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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Eccentricity and Conic Sections

Made an Eccentricity Graph that shows the transition from circle, through ellipse to hyperbola.

Only problem is at e=1 which is theoretically a parabola, but comes out as rubbish (I made it a line to cover up the problem) ... any suggestions?

I want people to easily see how the conic-sections are related to e.

Code for "a" and "b":

if (e < 1) {
	a = 1;
	b = Math.sqrt(( 1-e*e)*a*a);
} else {
	a = 1;
	b = Math.sqrt((-1+e*e)*a*a);
}

Which is then plotted by this code (in a loop with "t" going from 0 to 3):

if (e < 1) {
	xVal = a * Math.cos(t);
	yVal = b * Math.sin(t); 
} else if (e==1) {
	xVal = t;
	yVal = 0; 
} else {
	xVal = a / Math.cos(t);
	yVal = b * Math.tan(t); 
}

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Eccentricity and Conic Sections

Nice toy!
The one bug I can see is that when you have 1<e<<2, the hyperbola turns into vertical lines at the graph's boundary when it should just disappear.

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Why did the vector cross the road?
It wanted to be normal.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Eccentricity and Conic Sections

Thanks mathsy, yes I should mask that out.

Any ideas on how to illustrate the e=1 case?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Eccentricity and Conic Sections

A new version, and I put it on Eccentricity

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman