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First, I'm a high school senior, and am over 18, so don't ban me.
Science fair is coming up. Due to the fact I am in a small state, if I place in the top three of my category in the school, I am guaranteed to advance to the state science fair. As almost no one is doing this, this is almost guaranteed. From there, I can get scholarships, and potentially advance to international, where I can get a shit ton of scholarships.
Here's the thing: I love math. I plan to major in math, and most likely go on to grad school. So, does anyone have any somewhat obscure areas of mathematics that I could do a project on? I'm fine with having to put in effort to learn the required things, as math is my passion, as long as it is feasible within the year. I don't want a suggested project; I am just wondering what some interesting, higher-level areas of mathematics that I could learn within the next few months are, that could hopefully help me place at science fair.
Thanks a bunch, /sci/.
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>>8465575
>yfw you realize 1+2=4 is true for sufficiently large values of 1 and 2
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>>8465575
Check the brachistochrone, it requires a bit of calculus and diff equations but you could like... design something like... a ramp where a the balls reach certain point in such time.
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>>8465592
I'll look into that. Thanks man!
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>>8465575
What makes a project interesting is if there's something visual that can be presented.
Vectors and and complex numbers are nice, because they can be displayed as geometric objects using software.
Here's two pages I wrote a long time ago that allow the user to interactively explore some mathematical functions:
http://w3.romascuola.net/gspes/pgc2.htm
http://w3.romascuola.net/gspes/pgc1.htm
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>>8465575
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>>8465602
Those pages you wrote look really well done. Thanks for the suggestion, by the way.
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>>8465575
I can think of a few things. Why not explain Escher's art using hyperbolic geometry concepts? Or maybe how catenary chains are used in architecture? I was going to suggest a geometry based project, since that usually caughts people attention, but I don't think it would get you further than the state competition. Either way, maybe you could build some models of projected polytopes.
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>>8465614
Thanks for the suggestions!
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>>8465614
This, look up how the catenary curve is derived, it's pretty cool. Then try to build one and show how the forces act on it.
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A good area in terms would be thermodynamics as you can take it either from a calculus or statistical approach.
Even looking at something as simple as 'how does heat dissipate through a steel cube and into the surroundings' can yield some interesting maths
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