Mathematical Question || Is a Circle a Polygon?

[Gamefandan]

HOW2MATH?

Is a circle a polygon? Monocle doesn't know so now I make topic, lol.

Let's get right to it then!

The formula to find the area of any regular polygon is (While a symbolizes apothegm and p symbolizes perimeter.) ap/2

NOTE: An apothegm is basically the radius of a regular polygon, in that it is half of the height. Please do not confuse the radius and apothegm of a regular polygon, as they are two different things.


The formula to find the area of a circle is (While π symbolizes the exact value of pi and r symbolizes radius.) πr²

NOTES:

π = c/d (c = circumference [Perimeter of a circle] d = diameter [Twice the radius, think of it as a 'height' of sorts])

So area of circle can also be portrayed as cr²/d


Now, the hard part. Setting the two formulas equal to each other.

ap/2 = cr²/d

Let's think of these two equations a little differently.
Let's replace c [circumference] with p [perimeter] Since they are basically the same thing.
Let's replace r [radius] with a [apothegm] since, once again, they are basically the same thing.
In replacing radius with apothegm, we must also say that since d [diameter] is 2r:
d [diameter] is now 2a [apothegm multiplied by two.]

Let's see what we get:

ap/2 = a²p/2a

In the second equation [a²p/2a], you'll notice that we may now cancel the 'a' that is within the denominator of the fraction and one of the 'a's within the numerator of the fraction:

a²¹p/2a

Thus, we find that they are equal. Such that:

ap/2 = ap/2


Does this provide concrete evidence that a circle is, in fact, a polygon?
Is it safe to say that a circle is a polygon with infinite sides?
And if so, isn't infinity incalculable?
Does this mean we will never truly find the exact area of a perfect circle?
Hue?

[Ad Bot]

[Night Fox]

no

[Teneksi]

INFINITE POWER SIDES

I wouldn't consider it a polygon, no.

[Stocking]

A circle has one side.

Also, 0.999... = 1 まほ～

[SpreadsPlague]

A circle has one side.

Also, 0.999... = 1 まほ～

was about to say this damnit stocking

but 0.9 repeating isn't 1 D:

[Gamefandan]

TitsMathematical evidence or GTFO.

[Night Fox]

Mathematical evidence or GTFO.

no

[Gamefandan]

Because being uneducated makes you cool, right?

[Night Fox]

Because being uneducated makes you cool, right?

no

[SpreadsPlague]

apparently this topic is a battlefield

some argue it has infinite sides and thus infinite corners, but some argue it is one continuous side. then there are those who believe it has no sides.

I suppose it varies depending on what your view of a "side" is

[Messes]

Because being uneducated makes you cool, right?

Nope, being in your DM does 

[Teneksi]

But a circle, theoretically, doesn't have exact sides, which defines a polygon (a closed figure with straight sides). It's a concrete shape with area, but it isn't a polygon.

[Stocking]

was about to say this damnit stocking

but 0.9 repeating isn't 1 D:

x = 0.999...

>Define variable

10x = 9.999...
10x-x = 9

>Subtract one x.

9x = 9

>Divide both sides by 9.

x = 1

>まほ～

[SpreadsPlague]

x = 0.999...

>Define variable

10x = 9.999...
10x-x = 9

>Subtract one x.

9x = 9

>Divide both sides by 9.

x = 1

>まほ～

0.9 repeating + 0.9 repeating is not 2
1+1 = 2
therefore 0.9 repeating can't be 1

?

[Teneksi]

x = 0.999...

>Define variable

10x = 9.999...
10x-x = 8.999...

You couldn't say that 1.999... - 0.999... = 1 unless you actually added 1 to it to begin with, which you didn't.


10x isn't perfectly 9.999...