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## #1 2006-08-23 00:27:02

richardbird
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### Complex curves

A bounding curve is formed by the graph lines:

x = y(a/b) and x = y((a+1)/(b-1))

where a and b vary continously over a range say a = 1 to 10, b = 1 to 10.

What is the equation for the bounding curve?  (it resembles x = 1/y)

If the y axis is tilted at 60 degrees to the x axis, (instead of 90 degrees) a 'squashed' curve is formed. What is the equation for the curve with D degrees as a variable parameter?

Is there a name for this family of curves?

Many thanks!
Graphs for the curves are on URL

http://www.richardbird.info/Etch%20segments.htm

Last edited by richardbird (2006-08-23 00:46:03)

## #2 2006-08-28 23:47:29

John E. Franklin
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### Re: Complex curves

Etchilhampton, hmmm...  sounds neat.
Also for the right triangles, see pythagorean triples, where q^2 = 2mn.
Because if q^2 is a constant k, then k = 2mn, and n = k/2m, which is a hyperbola.
May just be a coincidence.  Not sure if the curve fits your etchilhampton thread-and-nails picture...

igloo myrtilles fourmis

## #3 2006-08-29 11:51:54

John E. Franklin
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### Re: Complex curves

How's this for the 60 degree curve?
x = 1/y + y/2
I haven't graphed it except in my head, so it might be wrong.

igloo myrtilles fourmis

## #4 2006-08-29 12:04:06

John E. Franklin
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### Re: Complex curves

Woops, I was wrong.
not y/2 for 60 degrees, try this:
For D degrees, perhaps...
x = 1/y + y tan(90 - D)

igloo myrtilles fourmis