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.

Easy Math Editor

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Comments

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 $0$

Michael Mendrin - 5 years, 7 months ago

@Pi Han Goh @Michael Mendrin @Otto Bretscher

Kartik Sharma - 5 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$