Can someone give an example of cosine similarity, in a very simple, graphical way?

Question

Cosine Similarity article on Wikipedia

Can you show the vectors here (in a list or something) and then do the math, and let us see how it works?

I\'m a begin

Answer 1

For simplicity I am reducing the vector a and b:

Let :
    a : [1, 1, 0]
    b : [1, 0, 1]

Then cosine similarity (Theta):

 (Theta) = (1*1 + 1*0 + 0*1)/sqrt((1^2 + 1^2))* sqrt((1^2 + 1^2)) = 1/2 = 0.5

then inverse of cos 0.5 is 60 degrees.