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November 27th, 2013, 08:37 AM   #1
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Exploration in Maths

* I know this is a very long post but it would mean the world to me if you could read it. I would really appreciate it.

Wll hi guys, so I'm in the final year of my IB diploma programme and in maths we have a component known as internal assessment in which you're supposed to write a so called Mathematical Exploration:
"This mathematical exploration is a short report written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area.The final report should be approximately 6 to 12 pages long. The report should include a detailed bibliography, and sources." - IB

Yeah so I initially started to think about ideas back in July, and already then I knew I wanted to do something calculus orientated. Some people suggested that I could do "mixing problems" and set up a differential equation to describe the rate of change in a contaminant, or even a lake because a real world example is what I should really go for.

I should use calculus to explore real life problems. So I actually found a document of a person who had set up their own model describing how the rate of contaminant changed over time using Calculus and then he applied this to some lakes in real life which I thought was cool.
So I showed my teacher this document and she said I couldn't do that as I would take somebody else model and it wouldn't be my authentic work. So I had to switch idea.
Now for the past months together with my struggle in the IB I've gotten many ideas, but I've always been centered around calculus.

The teacher sat down with me and told me what I was interested in and we dug deap until we decided to do something with airplanes.
Airplanes are a huge fascination of mine. I love the engineering, the structure, it's greatness. I even love airports. The strange thing is that I'm super afraid of flying airplanes (partly because I've watched all Mayday episodes).

So initially I thought lets create a model to optimize a flight profile for the least amount of fuel consumed. I then thought I would look at which airplanes to take for different trips. At which altitude you should fly, what speed you should have, when should you start descent etc... to optimize flight profile for least amount of fuel consumed.
This turned out to be really hard as there were many variables involved and I had to give up that idea after to 15+ hours research if not more...

Then I went on by thinking well lets look at airplane descent and try to model the descent of an airplane. I would then look at different airplanes at different airports.
Which speed should the airplane have initially when should it start to descent etc...
I found a model on the internet which did model this but after 8 hours with it I gave up, I thought it was a bit too hard to comprehend.
I thought I could use the model and then compare with real data and probably see that they were not the same and then discuss this.
In theory it was a great idea but once again I couldn't pull through.

So then I took a step back and thought what made me interested in planes, and then I thought about the dimensions, and structure etc...
The wing loading and flexibility of airplanes are super important to me when I choose a trip by airplane. Since an increase in wing loading and flexibility decreases any turbulence felt by me in the fuselage and that is a dealbreaker for me.
I also always sit by the wing as it's statistically the safest place to sit at (but also the noisiest).
In the airplane the three structures which are the most important to me and the ones I worry about the most, are the wings, the engines, and the rudder/stabilizer.
I'm especially scared that the rudder/stabilizer will malfunction or get stuck, as it will often have fatal consequences.

Now I said this to my teacher and she was like: "You should compare the dimensions of different aircrafts, perhaps those big ones with small ones, and surely you can get some calculus there"
That was what she said, now after spending about 25 hours trying to find out what to do I'm getting really demoralized and at the same time the school is giving me a rough time (understandably so but really I have been trying a lot)
I have collected dimensions of four different aircrafts, two long-haul and two short-haul. At least I've tried to find as much data as I can. I especially got a lot for the Airbus A380 but now I'm like what am I supposed to do with the data, which essentially is only dimension data. Where can I use my calculus, and then what....

After spending more than 60 hours on this I'm getting really demoralized and sad really, and I can feel the pressure increasing. What should I do guys really feeling hopeless at the moment. The school is really getting sick of me too.

In this "Maths Exploration" the maths definitely does not have to be complicated, this is a very good example of a maths exploration which scored a perfect 20/20

The assessment criteria are these and I would really appreciate it if you took a look at them.

I really need your help guys

I just need my topic and then the writing stage will go much faster

Cheers guys!

