Mathematical topics for high school investigation

[Rodrigo Olivera]

In the IB diploma program, they ask for a "Mathematical Exploration", where I have to deal with a topic with mathematical tools.
For example:
How to get the perfect exit of Gymnastics Bars?
In "exploration" you have to see the measurements, the angles, velocity trajectories, mathematical tools.

They recommend some subject in which he uses many mathematical tools, preferably something that applies to the common life. It is for secondary so it is not a complicated issue.

Recommendations of mathematical tools: functions, vectors, estadistics

I would appreciate it as you have no idea.

 

[fresh_42]

Useful in everyday life, especially when it gets toward a driver licence, could be the investigation of how a car's velocity has to be adjusted in a curve on different weather conditions, i.e. friction coefficients, in order to stay alive.

On the pizza box is printed: 15 min in a preheated oven at 220°C. How long is it, if one puts in the pizza write at the beginning and how does it depend on the oven.

You want to paint your room. How much paint do you need, how do you know the right amount of color you have to add to the white basic paint etc.

Another school book exercise is often a plane's flight route where wind comes into play from various directions and maybe varying intensities.

 

[jedishrfu]

Some sports analysis could be interesting

Flight of a frisbee, soccer ball or boomarang

Kicking power and the flight path or a variation with spin and ball bending.

There was that video about the magnus effect in dropping a basket ball with spin from a dam.

Another would be the effects of a leak on your water bill. I heard that one drop per seond was equal ti 3000 gals per year.

 

[scottdave]

I have been a judge at several science fairs - subjects include Mathematics, Physics, Engineering, and Life Sciences. Some of the ones that I found the most interesting were ones which had to do with something that the student was involved in. Examples are ballet, paintball, soccer and other sports, musical instruments. One person even had a dad who played in a rock band, and analyzed optimal positions for the speakers.

 

[jedishrfu]

Paperplanes would be interesting. You could compare designs surface area, balance to flight distance and duration or use different paper materials. You could try various trimming atrategies on a given and see how it performed.

 

[Aufbauwerk 2045]

I think all the above are good ideas.

Are you allowed to use computers? Do you like to program? Writing a simulation of something, maybe with some simple animation, could be a reasonably ambitious project, yet only involve high school math. As for what is that "something" there are many possibilities. Maybe someone else can suggest.

As for the common life matter, one subject that comes to mind is traffic flow in a city. Could I design a little town and have a top-down view of cars going around on streets? How would I set it up to minimize congestion?

 

[jedishrfu]

For the programming aspect the OP could check out the open source physics site. There are many simulation examples available that run in Java. You could find one and do the physical experiment and show how the simulation matches it and deviates from it. The examples are all in Java and it's best to use the Eclipse IDE to work with the code.

Www.compadre.org/osp

 

[Aufbauwerk 2045]

I like what @jedishrfu suggests, but it seems more appropriate for a physics exploration. Since this is a "mathematical exploration" I think they are not looking for physical experiments.

I've looked in the past at the IB program, but I never looked in detail at the math explorations. Perhaps there is someone on PF who has done one of these projects or maybe has even taught for the IB? Here in the USA we are not so familiar with it, I think.

I see there are resources online, including lists of suggested topics for the Mathematical Exploration, but the list depends on which program you are in. You say secondary: is this the same as IB SL?

Here is an online forum dedicated to the IB.

http://www.ibsurvival.com

This is a site they link to concerning Maths IA HL and SL. Does this apply to you?

https://ibmathsresources.com/2013/09/03/maths-ia-exploration-topics/

Perhaps if you specify what program you are in, and what list of potential topics is appropriate for you, then people on PF may have some more suggestions.

By the way, American students may only know about AP courses. They may want to look into the IB program as an alternative.

 

[hilbert2]

An idea:

Suppose $P(x)$ is a polynomial, and $x_0 , c$ are real numbers. Investigate what conditions are required for the iteration

$x_1 = x_0 + cP(x_0 )$
$x_2 = x_1 + cP(x_1 )$
$x_n = x_{n-1} + cP(x_{n-1})$

to converge towards a solution of equation $P(x)=0$.

You can check that this works for $P(x) = x^2 - 2$, $x_0 = 1.3$, $c = -0.1$.

 

[jedishrfu]

The OP hasn't been back to PF since Sunday ie 5 days ago so I think we should wait until he returns as he has probably selected a topic and neglected to tell us...

 

[Buffu]

it's best to use the Eclipse IDE to work with the code.

I recommend vanilla vim just like a real programmer. :)

 

[jedishrfu]

I recommend vanilla vim just like a real programmer. :)

Yeah, that's great. However, real programmers use an IDE nowadays in addition to vim. The IDE is great for project management, code refactoring and debugging and is not to be given up so easily. VIm comes in handy when you are on a production box where usually minimal tools are available.

In any event, the Open Source Physics site delivers its code as an Eclipse workspace, unzip and you're good to go. It will work on Netbeans too Netbeans can import Eclipse projects.

 

[Buffu]

Yeah, that's great. However, real programmers use an IDE nowadays in addition to vim. The IDE is great for project management, code refactoring and debugging and is not to be given up so easily. VIm comes in handy when you are on a production box where usually minimal tools are available.

In any event, the Open Source Physics site delivers its code as an Eclipse workspace, unzip and you're good to go. It will work on Netbeans too Netbeans can import Eclipse projects.

Mostly I made a bad joke :(.

Eclipse is very good but I feel like it messes up my somewhat large projects. I tend to lose interest in them. But then again I never used Eclipse for Java I only used it for C++.
Not to say it is very heavy, it has much more than a hobby programmer needs.

Using vim also somewhat gives a fake sense of doing some thing advance even if it is just Hello world, lol.