People are awesome & Math is beauty

The white circles albeit traveling in a straight line across the circle exhibit a more collective circular behavior.

Here’s a much more real world scenario which follows similar guidelines:

If you notice, the motion of all the workers individually are also periodic in nature, but each of their motion is slightly out of phase leading to this beautiful symmetric behavior that constitutes this gif.

Truly mesmerizing!

The mathematical sciences exhibit order, symmetry and limitations; and these are the greatest forms of the beautiful

– Aristotle

** Radial engines too BTW:

Advertisement

Beautiful proofs (#1) : Divergence of the harmonic series

The harmonic series are as follows:

And it has been known since as early as 1350 that this series diverges. Oresme’s proof to it is just so beautiful.

Now replace ever term in the bracket with the lowest term that is present in it. This will give a lower bound on S_1.

Clearly the lower bound of S₁ diverges and therefore S₁ also diverges.
But it interesting to note that of divergence is incredibly small: 10 billion terms in the series only adds up to around 23.6 !