10 Simple Questions That Still Totally Baffle Scientists
1. Circles, Man, How Do They Work?
You learnt how to calculate the different values of circles in school, right? C = 2r and all that. The problem is that pi () is a bit of a complicated concept. It is an irrational number and it can't be represented by terminating or repeating decimals meaning that we can't calculate its "true" value. So, if you had a circle with a diameter of 1, then its circumference would be equal to pi, but as we don't know the value of pi then that would mean that we don't know the circumference of the circle. This sounds stupid because it is. We demonstrably do know the circumference of a circle because we can measure it but, mathematically speaking we don't. Sort of.
Okay, this actually isn't strictly true. The problem is that we can't express pi by writing it down in numbers, our way of communicating values is just not sufficient. However, if you were to draw a perfect circle (like, mathematically perfect, not just pretty), then the circumference of that circle would be an accurate expression of pi (and, incidentally, an accurate representation of a pie).
The Greeks hated irrational numbers so much (and you can kind of see why) that when a bloke named Hippasus came to realise that 2 was an irrational number, rather than sparking deep philosophical debate, Pythagoras promptly had him drowned for upsetting his nice, ordered world view.
The story is likely apocryphal, but it goes some way to show how infuriatingly baffling the whole thing is.
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