help me choose a math research topic

I am 14 (15 in a couple of weeks) and am taking part 3 of 3 math in my school and am a 10th grader. For those of you who know, i am taking sequential III honors class in new york and am required to do a research paper. I have less than a month to choose the topic and i want to know your advice and suggestions.

We don't have any specific topics we must choose, but for someone like me. A year before pre-calculus, what would you recommend that i do a math research paper on? Last year i did it on cryptology and developed a couple of functions in vb for encryption/decryption. This year i am hoping to do a little more programming and enter it in a math fair competition. I am hoping to develop a presentation and a program to match the presentation.

Any ideas?

Personally I am a fan of Dynamic Programming, but there isn't a lot of math (but still some) involved. if you want a combination of math and computer science, i would suggest either:

1) a mathematical/tactical game and make an AI for it (e.g. chess,checkers,Hex,4x4x4 Tic Tac Toe)
2) do something with Computational Geometry/Algebra, such as graph theory, or maybe to something specific such as 3D game specs (hey 3D games are made up of only triangles and stuff) etc

hope this helps

If you write a 3D engine from scratch (i.e. no DirectX) then you've got a heck of a lot of Maths. If you decide to do it, I can provide some references for you to look at.

well i am thinking more of direct3D and so but i am interested in seeing your references even though MXALPHA may or may not be interested.

btw i did a RayCasting Engine last year, and shows perspective so it looks 3D even though it is technically 2D. however it does not pertain a level of difficulty that you would normally encounter when you do a 3D engine from scratch -- as the latter can't be done by just any people except the most experienced game developers.

One of my courses at Uni last year was Computer Graphics, and the second half of the course was the 3D graphics part, it went through all sorts of different stuff, and it's not that bad. Of course, if you really want to go from scratch that's even more fun. We started first off with how the eye works and an overview of colour theory. When we moved onto the actual computer bits of graphics, we started with "How to draw a line", then "How to draw circles/ellipses", "How to draw filled polygons", clipping, polygons infront of/behind other polygons, how to resolve circular overlappings (A obscures B obscures C obscures A), bezier curves, XORing, bit transfers, 2D transformations, ... so when you want to get right down to the real nitty gritty (if you're turning your back on the Direct3D functions, why not turn your back on the VB line function? lol) you've got to decide where to stop.

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Originally posted by Evil_Giraffe
One of my courses at Uni last year was Computer Graphics, and the second half of the course was the 3D graphics part, it went through all sorts of different stuff, and it's not that bad. Of course, if you really want to go from scratch that's even more fun. We started first off with how the eye works and an overview of colour theory. When we moved onto the actual computer bits of graphics, we started with "How to draw a line", then "How to draw circles/ellipses", "How to draw filled polygons", clipping, polygons infront of/behind other polygons, how to resolve circular overlappings (A obscures B obscures C obscures A), bezier curves, XORing, bit transfers, 2D transformations, ... so when you want to get right down to the real nitty gritty (if you're turning your back on the Direct3D functions, why not turn your back on the VB line function? lol) you've got to decide where to stop.

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I like this!! i'll look into it, but what you guys are talking about is WAY too complex math. I'm a year before pre-calculus!

i know, thats why i recommended ray casting engine if u want to do graphics!

no... lol... 2 complex!!

how does game AI sound?

that sounds good!!

my brother knows people who work in harvard and he is trying to get me a summer internship there and i want to get something with like ai or hardware. And this might be a good idea!!

Is AI math complex?

ok why don't you consider doing 4x4x4 tic tac toe? i've done something like that and I have an AI that so far no one is able to beat it if you let it go first. if you need something mathematical, you can analyze the game using mathematics, such as proving why the first player will always win.

personally I'd do the raycasting engine...sounds really cool :cool: I just started precalc last wednesday (haven't started yet, still reviiew) and raycasting sounds good. Its just geometry :) I've been thinking of taking a shot at that for about a week now ;)

and just be aware...not many people (especially teachers!) understand computers. They might not see much math in what you're doing. People like flashy things, that why I thought a raytracing example may be best, its a little more interactive, and gives an illusion of 3D, which you can boast took lots of math ;)

AI may get tough, but ChuckB (i think) has made a fabulous program you may want to take a look at.

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Originally posted by bugzpodder
ok why don't you consider doing 4x4x4 tic tac toe? i've done something like that and I have an AI that so far no one is able to beat it if you let it go first. if you need something mathematical, you can analyze the game using mathematics, such as proving why the first player will always win.

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but the first player doesn't always win.

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Originally posted by SteveCRM
personally I'd do the raycasting engine...sounds really cool :cool: I just started precalc last wednesday (haven't started yet, still reviiew) and raycasting sounds good. Its just geometry :) I've been thinking of taking a shot at that for about a week now ;)

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Umm... i just started like geometry or whatever it's called now. We did geometry and trigonemtry, and now we're doing factoring like 3rd degree equations and complex fractions.

no the first player does win, by experience (my program seriously haven't lost one match) and also by mathematical proof (do some research to find out). anywayz i think this idea is great esp if u don't know too much math and programming/AI

i'll look into it!

oh sorry, I did geometry -> alg 2 -> precalc....keep forgetting the norm goes alg2 -> geometry -> precalc.

good luck on whatever you do :cool:

thx! i hope so. I did good on my last year cryptology project. Create i believe two functions, encrypt and decrypt. It wasn't too complex... i would've went to the math fair but the submission date was too late for my teacher to enter me into it.

MXAlPhA,

Could you post some parts of your cryptology project from last year? I am really interested in cryptology, and I'd like to learn a bit more about it. Thanks!

ok...

Firstly, the problem with programming AI for tic-tac-toe, even 4x4x4, is that once you figure out how to play not using a computer, you can program an 'unbeatable' code, which never lets u win. However, this gets quite boring quickly, as there is really no point anymore. A more interesting approach would be to teach a program to learn how to play 4x4x4. You could do this by playing against yourself, and this way the computer can 'watch' you, see what u did when u lost, what u did when u won, etc. and can learn to play like you do. This way, the program is always changing. (You could then play it, an see if it is better than u :p)

However, AI definitely has a great potential for the future.

I have a similar problem, as I am doing IB and want to do my extended essay in the area of Maths (:eek: shock horror :eek: )
Hoever, what i am thinking of doing is studying a series i just invented one day, called Marko Numbers^(c). This is just the number of times before the sum of a number's factors (not including itself & 1) must be taken before it is a prime.
i.e. 12 -> (2+3+4+6)=15 -> (3+5) = 8 -> (2 + 4) = 6 -> (2+3) = 5
5 is prime, so the Marko Number^(c) of 12 is 4 (there are 4 "->"s)
This series acts strangely, with some loops appearing (45->72->45 etc), but all of the loops so far are 2 numbers long. What i am wondering is, are there any loops with 3 looping numbers??