Very famous result on what e actually is:
Still famous but not as famous result on what e is, esp amongst HSC students:
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Yeah, but sometimes it's actually more convenient to define functions by their power series representation and then prove other things about them.Tbh isn't the first statement really just a Taylor series?
Yeah, but sometimes it's actually more convenient to define functions by their power series representation and then prove other things about them.
This is, of course, assuming that every birthday date is identically probable, and that leap years do not exist, and that birthdays are treated as truly random. Under these conditions, a group of 70 people have a 99.9% chance of two people sharing a birthday.There is approximately a 50% chance of two people sharing the same birthday in a room of 23 people
That's not a bad thing, there are unsolved problems in stats applicable to the real world such as p-values, error values, correlation vs. causation, interpolation of data, etc.Certainly not a pure mathematician, but Cauchy's Integral Formula stands out for me.
Then I moved to stats.
The Kakeya Needle Problem: What is the smallest area of a parking lot in which you can have a needle of length 1 turn around 180 degrees and return to its starting position, pointing in the other direction?There is a lot of highly theoretical mathematics here.
Does anyone have more real-world mathematical statements?
(The birthday problem was a good one)
This isn't very "practical" though, since the car / needle needs to be made arbitrarily thin if you want the area to be arbitrarily small. For anyone interested, there is a Numberphile video on the Kakeya Needle Problem: www.youtube.com/watch?v=j-dce6QmVAQThe Kakeya Needle Problem: What is the smallest area of a parking lot in which you can have a needle of length 1 turn around 180 degrees and return to its starting position, pointing in the other direction?
Answer: The area can be made arbitrarily small through a series of divisions and transformations of the shape required for the needle to turn around. Hence, no smallest area exists.
Well the problem never stated any width. It is a mathematical solution, after all.This isn't very "practical" though, since the car / needle needs to be made arbitrarily thin if you want the area to be arbitrarily small. For anyone interested, there is a Numberphile video on the Kakeya Needle Problem: www.youtube.com/watch?v=j-dce6QmVAQ
Haha yeah, it is an interesting result, I just meant that it's not really real-world as braintic wanted.Well the problem never stated any width. It is a mathematical solution, after all.
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