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Math EE - Calculus - Pursuit Curve; question about RQ and word count

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Hi. I have chosen to write an EE on math about pursuit curve, which involves calculus. I have a few general questions about the format of a math EE after reading the EE guide --

1) Is there actually a lower word limit for math EE, since it involves graphs, equations etc. that will not be counted toward word? I'm just worried that to make up 3-4k words with graphs in between, my paper is going to be super long, not to mention the requirement to double-space.

2) How can I form my research question? From all the EE samples I have seen so far, all of them took a research question from math competitions. Is it possible to form a research question on my own? Are there any examples?

Then about the pursuit curve in specific --

1) I was able to find out about the equation of the simplest pursuit curve (the linear pursuit curve), and graph a circular pursuit curve with Mathematica. Though both of the linear and the circular curves are pursuit curves, they don't seem to be related that much. I'm wondering how I can make a research question to unify these two curves, or what else I should do about this topic. (I really like the topic btw)

Thanks for your help in advance :)

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Pursuit curves sounds like it could be a very interesting topic for a math EE! I did my EE in math as well so I suppose I could offer some advice.

1) I don't think IB enforces a specific minimum word count for math EEs, but it is permissible for them to be shorter since equations do not count towards the word count, and those will (usually) make up a significant part of your essay. Having said that, don't expect to write your essay as simply a list of equations since a good math essay will not only present a concept using symbols but will also explain what the symbols represent in ordinary English.

2) In the case of a math EE, it's often a good idea to work towards some specific goal. For example you may seek to find the answer to a contest-type problem, or perhaps you might prove a specific theorem, find/analyze an algorithm, or generalize a familiar concept.

For example, I went with the generalization route, and sought to generalize the formulas for the area of a circle and the volume of a sphere to higher dimensions and to certain non-euclidean spaces (Lp-space). PM me if you'd like to see my essay as an example. (FWIW it received an A)

In your case, for example you may wish to outline an original method for computing such pursuit curves, or perhaps proving/applying certain properties of pursuit curves (to give a vague idea). Think about, what is it that sets pursuit curves apart from arbitrary curves, and what relationships can you find between the paths of the predator and the prey? Hopefully this will point you in a useful direction. The important thing is to come up with a specific goal that you can work towards. And if you find yourself with one week before the deadline and you haven't achieved your goal, don't be afraid to either relax your goal or to show that you've made partial progress towards a solution. (Or, if you've solved your problem in time for your first draft and have tons of space left, extend your goal to something more ambitious, like I did :D)

Also just one more note, your RQ does not have to be phrased in the form of a question. In fact I don't have a single question mark in my entire EE (except for one of my references). Although a question might work better in your particular case, so try to experiment with your phrasing.

Hope this was helpful, and good luck!

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