What Are Conic Sections and Why Do They Matter?

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SUMMARY

Conic sections are curves obtained by intersecting a cone with a plane, resulting in shapes such as ellipses, parabolas, and hyperbolas. These curves are fundamental in mathematics and physics, appearing in natural phenomena such as projectile motion and planetary orbits. Their significance lies in their ability to represent the simplest equations, making them essential for understanding various physical systems. The discussion highlights the confusion surrounding their intuitive understanding and emphasizes the need for clarity in their applications and historical context.

PREREQUISITES
  • Understanding of basic geometry concepts, particularly shapes and curves.
  • Familiarity with algebraic equations and their graphical representations.
  • Knowledge of physics principles related to motion and orbits.
  • Basic historical context of mathematics and its evolution.
NEXT STEPS
  • Study the properties and equations of different conic sections: ellipses, parabolas, and hyperbolas.
  • Explore the applications of conic sections in physics, particularly in projectile motion and orbital mechanics.
  • Learn about the historical development of conic sections and their impact on mathematics.
  • Investigate the mathematical derivation of conic sections from the intersection of cones and planes.
USEFUL FOR

Students, educators, and professionals in mathematics and physics who seek to deepen their understanding of conic sections and their relevance in real-world applications.

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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