Science ideas needed, please help?

Hi, i need a highly challenging science project idea for the Siemens Competition. I am highly interested in math (will be taking pre-calc), physics, and chemistry.

Last year i took geometry, i love to prove some of the postulates. But i can't think why it is important to prove besides helping ppl understand how come the postulates make sense.

But anyway, please help me, give me some ideas and explain, if you can why it is important to find out or invent.thank you ton!!!

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