Proofs without Words using gganimate

I recently watched the 2 part workshop (part 1, part 2) on ggplot2 and extensions given by Thomas Lin Pedersen. First of, it was really nice of Thomas to give the close to 4 hour workshop for the benefit of the community. I personally learnt a lot from it. I wanted to try out gganimate extension that was covered during the workshop.

There are several resources on the web that show animations/illustrations of proofs of mathematical identities and theorems without words (or close to it). I wanted to take a few of those examples and use gganimate to recreate the illustration. This was a fun way for me to try out gganimate.

Example 1:

This example is taken from AoPS Online and the result is that sum of first $n$ odd numbers equals $n^2$.

$$1+3+5+\dots +(2n-1)=n^2$$

The gganimate version of the proof (using the method in AoPS Online) is shown below (R code, html file)

Example 2:

This example is also taken from AoPS Online and the result is:

$$1^3+2^3+\dots +(n-1{)}^3+n^3=(1+2+\dots +n{)}^2$$

The gganimate version of the proof (using the method in AoPS Online) is shown below ( R code, html file):

Example 3

This example from AoPS Online illustrates the result

$$\frac{1}{2^2}+\frac{1}{2^4}+\frac{1}{2^6}+\frac{1}{2^8}+\dots =\frac{1}{3}$$

The gganimate version of the proof (using the method in AoPS Online) is shown below ( R code, html file):

Example 4

According to Pythagoras theorem, $$a^2+b^2=c^2$$ where $a$, $b$, $c$ are sides of a right angled triangle (with $c$ being the side opposite ${90}^o$ angle)

There was an illustration of the proof of pythogoras theorem in a video from echalk.

The gganimate version of the proof is shown below ( R code, html file)

In summary, it was great to use gganimate for these animations since it does all the magic with making transitions work nicely.