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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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  Easy Math Editor

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**bold** or __bold__ bold

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[example link](https://brilliant.org)example link
> This is a quote
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    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears 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} \( \boxed{123} \)

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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 \(0\)

Michael Mendrin - 2 years ago

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