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[Vector]

A piece of paper stuck through a party hat at an oblique angle forms a line shaped like a parabola. It would seem that a great many formulas can be replicated in this way.

Yes!  Good job.  Now, an extension question: how do we get a straight line?  A point?

(Also, I'm sorry if I sound vaguely patronizing, but I had to withdraw from school and so I'm running low on my saved up reserves of mathematics.  I'm honestly excited to see you learning this)

[Heron TSG]

Let's see... a point could be gotten by sliding the paper between the two cones (where the tips come together) and a line could be formed by placing the paper along one edge of a cone, through the point where the cones touch, and down the opposite side of the other cone.

(It's okay. It's nice to have someone to talk to about math on the intertubes.)

EDIT: I'm sorry to hear you had to withdraw from school. What happened?

[Vector]

Being some flavor of what seems to be bipolar happened.  At length.  When I realized that it felt like my mind was about to shatter, I left school and declared I'd have to come back and fight another day after becoming more experienced and less insane.

[Heron TSG]

Ouch. One of my stepsisters is bipolar, and its rough from what I hear. Good luck on your experience-gaining journey.

[zchris13]

As a high school student in Calculus, I shall attempt to find a keyboard so as join this discussion.

[Heron TSG]

Welcome to the thread! An idea came to me today. If I can get a few people together, it'd be fun to learn math together. Obviously, this would have to be math that none of us have learned before, so we could be getting into some pretty wacky stuff.

[Vector]

Welcome to the thread! An idea came to me today. If I can get a few people together, it'd be fun to learn math together. Obviously, this would have to be math that none of us have learned before, so we could be getting into some pretty wacky stuff.

... *raises hand*

*shot*

In more seriousness, I'd be willing to help supervise such a group, if you wanted.  I know a bit of math.

[Cecilff2]

If you want to see some neat stuff, try linear algebra.  If you want to learn more about the inner workings of maths, try Abstract Algebra or Real Analysis.  These are all college level courses, but it's not too hard to get a grasp on linear algebra.

[Osmosis Jones]

Ooooh if you want to learn some new maths, I have a shitload of calculus resources left over from my maths 301 days if you want. Not just the boring stuff either, but advanced differential complex analysis, Bessel functions, tensor algebra, all sorts of fun stuff.

[AbacusWizard]

Conic sections are awesome. One thing that really fascinates me about them is the variety of different ways they can be defined: each one can be thought of as the intersection of a plane and a pair of cones, or as the graph of an equation on the xy-plane, or even as a compass-and-straightedge Euclidean construction! (Note: technically, you can't construct a parabola, hyperbola, or ellipse using compass and straightedge, but you can construct an arbitrary point that's guaranteed to be on a parabola, hyperbola, or ellipse, and if you do that enough times you get a pretty good picture of the curve.)

Challenge: while you're playing around with the paper and party hats, see if you can figure out the exact requirements on their arrangement that determines whether they produce a hyperbola, parabola, or ellipse. At which angles do they switch over? Why?