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OK so I have to do a research paper/presentation on an experiment/project that relates to my precalculus class. Only problem is that I was given no topics to choose from and I couldn't find any real good ones online. Can anybody give me some good ideas/topics that I can do? (P.S. if its fun then that's a plus :D)

user1729
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Ronnie.j
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  • I want some ideas/topics for my precalc project but I have no leads as to what to pic so im asking you fellow math braniacs if you have any ideas that i can research/experiment on – Ronnie.j Sep 14 '11 at 01:27
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    I'm sorry, I didn't mean to be unclear. I'm not certain if this question belongs on this site - that's what I was getting at. I answered your question (although I don't know if it fits). In general, I like the idea that you ask a question in the best place for it to be answered, but questions like this are likely best for your teacher. We don't know what happens in your class or the scope of the task. But perhaps you'll strike it rich here. – davidlowryduda Sep 14 '11 at 01:29
  • oh i just need any ideas related to math basically, said my teacher lol – Ronnie.j Sep 14 '11 at 01:37
  • is there any way to make this question "big" so that i might get many ideas? – Ronnie.j Sep 14 '11 at 01:38
  • Ronnie.j, I think this is a nice question, give it some time and it may indeed get big. – Dan Brumleve Sep 14 '11 at 04:20
  • @ShantDanielian: Interestingly, OK was the original spelling, so it is debatable as to whether changing OK to okay is even valid! See here. – user1729 Aug 09 '13 at 11:15

4 Answers4

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I have no idea what does or does not relate to your precalc class. But I hope that the construction of 3d figures as stacked 2d images fits, because I think it's very beautiful.

For instance, enter image description here.

Depending on the things that you do in your class, these shapes might be different. But I think they're beautiful and fun. If you're very careful, you can even approximate certain volumes by adding up the weights of the pieces of paper (or whatever material), which suggests some deep things in math. Like calculus, in a way.

Or perhaps I'm completely off mark - just an idea.

davidlowryduda
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  • Thanks, i jst need any idea that relates to precal/calculus – Ronnie.j Sep 14 '11 at 01:28
  • For a topic title, i would put 3D images on 2D pictures. Is there anyway you can like explain/evauluate on your topic? – Ronnie.j Sep 14 '11 at 01:43
  • as in what you are doing, i can tell that your shaping paper in different positions that by itself, looks 2 dimensional, but but together, looks 3 dimensional. I am very interested in your topic and would like to learn more about it – Ronnie.j Sep 14 '11 at 01:45
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    Incidentally, the equation on paper graph is incorrect. It should read $$z=\frac{\sin\sqrt{x^2+y^2}}{\sqrt{x^2+y^2}}.$$ – anon Sep 14 '11 at 08:23
  • I agree, it's beautiful! How do you get the edge marker to be a constant width? Do you cut first, or mark first? – TonyK Sep 14 '11 at 11:33
  • @Tony: I did not make these, actually. I just happen to see them once. I have since made some, though. And I cut first. – davidlowryduda Sep 14 '11 at 17:29
  • @mixedmath where do i go about making this? – Ronnie.j Nov 18 '11 at 00:25
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When i was given a similar choice, i chose this, seemed fun and also pretty useful

http://en.wikipedia.org/wiki/Inclinometer

will take some effort into building it, but is a good idea nevertheless

Bhargav
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  • so your idea is to build one? – Ronnie.j Sep 14 '11 at 01:38
  • ya, just make a wooden protractor (http://en.wikipedia.org/wiki/Protractor) and then what you do is, hand a thread at the 0 degrees point and then use it, if u r really interested in much more precision, you can even build a stand, i more of recommend http://en.wikipedia.org/wiki/File:Clinometerlow.jpg this. Because its easy to make and simple to use. My teachers appreciated it a lot. And mor eover the above ones in the inclinometer page of wiki will be costly in my opinion – Bhargav Sep 14 '11 at 01:45
  • haha thanks for the ideas, much appreciated :) – Ronnie.j Sep 14 '11 at 02:30
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You could do something with trigonometry. I remember playing the “hand rule game”. This is a game that helps you remember the sine and cosine of $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$.

The game consists of the following:

Starting from little finger to thumb fingers, assign the five angles commonly encountered in early trigonometry. Little finger – 0, ring finger – 30, middle finger – 45, index finger – 60, and thumb – 90 degrees. Ensure that the palm side is up while assigning.

Now, the trick is the (square root of the number of fingers below the angle finger) / 2 is the value of sine of that angle. Thus, the sine of 30 degrees is the square root of 1 divided by 2 = 1/2.

Demonstrate this trick first and then design a quiz based on it. You can play a rapid quiz with friends in a group. A volunteer displays the cue angle by marking it on the finger and the others tell the answer. It can help create a shortcut to calculations and save you a lot of time in exams.

James Garrett
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For some fun, how about jump rope, or if you can recruit a couple more partners, Double Dutch?

Use a camera to take some pictures of the activity, and print them out to analyze and include in your report. What is the shape of the image of the rope? Perhaps it resembles part of a sine wave, or a parabola. Try it with the rope in motion, and also just dangling from two hands. Does it matter what angle the photograph is taken from? Does the distance of the camera from the rope change anything? What functions you have learned about fit the image of the rope most accurately? Do certain functions fit better than others under different circumstances? Can your formulate a hypothesis explaining the results?

If you have a digital camera to bring to class, you can repeat the experiment while giving your report, and I imagine this would make for a lively demonstration.

Dan Brumleve
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