• We’re currently investigating an issue related to the forum theme and styling that is impacting page layout and visual formatting. The problem has been identified, and we are actively working on a resolution. There is no impact to user data or functionality, this is strictly a front-end display issue. We’ll post an update once the fix has been deployed. Thanks for your patience while we get this sorted.

Is a plane figure with an infinite set of lines a circle?

The original question doesn't really make sense. A circle is defined as the set of all points equidistant from a single point.
 
If you had a plane figure which was a polygon which had an infinite number of sides - would that be a circle?
 
What is an infinite set of lines? Is that a way of saying an infinite number of lines or some finite number of lines that are infinitely long? I hate mathematicalese.

Originally posted by: episodic
If you had a plane figure which was a polygon which had an infinite number of sides - would that be a circle?
Click to expand...

Is an octagon just a circle when viewed at a lower resolution?
 
Bad question. If they are infinite length you might have a plane or set of planes, but thats just about it.
Unless you mean like infinite lines to create curves and stuff, either way... post less drunk questions or something.
 
Originally posted by: episodic
If you had a plane figure which was a polygon which had an infinite number of sides - would that be a circle?
Click to expand...

nothing could have an infinite number of sides other than a circle. However, a circle has no sides.
A side of a figure is essentially considered a line that connects two points, that meet end points of two other sides, and depending on the direction of these other sides, would eventually form an enclosed figure.

A circle has no sides. Zoom in far enough, and at no point will there be anything resembling a mathematical line. Remember, a side is considered a straight line at some point.

So to answer your question concisely, there is no mathematically possible figure that could be said to have an infinite number of sides. You're closest bet is a circle, but isn't the only - anything that could be called an ellipse would fall under the same category, though neither has anything resembling a side.

With a circle, no point, no matter how crazy close you get through zooming into infinitely long decimal coordinate values, will ever be further away from the center point.
 
Originally posted by: Jeff7
A circle is just a line passing through an intense gravity field. 😛
Click to expand...

One of these days you need to find yourself somewhere near central Ohio. There is a small ATOT gathering that must take place, because the two of us need to share some delicious brew. :beer: 😀
 
Originally posted by: destrekor
Originally posted by: Jeff7
A circle is just a line passing through an intense gravity field. 😛
Click to expand...

One of these days you need to find yourself somewhere near central Ohio. There is a small ATOT gathering that must take place, because the two of us need to share some delicious brew. :beer: 😀
Click to expand...
I might have a tough time finding ????????????.

 
Originally posted by: blamb425
Originally posted by: bolomite
The original question doesn't really make sense. A circle is defined as the set of all points equidistant from a single point.
Click to expand...

That's a sphere 😛
Click to expand...

in 2-d its a circle, in 3-d its a sphere
 
(assuming the lines are randomly distributed) A plane with infinite lines is a plane where: for every x and y there exists a point (x,y).

In other words, the plane is completely filled in.
 
I am not a mathematician (IANAM), but...

As the number of lines in the polygon approached infinity the length of each edge of the polygon approaches zero, thus approaches becoming a point, thus approaches the definition of a circle which is the set of all points equidistant from a single point.

Oddly enough this question is similar to .999... = 1. If you believe .999... = 1 then it shouldn't be too much of a leap of faith to believe the former.
 
Originally posted by: Leros
(assuming the lines are randomly distributed) A plane with infinite lines is a plane where: for every x and y there exists a point (x,y).

In other words, the plane is completely filled in.
Click to expand...

False. Consider the standard x-y plane. I place a line at every positive value of x, i.e. my lines are x=1, x=2, x=3, etc. Now I have an infinite number of lines but the plane is not at all filled in.

The key here is the difference between countable & uncountable infinity.

Originally posted by: episodic
If you had a plane figure which was a polygon which had an infinite number of sides - would that be a circle?
Click to expand...

Technically, no. First, as argued by destrekor, a circle has no sides; it is not a polygon. But then again, a polygon cannot have an infinite number of sides, b/c it would cease to be a polygon.

Secondly, you'd have to be working with a regular polygon. If I created an irregular, concave polygon, then that most certainly would not look like a circle, ever.

But I'm sure we all understand the spirit of what you're asking. If you consider a sequence of regular polygons (whose vertices are equidistant from a point) with more and more edges, the area and perimeter will, in the limit, approach that of a circle.
 
You must log in or register to reply here.

TRENDING THREADS

Back
Top