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lertola2
04-18-2011, 06:38 PM
Hi all,

I have a geometry problem that I have been trying to figure out for a few hours but I don't seem to be getting any where with it. I know this is a bit off topic but I am hoping someone here has the math knowledge to point me in the right direction.

This weekend I downloaded Processing programing language (http://processing.org/) and I was able to use it to write a small program that draws the fractal image shown in the upper right of the attached image. But I noticed that there is a special number that will make the fractal fit perfectly in a triangle. I can use trial and error to get very close to this number but I would like to calculate it accurately. The attached image illustrates the problem. In the program I move points B and C along line AD to draw different versions of the fractal shape. The number I want to calculate is the y value at point F. Does anyone have an idea on how to find that value?

Thanks,

-Joe

Silkrooster
04-18-2011, 10:09 PM
Isn't it suppose to be height x width divided by 2? For the length of point A to Point F

Height is point C to point F

width is point A to point D

lertola2
04-18-2011, 10:30 PM
Isn't it suppose to be height x width divided by 2? For the length of point A to Point F

Height is point C to point F

width is point A to point D

What? I don't get you.

bazsa73
04-18-2011, 10:45 PM
need the angle between the AE AB vectors or any non perpendicular angle

Silkrooster
04-19-2011, 12:05 AM
What? I don't get you.

I beleive that is the equation for house rafters.
Height x width divided by 2 or 1/2 the width x the height. Its been quite a long time since I have seen the equation. So I could easily be wrong.

THREEL
04-19-2011, 12:12 AM
need the angle between the AE AB vectors or any non perpendicular angle

I agree! I think there is a piece of info missing, namely an angle, besides the 90's that are already present.

But, I will tell you what we do have. We do know that the ratio of line segments AE and EF are proportional to AC and CD. Therefore, AE/EF = AC/CD. Also, we know the line segment AC = 0.6 and line segment CD = 0.4. With that being said, The ratio would be AE/EF = 0.6/0.4, or AE/EF = 3/2. So, line segment AE is 1.5 times the same as line segment EF, or line segment EF is 2/3 the size of line segment AE. By looking at the diagram, we, also, see that at point E, x is less than 0.5.

From there, I just plugged in what I thought were reasonable numbers and solved. For example: If we let AE = 0.45, then EF must be equal to 0.30. Using the Pythagorean Theorem (a sq. + b sq. = c sq.), I plugged in the values: a = AC = 0.6, and c = AF = 0.45 + 0.30 = 0.75. I solved from there, which gave me an answer of b = CF = 0.45. y would, also, equal 0.45 at point F. You could solve for x and y at point E as well from here.

I maybe missing something here, but I do know that the ratio that is mentioned plays a big part in solving the x's and y's. Hope this helps!