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Kakeya's Needle Problem and Skewes' Number

Don't get confused! They are not realted to each other in the math world but yeah if you are a follower of Numberphile, you would relate them easily.

So, this and this are the videos inspiring this note.

But why I am posting this note is to understand both the topics in detail. The former one, I didn't understand at all , I don't know, I even couldn't watch the whole video(the professor bored me quite early).

Any help will be appreciated.

Note by Kartik Sharma
2 years ago

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Have a look at this starry graphic

You can see that a needle can turn completely around while staying in side of this figure, with both ends always on the perimeter of the figure. The area of such a figure can be made arbitrarily small, as we can see with this example

It seems counter intuitive that it's possible to have a needle turn completely around inside a figure which area approaches $$0$$

- 2 years ago