Eyes on Final Fantasy Forums > Reference > Study Hall > GoBo's Math Woes

[Tavrobel]

Oops. Did I do that?

[Jessweeee♪]

Originally Uttered by Vivisteiner

EDITGA: Yeah, Im not cheating, and yeah its 4/3. Ahh, I love fractions. Otherwise Id be writing 1.33333333333333333333333333333333333333 3333333333333333333333333333333333333333 3333333333333333333333333333333333333333 3...


(I think you get the point)

I hate long decimals, I just don't feel right putting a rounded answer on my paper ;_;

<3 the pi/e/i/etc. buttons on the calculator n.n

[Vivisteiner]

^Tbh, I actually prefer decimals. Im a physicist so I dont mind rounding. Its only those neeky mathematicians who say pi/3 instead of 1.05

[Tavrobel]

Because decimals are, most of the time, approximations, and not exact values of a given situation. Decimals also introduce more room for potential errors; when exact values are mistaken, usually the answer goes from correct to really wrong really fast, and is a form of consistency for our theoretical, perfect little worlds we have in our heads. Also, we hate significant figures. To the death.

[Jessweeee♪]

ugh...when I enter a science classroom it's just 2+2=5 for me all of the sudden ;_;

[Klyklops]

You should do your own homework. But I will do it for you this once. The easiest method is to use DeMoivre's Theorem, which presumably you know,

exp(iy) = (cos(y + 2(PI)n) + i sin(y + 2(PI)n)). n is an integer.
put x^3 = a*exp(iy). So y = 0 and a = 192/81.
Then

x = (a^(1/3))*exp(i(y/3))
x = (a^(1/3))*(cos(y/3 + 2(PI)n/3) + i sin(y/3 + 2(PI)n/3))

Here we have
y = 0
so


x = (a^(1/3))*(cos(2(PI)n/3) + i sin(2(PI)n/3))

Then stick in integers for n,

n = 0
x = (a^(1/3))*(cos(0) + i sin(0))
x = (a^(1/3)) = 4/3

n = 1
x = (a^(1/3))*(cos(2(PI)/3) + i sin(2(PI)/3))
x = (2/3)*(1 + i Sqrt(3))

n = 2
x = (a^(1/3))*(cos(4(PI)/3) + i sin(4(PI)/3))
x = (2/3)*(1 - i Sqrt(3))

n >= 3 just cycles through these solutions.

These solutions define an equilateral triangle in the complex plane. PuPu did it a really nice way, and yeah you have to get 3 answers.