OK, it all started when my Geomotry teacher was curious about the area of an elipse, so I got thinking. Here are a few of my ides, tell me what you think, and any possible counter examples. I am curious what others have to say about my ideas.
* = Multiply
+ = Add
- = Subtract
/ = Divided
= = Equals
Pi = 3.14
Area of an Elipse
Pi (A) (B) is what I think the formula is.
In a normal circle, it is
Pi r², or Pi r r
Since, all an eclipse is doing is stretching out the X and Y factors, you just change it from r² to (r)(r), giving one the A and the other the B value. I am pretty sure I even read this somewhere, but just making sure.
Volume of an Ellipsoid
If you didn't already know, the area of a circle is 4/3 Pi r³
I took this, and figured about the same idea as i did with the Area.
The volume of a circle is simply
4/3 Pi (A) (B) (C)
So I figure the same principles would work out, where the X, Y, and Z factors are just being stretched, does this seem right? So if you used this for a sphere with a radius of 5, it would still show as
4/3 Pi (5) (5) (5), same as 4/3 Pi r³
Perimeter of an Elipse
In case you didn't know the perimeter of a circle, it is
2 Pi r
So, let's say the radius was 5, it would look like
Now, I did research this, and only found HUGE equations! I tried many ways to shorten it, but nothing really worked, until I thought of a different approach. I was wondering if some of you would agree with something as crazy as this!
I was thinking, maybe, just maybe, you could think of
2Pi r As
Why like this?
I thought since their was only 1 radius, it might be possible it was the mean of the combined radiuses. I don't know the plural of radius, so I'll use that word :P . Anyone, tell me what you think of this, cause I think it might be possible.
Try to think of this hard, because it seems possible.
Of course, just because
2*Pi*r² is equal to
2*Pi*[(A+B)/2] with an equal radius, i will still probably be wrong, lol, since they are the same numbers i am averaging. But if somebody knows the real, long formula, can you compare them?
And I didn't want to even imagine the Surface Area of an Ellipsoid, lol, too much for me to think about, for it is late right now, and I'm tired as it is! Thanks for reading this, and thanks you in advance for any replies!