What Are Conic Sections and Why Do They Matter?

[quantizedzeus]

I'm totally confused...i don't understand conic sections. Why do these curves so special? They are described as results of a cone cut by a plane and the equations are constructed from the distances from a point and directrix. We find evidence of these curves everywhere-in projectiles, in planets' orbits and so on. But after trying a lot i still can't get them intuitively. I tried to study history of conics sothat i can understand what problems or consequences lead the mathematicians to build these ideas. But all went in vain. I'm still so confused. Can anyone make me understand what these things really are? Why are they so important in our daily life? Why are they constructed/described in many different ways? Plz help...please...and sorry for my bad english. And thank you so much for any kind of help.

 

[quantizedzeus]

No one to help...?

 

[tiny-tim]

hi quantizedzeus!

can you be more specific as to what you don't get about conics?

 

[quantizedzeus]

Why are these curves so special that they are found in nature so frequently?...

 

[tiny-tim]

a conic is the simplest possible curve (after a straight line), so it'll be the answer to the simplest possible equations

(but technically, it's not the orbit of a planet, since according to Einstein, that precesses)

We find evidence of these curves everywhere-in projectiles, in planets' orbits and so on.

these are actually the same thing …

a projectile is simply something that follows an orbit which intersects the Earth's surface

(so they aren't "everywhere")