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Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
Generating electricity without the use of fossil fuels is not just an engineering and industrial challenge, it is also a huge mathematical challenge.
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Inverse problems are mathematical detective problems. They can help solve crimes, are used in medical imaging, and much more.
The only way to find the exact volume is not by integration, but by filling the object (i.e. pepsi bottle) with water and pouring it out into a measuring cylinder. This is similar to the problem, allegedly given by Thomas Edison to a young mathematician, to find out the exact volume of his new invention, the light bulb. After spending days finding a function to represent the curved surface of the bulb and then integrating it to calculate the volume he told Edison the answer. Edison then inverted the bulb and filled it with water and then measured the volume of the water, and replied "Yep, that seems about right." Now that's how an engineer would approach it.