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Maths/Physics Extended Project Ideas

Hey,
I've been asked to do an extended project in school, its not the official qualification but it apparently has the same weight on a personal statement (4000 word essay + presentation).
I've got 2 weeks left to do it (given 3 weeks in total ) and am really struggling for ideas.
I'm looking for anything in Maths/ Physics or a bit of Chemistry preferably something that somehow fits on an engineering (Chemical?) personal statement.
Here are some failed/possible ideas I had with reasons:
1.Game Theory-->in D2 so not really off the spec
2.Can Robots be made creative enough to invent their own language?--> maybs not many sources for information though
3. Is wireless electricity viable?--not sure
4.How have the encryption methods of today been influenced or evolved from ancient methods?- not sure again
5. Maths of Deal or No Deal-->possible but not enough scope to be near 4000 words

Essentially, I have some ideas but they're terrible and I'm very indecisive.
Help appreciated!
Thanks

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