# Rayne Answer this Mathimatical Question

• 04-26-2011, 06:40 PM
Kirby
A teacher told this to be in 5th grade, and since then I have taken it as fact. Usually no one is able to go against it, but the few who do, are super smart, and to be honestly there logic confuses me. And apparently, according to them, I am wrong. Rayne seems like the person in between, that I could understand.

Ok here it is: "A circle is a regular polygon, with an infinite amount of sides."
• 04-26-2011, 06:51 PM
Tony
A circle can be thought of as a polygon with an infinite number of sides. As the number of sides increase, the length of each side gets smaller until you technically just have a series of points right next to each other. The same kind of concept is attributed to a line. It's basically an infinite number of points next to each other. In fact, early mathematicians estimated Pi by taking regular polygons with large number of sides, getting the perimeter and dividing by the diameter. As the number of sides of a regular polygon increase, the more the shape approximates a circle. You can see below with the 10 sided polygon, the decagon and a 20 sided polygon. The 20 sided polygon looks more like a circle than the decagon and there are programs that you can add additional sides and see how it looks more and more like a circle with more sides.
• 04-26-2011, 08:47 PM
Kirby
Yes, thats exactly what I though for years, but if you ask a read math pro, they will adamantly attack that statement, pity is though I don't know what they are saying. :(
• 04-26-2011, 09:43 PM
Rayne
well its certainly 'like' one but it isnt definitively a polygon
• 04-26-2011, 10:04 PM
pichubro
A circle is not a polygon because it doesn't have sides.
• 04-26-2011, 10:04 PM
Rayne
hmm but after thinking about it for a bit, yes a circle can definitely be considered to be a polygon when the limit of its sides approaches infinity. thats not the sole definition of a circle but i dont see anything wrong with that idea.

what do these 'math pros' say?
• 04-26-2011, 10:12 PM
God
it seems like thats just a way to consider a circle, but you couldnt properly say it IS one or it ISNT one. i can think of more arguments in favor than against though. id also want to see what the MATH PROS say.
• 04-26-2011, 10:14 PM
Rayne
the locus of all the points on a plane which are equidistant to a single fixed point is the best definition. use this to confuse and get back at the 'math pros'.
• 04-27-2011, 04:34 AM
Kirby
:lol:

yeah I kinda worded that bad
• 04-27-2011, 04:51 AM
Pants
here's the basic theology behind the circle.

Every tangent of a circle is a side. There is a realistic limit of points on a circle's radius to which a tangent can reside, but mathematically there can be any amount of decimals behind any degree on a circles radius, so there is a mathematical infinite limit based on infinitely small changes in movement. Realistically though, we tend to think of 360 planes/tangents on any 1 circle to simplify our works with them.

all you 'math pros' throw in any added info you like ;)
• 04-27-2011, 07:16 AM
Rayne
Quote:

here's the basic theology behind the circle.
did the circle god write that in the circle bible
• 04-27-2011, 07:19 AM
Rayne
also

Quote:

Originally Posted by Pants, and the beast dwelling within
Every tangent of a circle is a side.

untrue. to be a side it would have to be two dimensional. a tangent, by definition, is tangent to a point. if you consider the circle itself consisting the entirety of the plane, tangents wouldnt exist.
• 04-27-2011, 07:57 AM
Pants
each tangent is a relative side to be considered infinite. every point on a circle has a line that does not intersect the circle (tangent), and that is considered a tangible side. a circle has infinite sides and at the same time no sides.

every tangent IS in fact a side, because if one defines a circle as 360 points that are connected an equal distance from one another at a specific angle from one another, in between the points would be incredibly small straight lines connecting them, and the same can be said with infinite points on a circle, and each must have a straight line connecting them within infinitely small planes.
• 04-27-2011, 08:08 AM
Seymour
ROUND 2: RELATIVITY!
• 04-27-2011, 11:22 AM
Rayne
Quote:

Originally Posted by Pants, and the beast dwelling within
each tangent is a relative side to be considered infinite.

makes no sense

Quote:

every point on a circle has a line that does not intersect the circle (tangent), and that is considered a tangible side.
makes no sense

Quote:

a circle has infinite sides and at the same time no sides.
wait

Quote:

every tangent IS in fact a side
what

Quote:

because if one defines a circle as 360 points
WHAT

Quote:

that are connected an equal distance from one another at a specific angle from one another, in between the points would be incredibly small straight lines connecting them, and the same can be said with infinite points on a circle, and each must have a straight line connecting them within infinitely small planes.
uh
• 04-27-2011, 11:28 AM
Rayne
i sorta see your point but youre approaching it the wrong way. a point =/= a side; as such, tangents have nothing to do with it. as the sides of a regular polygon, or basically any closed figure, approach infinity then it does resemble a circle. it isnt a circle though; it approximates a circle. im sure that the fact has practical applications since greek mathematicians, like shadowraven said, used that theory to obtain an expression for pi. however a true circle is one that, by definition, does not have any sides.

this is a guess but i have a feeling that you got this whole tangent idea from the derivatives of curves. if so then i question your understanding of calculus.
• 04-27-2011, 01:01 PM
Pants
simplification makes math so much easier. that was the point of the "360 side" idea. since all mathematics are relative, its easier to explain a mathematic concept by bringing out the simplest concepts.

my theory is pretty simple to understand. because the point of a tangent lies on any 1 line, and in the infinitely (realisticially) small, multiple points are on that line without intersecting the circle, and therefor are a side.

in complete contrast, a mathematically perfect circle has an infinite number of connected points, and there are no 2 points on any 1 line that doesn't intersect with the circle, making it an object with no sides. You can also argue that every tangent (which there are an infinite amount of) are each "sides", or more correctly, points of contact.

so any answer can be correct depending on the mechanics of your arguement (unless you say an "inside and an outside", in which case you need to get shot).
• 04-27-2011, 05:17 PM
Qoorl
Circle's ain't polygons... they don't have any flat pieces... they're made out of curves!
• 04-27-2011, 07:37 PM
Rayne
pants, though the majority of your post is filled with false assumptions, faulty logic, and generally makes no sense, you are FUNDAMENTALLY correct: a circle can be thought of as consisting of an infinite number of points. where you are wrong however is assuming that this means two of these elementary points can be joined to form a line. but that itself is impossible because there are infinite points. any infinitesimally small line you draw between two points on the circumference will be a chord and thus you will be neglecting the, again infinite, number of points that lie between those two points.

infinity is a meaningless term. most of the time it refers to an arbitrarily large number that mathematicians, and physicists, use to approximate a value or for a simplified definition. however neither mathematicians nor physicists like infinity and go through great lengths to remove it from their equations and to use the idea of a circle consisting of an infinite number of points to raise the theory that a circle has infinite sides is faulty logic, because you could go on approximating the circle for the next billion years and still wouldnt be able to draw a true side.
• 04-27-2011, 08:11 PM
Kirby
There is that math pro shit.
• 04-27-2011, 08:49 PM
Rayne
my logic isnt very hard to understand kirby!

and i am certainly no MATH PRO
• 04-29-2011, 10:50 AM
Peeki
i think the logic rayne put up on the circle being a polygon as n of sides approaches infinity is plausible.

i'd think, fundamentally it isn't a polygon, but infinitesimally, it could be one.

circles are really cool, especially with their intricate natures. no wonder they've been associated with perfection.
• 05-01-2011, 11:23 PM
KhaosMonsterEnergy
I'm pretty sure if you take a circle and zoom in on it super closely there are sides.
• 05-02-2011, 01:22 AM