I am a sixth grader and am studying calculus so hear me out! I can prove a circle is polygon:
Note:This theory complyies with the fact that a divergent series correlates to a convergent series
Let Dx represent a point on any circle plotted on a regular cartesian coordinate system. Let Ax represent the angle of arc between two adjacent points (right next to each other).
As the limit of Dx approaches a very high number or infinity for that matter, the angle of Ax approaches 180 degrees. proving this we draw a tangent (or actually a secant) touching the area between both points and they will both be parralell. Please leave feedback positive or negative but intelligent answers only with explanations! Thank you!
2007-06-09 15:44:38 · 9 answers · asked by Harry K 1 in Science & Mathematics ➔ Mathematics
In a sense a circle can considered to be a infinite sided polygon. The circumference will be made up of infinitesimally small line segments of length, ds and angle at the center dθ. You could actually use this concept to derive the arc length formula as the number of sides, n goes to infinity.
2007-06-09 16:04:49 · answer #1 · answered by Dr D 7 · 2⤊ 1⤋
Hey harry.
The problem with this is it doesn't prove that it is a polygon. As we get closer and closer to Dx the arc angle does approach 180 degrees, but that's the key: it only approaches, it never reaches it. If you ever reached the point where it is 180 degrees, then you can also demonstrate that it no longer meets the original definition of a circle in a cartesian coordinate system: a set of points that are equidistant from a certain other point. If there are any two different points on a circle where the arc between them is 180 degrees, it is not mathematically possible for these points to be equidistant to the center of the circle. Nice try, keep studying :)
2007-06-09 16:08:28 · answer #2 · answered by Anonymous · 1⤊ 1⤋
Yes you are absolute right in that the circle is the limit of a regular polygon as the number of sides increases to infinity. But you can't say that a circle is a polygon.
For example, the following sequence of numbers are all rational:
3.14, 3.141, 3.1415, 3.14159, 3.141592, 3.1415926, 3.14159265, ....
Yet their limit approaches the number pi which is an irrational number. You can't say pi is rational. Similarly you can't say a circle is a polygon.
You will learn later in your studies that when you start messing around with infinity, the results aren't always what you would expect! It is for this reason that in the 1800s, mathematicians had to create a formal system of rules and definitions to handle operations involving infinity in a consistent manner.
2007-06-09 17:15:31 · answer #3 · answered by Someone Angry 5 · 0⤊ 1⤋
Nice job. Yes, a circle is an infinitely sided (regular) polygon. Get used to this weirdness in calculus . . . Take any smooth curve, no matter how curvy, and as you zoom in on it (take the infinetesmal limit) it can be considered straight at that point!
2007-06-09 16:45:44 · answer #4 · answered by supastremph 6 · 0⤊ 1⤋
Im thinking that your a 6th grader and you should wait untill you get older and study more maths before creating your own theories, cause you don't know all that is out there. Do more study cause at the moment your only learning the basics of things. Get to univerisity level maths and than you start learning the hard stuff and how different theories interlink with each other.
2007-06-09 15:48:57 · answer #5 · answered by brat 5 · 0⤊ 2⤋
The definition of a polygon is a closed plane figure bounded by straight sides. Circles are not bounded by straight sides, but arches. I would have to disagree.
2007-06-09 15:49:40 · answer #6 · answered by Emily 2 · 1⤊ 1⤋
infinity isn't any acual fee it recommend a relative fee that's incredibly great. for eg. for us motor vehicle somewhat one is incredibly small yet for an ant or a bactaria that infant is infinity length. further if somebody announcing that he executed infinity artwork ability he executed many works that in the time of accordance to him is incredibly great. yet for somebody may well be it great or not. so, i define infinity is that no. extra suitable than one which you would be able to think of at a time. so, it incredibly is different in accordance to circumstances. that why it incredibly is noted as undetermined fee. so, infinty isn't something purely very very very great fee as much as available.
2016-11-09 23:16:16 · answer #7 · answered by chatan 4 · 0⤊ 0⤋
I think that that is write but i have only scrached the surface of calculus. I am only a sophmore.
2007-06-09 15:56:42 · answer #8 · answered by creede_horse_lover 2 · 0⤊ 1⤋
it wouldn't actually be a circle, just "more" of a circle
2007-06-09 16:01:45 · answer #9 · answered by Anonymous 1 · 0⤊ 1⤋