# Serious Math help needed =-(

1. Nov 27, 2005

### Euphoriet

I'm trying to find the area for the Koch Snowflake.... I cant really figure it out... I found a couple of equations online (I cant really understand how most work.. or how they have been "derived".. including the mathworld one)

I'm looking at the following formula (seems to work.. but I cant figure out the (1-(4/9)^n)/(1-4/9) part.. something to do with an infinite geometric series right?
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Equation:

(sqr(3))/4) + [ ((sqr(3)/12 )) * (1-(4/9)^s)) ] / (1-4/9)

(sorry I could not figure out the pretty print stuff either.)
s = stage of snowflake/fractal, starting from 0

2. Nov 27, 2005

### Euphoriet

3. Nov 28, 2005

### HallsofIvy

Staff Emeritus
Yes, that is the sum, from i= 0 to n-1, of (4/9)^i

Uh, that's not an equation! There is no "=". I'm not sure what you want to do with it. Add the two fractions? If so, then, of course, 1- 4/9= 5/9 so "(1-(4/9)^s/(1- 4/9)" is
$$\frac{1-\left(\frac{4}{9}\right)^s}{1- \frac{4}{9}}= \frac{1-\left(\frac{4}{9}\right)^s}{5/9}= \frac{9(1-\left(\frac{4}{9}\right)^s)}{4}$$
I come out with, for the whole thing,
$$\frac{\sqrt{3}+ \frac{3\sqrt{3}}{4}\left(1- \frac{4}{9}\right)^s}{4}$$

Double click on the "pretty print" (Latex) to see the code.