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9,956 hits 3.0 (1 vote) Share Favorite | Flag 5 years ago by emitchell

How many corners does a circle have?


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5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 12:12:25 PM EST (GMT-5)
Mathematically: None.
Graphically: Infinite.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 12:14:45 PM EST (GMT-5)
None, a corner is the intersection of two lines. A circle, on the other hand, is a single line.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 12:18:40 PM EST (GMT-5)
Psst. A circle isn't a line.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 12:25:00 PM EST (GMT-5)
Psst. Yes, it is.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 12:28:28 PM EST (GMT-5)
Not geometrically.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 12:40:43 PM EST (GMT-5)
Psst, yes, it is, geometrically. A circle is a series of points (a.k.a. a line) at an equal distance from a center point. The chord of a circle is line (there's that word again) whose end points both lie on the circle.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 12:55:24 PM EST (GMT-5)
Hmmm... a chord isn't an "arc"? A circle isn't a... circle? It's a line?

You're mixing graphical representation and mathematical definition.

A line is not a series of points. It is the distance between two points (displayed graphically by a straight mark on a piece of paper.

"Line" is a misnomer used to define any mark on a piece of paper (as you are using it).

Mathematically: None.
Graphically: Infinite.

Maybe you can understand this:
Circle: x2 + y2 = r2
Line: y = mx + b
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 1:19:26 PM EST (GMT-5)
Note entry 2
http://dictionary.reference.com/bro...

Mathematically: none
Graphically (given that the graphical representation of a circle requires a single line to be drawn at a regular interval from a set point and that a corner is the intersection of two lines): none,
You fail
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 1:26:17 PM EST (GMT-5)
Yeah ok... keep telling yourself that.

Following your incorrect line of logic, though... if a circle is a series of points... that means a line segment is between each set of points, so you have infinite line segments... thus infinite intersections, thus infinite corners.

Wow. You managed to be wrong about the same thing twice at the same time.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:15:36 PM EST (GMT-5)
No, then you would have a series of arcs or "curves" and guess what, a curve is the opposite of a corner.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:18:47 PM EST (GMT-5)
I'm with cirestan on this one. A circle has an infinite number of "corners".
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:21:11 PM EST (GMT-5)
circles dont have corners...
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:24:15 PM EST (GMT-5)
On Wednesday 10/22/08 - 4:18:47 PM KneeJerk wrote:
I'm with cirestan on this one. A circle has an infinite number of "corners".

Then you would be an idiot.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:25:34 PM EST (GMT-5)
A line goes on for infinity, a line segment does not, so you have to ask yourself does the circle stop when it gets to the point where it began again, or does it continue to go to infinity? Well, picture a spark of electricity going through the circle, it doesn't stop does it? No, it continues to go around and around and around to infinity. So yeah, a circle is just a big line that overlapses eachother, and last time I checked, lines don't have corners.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:27:23 PM EST (GMT-5)
On Wednesday 10/22/08 - 4:15:36 PM MightyRhinox wrote:
No, then you would have a series of arcs or "curves" and guess what, a curve is the opposite of a corner.


wait wait wait... I thought they were "lines".

Go ahead, tell me I fail again. You're the one that doesn't know basic geometric, or mathematic definitions.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:32:05 PM EST (GMT-5)
If it's a perfect circle, I'd imagine none. If there are any, just smooth that sh*t off.
5 yrs ago, 10 mos ago - Wednesday 10/22/08 - 4:58:05 PM EST (GMT-5)
Let me reiterate and clarify my original statement.
Mathematically speaking a circle is just the definition of an equation ( x2 + y2 = r2 ), thus it is perfect and has no corners. IT IS NOT A LINE. A line is the defintion of a different equation ( y = mx + b ). They are different.

Graphically speaking (or any actual "real" man made circle) a "perfect" circle is impossible to obtain. Drawn on a sheet of paper there will be tiny, even microscopic ridges, which will form corners. On a computer the display is still only binary and breaks down to tiny squares. In a machine shop a piece of steel on a lathe will still have "grain" and material imperfections. Even if you consider a bubble, it has sag because it is affected by gravity, so it's not even really a circle (or sphere), it's an ovoid. Thus the "infinite corners" answer for anything we call a "Circle".
5 yrs ago, 10 mos ago - Thursday 10/23/08 - 12:22:58 AM EST (GMT-5)
But wait a circle can also be defined as

Or




5 yrs ago, 10 mos ago - Thursday 10/23/08 - 12:25:32 AM EST (GMT-5)
Note that the mathematical equations are the definition, the circle is not.
Graphically speaking, if it's not a perfect circle it has no relevance to the question, but if you break everything down you eventual get to tiny little spheres, not squares.
5 yrs ago, 10 mos ago - Thursday 10/23/08 - 1:00:02 AM EST (GMT-5)
from the way I look at it, a circle has no corners
5 yrs ago, 10 mos ago - Thursday 10/23/08 - 1:37:33 AM EST (GMT-5)
On Wednesday 10/22/08 - 4:58:05 PM cirestan wrote:
Even if you consider a bubble, it has sag because it is affected by gravity, so it's not even really a circle (or sphere), it's an ovoid. Thus the "infinite corners" answer for anything we call a "Circle".


Bubbles are 3-dimensional. Circles are not. Gravity would not affect a circle.
And even if you had a microscope that could see the tiniest pico-particles, I assure you that you would not see any corners in a bubble.

You know, you're just digging yourself deeper into your failure-hole.
5 yrs ago, 10 mos ago - Thursday 10/23/08 - 1:54:17 AM EST (GMT-5)
None of you are smart.
5 yrs ago, 10 mos ago - Thursday 10/23/08 - 2:17:32 AM EST (GMT-5)
On Wednesday 10/22/08 - 4:58:05 PM cirestan wrote:
a "perfect" circle is impossible to obtain. Drawn on a sheet of paper there will be tiny, even microscopic ridges, which will form corners. On a computer the display is still only binary and breaks down to tiny squares. In a machine shop a piece of steel on a lathe will still have "grain" and material imperfections.


I thought it was implied that by "circle" you meant the concept of a circle. If you take it to that level, lines and corners also do not exist.
5 yrs ago, 10 mos ago - Thursday 10/23/08 - 2:26:00 AM EST (GMT-5)
Assuming we're talking about a hypothetical "perfect circle," and not a sketch on a graph, a circle has no corners. That's why there are 360 degrees in a circle instead of an infinite amount.
5 yrs ago, 10 mos ago - Thursday 10/23/08 - 3:16:17 AM EST (GMT-5)
On Thursday 10/23/08 - 2:26:00 AM Tezmata wrote:
That's why there are 360 degrees in a circle....


There aren't; 0-360 degrees is just the conventional range of angles possible for a pair of lines each of which connects the centre and the circumference of a circle (ie, radii). The question is about internal angles, which would be measured from the "outside"...

Regarding the question, I don't think we need to go beyond saying that circles do not involve any instances of the intersections of (straight) lines, hence have no "corners"; this is irrespective of the definitional points of lines and circles above.

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