What Are Conic Sections and Why Do They Matter?

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    Conic sections Important
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Discussion Overview

The discussion revolves around the concept of conic sections, their significance, and their applications in various contexts such as physics and mathematics. Participants express confusion about the nature of conic sections and seek clarity on their importance and different representations.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about conic sections, questioning their significance and the reasons behind their various representations.
  • Another participant asks for clarification on specific aspects of conic sections that are confusing to the original poster.
  • A different participant suggests that conic sections are fundamental curves that arise from simple equations, noting their presence in natural phenomena like projectiles and orbits.
  • There is a mention of a distinction between projectiles and planetary orbits, referencing Einstein's theory, which implies that orbits are not strictly conic sections due to precession.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the understanding of conic sections, and multiple viewpoints regarding their significance and representation remain evident.

Contextual Notes

Some statements made by participants rely on assumptions about the nature of orbits and the definitions of conic sections, which are not fully explored or resolved in the discussion.

quantizedzeus
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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.
 
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hi quantizedzeus! :smile:

can you be more specific as to what you don't get about conics? :confused:
 
Why are these curves so special that they are found in nature so frequently?...
 
a conic is the simplest possible curve (after a straight line), so it'll be the answer to the simplest possible equations :smile:

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

(so they aren't "everywhere")
 

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