## JSH: Back to conic section parameterization result

To understand that there really is something wrong here, you need only reflect back now on a rather simple mathematical result that has been known for centuries:

Given x^2 - Dy^2 = 1, in rationals:

y = 2t/(D - t^2)

and

x = (D + t^2)/(D - t^2)

and you get hyperbolas with D>0, the circle with D=-1, and ellipses in general with D<0.

You can see the D=-1 case from a well-known mainstream source at the following link:
See: http://mathworld.wolfram.com/Circle.html eqns. 16 & 17

That allows you to, say, graph ellipses or hyperbolas adjusting a single D number which is related of course to eccentricity.

That has been known for CENTURIES.

One would think that would be an undramatic thing, but the posting assaults against me when I noted the result and questioned why it's not more well-known should give you a clue.

These people killed an entire math journal. See: http://www.emis.de/journals/SWJPAM/

If you think it's rational to just say I'm some crackpot, and I can show you my re-discovery of a nifty little result known for centuries—except mathematicians look at "Pell's Equation" as a Diophantine equation so classified away from rational solutions—and know about a DEAD math journal killed in a spectacular way, then you cannot escape my assessment that your brain is screwed up.

Math journals don't just die. And physics people don't just ignore nifty little simple equations that can draw ellipses and hyperbolas where you just fiddle with one D number versus eccentricity, if their brains are working properly.

Try to think through the special circuitry that gets you to do dumb things.

It is the same circuitry that requires human misery, war and strife—for the good of the species.

Our species can now do better. Try to transcend your programming. It may be the biggest intellectual challenge most of you will ever face in your lives—understanding that your own brain is tricking you, for the good of your species.