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== Abstract ==

== Abstract ==

I will discuss some interesting properties of simple geometric objects (such as unit spheres and unit cubes) in high dimensions.

I will discuss some interesting properties of simple geometric objects (such as unit spheres and unit cubes) in high dimensions.

Our intuition about space is formed in two and three dimensions and this can often be misleading in higher dimensions. I will derive some surprising facts about unit spheres such as - the volume decreases with increasing dimensions and tends to zero.

 

Our intuition about space is formed in two and three dimensions and this can often be misleading in higher dimensions.  

 

I will derive some surprising facts about unit spheres such as - the volume decreases with increasing dimensions and tends to zero.

I will primarily be covering material from Chapter 2 of the following book - https://www.cs.cmu.edu/~venkatg/teaching/CStheory-infoage/hopcroft-kannan-feb2012.pdf

I will primarily be covering material from Chapter 2 of the following book - https://www.cs.cmu.edu/~venkatg/teaching/CStheory-infoage/hopcroft-kannan-feb2012.pdf