Ping
What about the origin of the zero?
How Andrew Wiles cracked the Taniyama-Shimura conjecture and therefore proved Fermat’s last theorem.
A big field of computer graphics is 3-d modeling and CAD. There are lots of topics there: geometry, boolean logic, wireframe systems, solids, surfaces, etc. Try googling “solid modeling cad math” for some inspiration or starting points.
Sudoku and Other Diversions [Free Republic].Don't forget to tell her that it's not considered cheating to find a source using the Internet, then go to a library and source (bibliographically) it through a hardcopy. That's commonly referred-to as "doing your homework."
Planarity.
Oooh! Haven't had to do one of these in a looong time!
Suggestions:
1) The Fibonicci thing indicated in another post.
2) PI - Teachers LOVE PI...
3) "Math in Everyday Life" - Many highschoolers take the attitude of "I'll never use this stuff." (Those people, as adults, are now stuck with bad home loans.) Inability to assess simple Time Value of Money problems causes MANY bad financial decisions. Geometry is very useful in construction, home repairs, and a million other things. Algebra solves many day to day problems. What mix of a and b to make the desired output, etc.
Prepare to be amazed... ;-)
pi or i (square root of -1) would both be interesting
I had an OpenGL book when I was in college. I might still have it. If I do, I’ll post back with the title and author.
Another interesting topic might be a discussion of fractals, with a side-track into visualization of fractals.
Or, more generally, visualization techniques for mathematics in general (see, e.g., this paper to get a sense of topic).
Can it be on statistics? I would think a statistical analysis on the election of 2000 would be interesting. Perhaps that could be a topic. Of course I am horrible in math and actually had to take statistics twice at Florida State...does not accept a D. lol.
How about the Fire Control Solution used by our Battleships in WWII?
Have you considered gaming math? Explain how the math of slot machines work. It’s simple really.
There is a group of about 300 FReepers that use their computers to help crunch proteins to advance medical research such as Alzheimer’s Disease, Parkinson’s Disease and many cancers.
In nature, misfolded proteins cause a slow buildup of poisons that eventually kill us. Computer simulation is the least expensive and quickest method to prove a conclusion.
The latest thread is here:
http://www.freerepublic.com/focus/f-chat/1929553/posts
A better thread with additional links is here:
http://www.freerepublic.com/focus/f-chat/1906532/posts
The main page at Stanford University is here:
From the front page of Folding@home:
“Folding@home is a distributed computing project — people from throughout the world download and run software to band together to make one of the largest supercomputers in the world. Every computer takes the project closer to our goals. Folding@home uses novel computational methods coupled to distributed computing, to simulate problems millions of times more challenging than previously achieved.”
Here are ideas concerning the paper:
1. This paper on MATH touches dozens of other disciplines, among them applied math, math and computers, pure scientific research, applied research, genetics and many more.
2. You will be able to show the interdisciplinary aspects of math and how it can advance other research beyond expectations.
3. Grab a PS3, load up F@H, and use it in your discussion. Talk about how the Cell processor uses math to speed up calculations to the PetaFLOP range. Also make for lots of pretty pictures, and all kids like game systems. Compare a PS3 running F@H with a desktop computer to see which is faster.
4. There is lots of material to pull from, lots of graphics to pretty up the report, and even Youtube videos to help explain the process if you make a multimedia presentation.
5. Show how you can combine all of the computers in the entire district into a gigantic supercomputer that will help cure someone’s grandmother’s Alzheimer's. This generates lots of statistics that can fill Excel sheets forever.
Some FReepers, Klutz Dohanger and josephw (I think) are education professionals that have converted computers to run F@H in the background. Klutz is the #82 folder in the entire world, and our team is #52 in the world. Many schools and colleges fold.
6. Look here for papers and results from F@H:
http://folding.stanford.edu/English/Papers
If you can understand these papers, then help explain them to us. Seriously.
“- 54.Calculation of the distribution of eigenvalues and eigenvectors in Markovian state models for molecular dynamics
- 53. Heterogeneity Even at the Speed Limit of Folding: Large-scale Molecular Dynamics Study of a Fast-folding Variant of the Villin Headpiece
- 52. Control of Membrane Fusion Mechanism by Lipid Composition: Predictions from Ensemble Molecular Dynamics.
- 51. Persistent voids: a new structural metric for membrane fusion.
- 50. Protein folding under confinement: a role for solvent.
- 49. Automatic State Decomposition Algorithm.”
And there are lots, lots more where these came from.
8. JMOL. Using math to simulate atomic scale interactions inside a computer. Look here:
9. In high schools, pretty pictures mean a lot (and take up space in a long report). There are dozens of images that can be used on Google. I still like the idea of a multimedia report. It is an honors class after all.
10. Ping generally and grey whiskers, who currently work with math or remember the math from long ago.
11. Ping me for questions that stump you.
In all seriousness, you could write a paper, come up with experiments that can be performed in the school that cost nothing except time, involve many branches of science, look good in a multimedia presentation, show how every day computers can be made to serve a higher purpose, start a race with other schools and universities across the world, and, if all else fails, you can tug on their heartstrings showing how this work can help save their GRANDMOTHER.
Hope that it helps.
I did one on how to lie with statics. Knowing how makes you question what you hear others claim.
A lot of these ideas are interesting, but may not be at all what the teacher actually wants. Is the teacher looking for equations/proofs or exposition? If the latter, then Wiles’ proof of Fermat’s last theorem would be an appropriate topic...if the former, then the teacher would expect the student to actually understand Wiles’ proof...in which case it would not be a good topic.