this with the perimeter of the polygon. Try writing down the perimeter for a triangle, a square, a pentagon, hexagon... You may need some help from your teacher or parent calculating these perimeters. If you keep going, you'll find something funny. The number of sides keeps going up and up, and the perimeter goes up and up. But the perimeter goes up much slower than the number of sides is going up. After a while, it will seem that the perimeter is just grinding to a halt - getting closer and closer to a value that it just can't seem to get past. That value will be the circumference of a circle! The same thing works for areas. The areas of all those polygons gets closer and closer to the area of a circle. That's really what your math teacher meant when he said that if you took "a regular polygon and put on an infinite number of sides it would become a circle". He was using a shorthand that he learned a long time ago. He didn't mean literally that it would BE a circle, but rather it would be more and more like a circle. -Doctor Mitteldorf

It's arguable though not important in real life.

[Rajiv]

Math is a drama queen. It can't seriously have that many problems.