* 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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Exploration in Maths

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