koch snowflake?

Question

I'm stuck in my math project and seriously need help. I'm working on the koch snowflake and need to write down successive values for An in terms of A0. A is the area, but now i need to know that pattern emerges. please help me, I have no idea what is meant nor what to do.

Answer 1

The first step when constructing the Koch snowflake is to add 3 triangles on the outside of the first triangle. After that you only add two triangles for each triangle you added in the previous step.

each triangle you add is going to be 1/3 as big (sidelength) as the previous triangle, so it will have 1/9 of the area.

So the area after the first step is going to be A0+3(1/9)A0 which is A0+(1/3)A0

For the seccond step we are going to add 3x2 triangles of size (1/9)²A0

and then, for the third step we will add 3x2x2 triangles of size (1/9)³A0

So for the nth step we will add 3x2^(n-1) triangles of size (1/9)^n A0

so now it would be nice to be able to use sigma notation but Yahoo answers is limited in that respect so I'll try to write it out in words.

The formula for the area of the Koch snowflake at step n is:
A0+(the sum i=1 to n) of (3 x 2^(i-1) x (1/9)^i x A0)

Hope this makes sense.

Answer 2

Type 'koch snowflake' into any search engine and you'll get almost 30,000 sites that discuss it. Start looking..........

Wiki has a fairly good article. If you can find a copy of Mandelbrot's 'The Fractal Geometry of Nature', he has a fairly good discussion as well.

HTH ☺

Doug

Answer 3

if u could be more specific... i could halp...

LET A 5
; calculate adjusted side-length
LET B 243
REPEAT A
LET B B/3
NEXT
; place pointer
POINT 150
MOVE 140
POINT 0
; start
GO SIDE
RIGHT 120
GO SIDE
RIGHT 120
GO SIDE
; finished.
END
; main loop
# SIDE
GO F
LEFT 60
GO F
RIGHT 120
GO F
LEFT 60
GO F
RETURN
; forward
# F
IF A > 1
; go deeper depending on level
LET A A-1
GO SIDE
LET A A+1
ELSE
; or just do a single line
DRAW B
ENDIF
RETURN