P.S. My maths knowledge is equivalent to that of a Maths HL IB student although I only study Maths SL.
shwareb is offline  
November 27th, 2013, 08:40 AM   #2
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Re: Exploration in Maths

Link for example of perfect score maths exploration: ... ions_e.pdf

These are the assessment criteria : ... r%3d8.html
shwareb is offline  
December 11th, 2013, 08:42 PM   #3
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Re: Exploration in Maths

Hi, I completely understand your struggle. I went through at least 20 hours of research to find data to accommodate my entire Exploration. My math teacher is getting annoyed because I keep coming to her with the same answer: "I have my Introduction, Rationale, Aim.. etc, but have no data." I've been meeting up with my teacher consistently for the past three weeks, and every time she discusses it with me it makes me feel a little more confident but as soon as start and just only faintly think about the exploration remebering all the things im missing and still have to add, I go back to square one and panic.
What I would suggest is that if you're struggling with the data part do not spend excessive amounts of time into it. Make a deadline and if you have got nothing by that date force yourself to change your topic. It definitely isn't worth it to spend much time just trying to find something to JUST support your exploration. Rather the math concepts being used, how they are applicable to real life, the reflection aspect and taking the reader through a 'journey of maths' so that reader learns something, are highly more time consuming then the data alone.
I really wish I knew even a little bit about planes and how they work, but unfortunately I do not.
Just in case you are wondering I was primarily doing the 'Modelling the Growth of Tumours'. This caused me major trouble with absolutely no data online, in books and articles that would help me at all, So i had to change it. For the lack of time i decided to use the knowledge concepts I've learned through the previous research i have done and change it to a slightly different but similar topic: 'Modelling the Growth of Computer Power over the past few decades'. This was much easier to find raw data for so I graphed it immediately and proud of my achievements went further into finding the equation and trend. Another talk with the teacher is all that was needed to rethink my decision. I now have changed my topic again to be 'Applications of Parabolas' which im hoping with be alot easier in terms of data finding and applying math to an everyday life. One of the assessment criterion is Reflection. This is my issue. Especially the 'Why is it significant?' part. I had no clue as to what the purpose would be or how it would be relevant to the reader or to myself. This is something i had to deeply think about. Now that i have something that is seen everyday I'm predicting this part will go well.
I wish you much luck on your Math IA! And remember we are the first group of students that have done this. Previous years they have been doing the portfolio. So dont stress yourself out. The teacher will have many problems just trying to interpret all the different topics and clearly, never mind understanding all the topics. But don't give up, keep trying you'll find something that will interest you.
Penelope is offline  
April 8th, 2014, 09:55 PM   #4
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maths exploration ib

Hi everyone,

i am having the same problem with my maths sl exploration. I am doing my on earthquakes and logarithms. i have completed my first draft and finding that they is not enough maths involved in it. I have tried to make an appointment with my maths teacher but he has been away sick and has not been able to give me the time. I am not mathematicaly inclined so i am not sure what i am doing and what is expected off me.

Can someone help please. If i upload my draft can some one read it and tell me what they think about it and were i can improve

meenaa is offline  
April 9th, 2014, 08:05 AM   #5
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@shwareb: Have you tried contacting Boeing and Airbus? You could write to the CEO (perhaps copying in the marketing director) explaining what you are trying to do and asking for some figures that would help you in your project.

Alternatively, you could perhaps compare the dimensions that you have to the weight of the aircraft to see how the sizes of various parts of the aircraft change with weight. Or look at how wing length / area compares to aircraft length / width /volume. Are there any differences in the location (half-way along, or more or less) of the wings or tailplane for aircraft of different sizes? What about the height of the tail-plane.

Looking further afield, can you find any statistics related to air safety that you could compare to different types and sizes of aircraft?

Last edited by v8archie; April 9th, 2014 at 08:12 AM.
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April 9th, 2014, 08:08 AM   #6
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Originally Posted by meenaa View Post
If i upload my draft can some one read it and tell me what they think about it and were i can improve
You can try. It might be a bit long though. Can you post the mathematical content (or a summary)? Perhaps that would be sufficient for someone to be able to suggest what you could add.
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