Im curious because my math teacher tried to say that it was a certain amount rather than infinite, because honestly i think that there are infinite lines of symmetry. And another one, does a pentagon have rotational symmetry? I asked my teacher after class and she said that pentagons dont have rotational symmetry, and i beg to differ because when an equilateral pentagon is rotated 72 degrees a new point lands where the previous point was hence forth it has rotational symmetry. Any help is appreciated, and thanks for reading.

Spam but I agree and it's totally relevant -.- A pentagon has 5 symmetry rotations. A circle either has 1 or 360, I don't know.

A circle would have infinite lines of symmetry since you could rotate the line about the circle by infinitely smaller degrees, and it would still be symmetrical. Just google it. I'm sure every site will say the same.

Are you sure your teacher is qualified to teach math? Yes a circle does have infinite lines of symmetry. And a pentagon (provided it is regular) has rotational symmetry of order 5. Or maybe the real teacher is locked in a basement somewhere and the person teaching your class either has a large supply of polyjuice potion or is a master of disguise.

Hmmm...I personally don't agree with "infinite symmetry" for a circle but a Pentagon certainly does have rotational symmetry. A circle is 360 degrees. To demonstrate multiple lines of symmetry you must use an axis point (the centre of the circle) and then rotate it by a particular angle. The general consensus that a circle has infinite symmetry is due to the fact you can draw a diameter anywhere on the circle and it is a line of symmetry. The notion is held that there are infinite diameters and thus infinite lines of symmetry. Of course for this to hold true the diameter line itself would have to be infinitely small, or non-existent; but then, if it is non-existant, how can it be there to indicate the presence of symmetry? Therefore, to exist, it must have a width and, while that width could be imperceptibly small, it is still a width. This means that, given an inordinately high enough number of them, you would eventually encompass the circle in diameters and resolve the maximum number of lines of symmetry achievable in the physical realm. When man discovers the smallest entity in the entire universe we will have that answer! So, while the symmetry of a circle is theoretically infinite; you could write the smallest width measurement of a diameter, covering the entire surface of the Earth in numbers to represent how miniscule it's width is, to some crazy number of decimal places, and you still wouldn't have demonstrated the smallest width possible. If, however, you discovered the exact measurement of the smallest entity in the universe, then using a measurement below that as the width of the diameter would be entirely irrelevant to any physical calculation in the real world and thus there would be a real definite number of lines of symmetry that a circle can physically possess. Such is the nature of infinity though; it is almost always theoretical, thanks to our limited understanding of the physical plane. It is a fall-back option used as an explanation to things we cannot fully comprehend, much like the Gods of Olympus that helped explain Volcanoes and Lightning Storms. I'm sure that's what your teacher was getting at. Wow, she must be smarter than she looks eh! Shame about the Pentagon...

I agree with your point and have shared this thought for many years, so, if the diameter has to have a width, you could increase the number of lines of symmetry by increasing the size of the circle right?

That is true but it's so ridiculously high that saying infinite is easier and probably easier to understand to most. You can say the closest star to the sun is 39,900,000,000,000 km away but it's easier to comprehend as 4.35 light years away.

A circle is also 1 296 000 seconds of arc, which nullifies the arguement that 360 degrees must equal 360 lines of symmetry. A second is the smallest unit to measure degrees.

I think that even if you fill the circle completely with diameters, no matter how small, you can always just cut off half of them to make room for more. Theres no limit to how small a number can be.

If I read this correctly you are saying that a line or line segment has both a length and width, and we must take into account the width when finding symmetry, but this is wrong. In the definition of a line and line segment it is stated that both have 0 width and only length. The thing is math does not always directly correlate to our physical world and can be thought of as a world of its own. So in conclusion yes a circle has infinite lines of symmetry and lines and line segments do not have widths.

Theoretically, there is no circle, just a bunch of lines making the illusion of the perfect circle, maybe your teacher was trying to be a turd and was being literal.

If it were lines, wouldn't that have 0 lines of symmetry? A line drawn would be considered a bisector not a line of symmetry.