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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?

3816

Off Topic / Re: jizz in hair?

« on: March 21, 2011, 06:40:34 PM »

Quote from: Iban on March 21, 2011, 06:39:35 PM

aren't you into that

Only if it's Iban.

3817

Off Topic / Re: Ask Mistur Monocle.

« on: March 21, 2011, 06:38:30 PM »

Quote from: Monocle on March 21, 2011, 06:38:06 PM

Not even going to read that.

</3

Fine, I'll make a topic then. :C

3818

Off Topic / Re: Ask Mistur Monocle.

« on: March 21, 2011, 06:37:25 PM »

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?

3819