why does a circle turn into a straight line if u keep increasing its radius?

Answer 1

It doesn't, but the sheer size of the circle means that the curve is less obvious - Consider a 400 meter track race - The Inside lane has a much tighter curve than the outside. Expand this ad infinitum, and you don't notice the curve at all - It's not actually a straight line, but it feels like it.

Answer 2

It's all well and good disproving this questioner's question with formulae and the like (or simply saying he's wrong - how rude!) but I think it's a great question and one worthy of discussion.

The edge of a circle gets straighter as the circle increases in size so of course if you had an infinitely large circle the edge would be straight. With this in mind, you could say that ANY straight line is in fact curved an infinitely small amount !!!

OK so an infinitely large circle will only ever exist in our imaginations, but isn't that a perfectly valid place to occupy if you're an amusing mathematical question?

Most of Chaos Theory is impossible to recreate - that's why it's called a THEORY !!!

Well done Bhavic - you got lots of people talking anyway!

Cheers

KaiBosh

Answer 3

As people have said, it doesn't. However, you may have heard that as the radius of a circle tends to infinity, the circle tends to a straight line. This is because strange things happen when numbers "tend to infinity" - but few are demonstrable because there is no real thing that is infinitely big. If your circle was as big as the galaxy, or even the Universe, it still wouldn't have an infinite radius, so still wouldn't be a straight line.

Answer 4

The answer to this question is to do with what happens when things tend to infinity.

To better understand this, you must understand that a radian is an angular distance measured around a circles circumference that is equal to the radius of the circle.

As the circles radius increases, the curvature of the circle seems to become less due to the distance travelled around the circumference needing to travel one radian becoming greater. This can be better understood when looking at the simple formula for a circles, circumference, i.e C=2 x pi x r. Therefore, as a circles radius tends to infinity, it's circumference also tends to infinity, which means that in order to travel one radian of distance around it's circumference becomes impossible, which is hence another way of saying that the circles circumference is a straight line.

I hope this makes sense, as it's kind of hard to put into words.

Answer 5

It doesn't as such.

The formula to find the circumference of a circle, (C), is:

C = 2πr

As you increase the radius, (r), C will increase.

Now look at the limit as r tends to infinity:

Lim (2πr) = ∞
r→∞

So, if r 'is' infinity, then the circumference is also infinite.

It's still a circle, but an infinitely large one!

If you were to look at any particular part of the circle's circumference, due to the infinite nature of the circumference, there would be no observable curvature; a straight line.

Remember it's still a circle though! Ah, the joys of dealing with infinity...

Answer 6

Take any point in that circle, and watch what happens to that point while you increase the radius, you'll see that the curve where youre point is will flatten out. That is where the straight line thing comes in. Eventually that curve you see will dissappear and you'll see a straight line, even though its still a circle if you look at the entire thing.

Answer 7

Let us write the formula for the circle:
x² + y² = r²
where r is the radius and the circle's center is at the origin.

When r is a very large value, the limit at infinity is ∞. Then the equation is:
x² + y² = ∞²

Or...
x² + y² = ∞

Try substituting values for x (or y) and solve for y (or x, respectively). Here are some arbitrary values for x and y
(2,±∞), (±∞,2), (-33,±∞), (±∞,-33)
(4,±∞), (±∞,4), (9.3,±∞), (±∞,9.3)
(0,±∞), (±∞,0), (±∞,±∞)

Thus, we see that all the solutions lie "around" the transfinite xy-plane. We cannot perceive the solution set as a straight line, when seen this way. (We cannot even perceive it as circular or rectangular). That is what happens when things approach infinity.
^_^

Answer 8

a circle doesnt turn into a straight line if the radius is increased to infinitie also!!!!!!!! the earth has a large radius but that doesnt mean its a staright line. its just that the whole circle isnt visible nd looks like a line from a distance.

Answer 9

Just look at the Earth, one giant circle [well sphere but who's checking] The best way that I can imagine it is that if a circle didn't turn into a straight line it would have to either meet up or cross its own path before long, and would result in a spiral. To prevent itself from becoming a child's doodling it straightens itself out 'til it can't bear to be incomplete anymore and then meets up with itself.

Answer 10

You can look at a circle as a polygon with an infinite amount of sides. Consider the progression from square to pentagon to hexagon all the way to an infinitely sided shape and you'll get the picture. When you start expanding this you'll still never be abel to see those lines.

However if the circle was really big you wouldn't be able to see the curvature. It would have to be a REALLY big circle considering it is possible to see the curvature of the earth when you're at see and you can see boats dissapearing under earth's curvature.