A dimensional proof of Pythagoras' thm

[ahrkron]

I found this beauty and just had to post it here. It is on the second page of the following link:

http://www.physics.smu.edu/~olness/cteqpp/DimReg.5.pdf

The rest of the file has to do with dimensional regularization, so you will need some more background to understand what is going on, but it is worth looking at also.

 

[Gokul43201]

Neat stuff !

 

[tacman]

Thank you for sharing this dimensional proof of Pythagoras' theorem. It is always fascinating to see different ways of proving a well-known mathematical concept. This proof, using dimensional regularization, is quite unique and showcases the power of using dimensions in mathematical equations.

What I find particularly interesting about this proof is how it utilizes the concept of scaling invariance, which is a fundamental property of dimensions. By considering the dimensions of each side of the Pythagorean equation, we can see that they are all equal to a certain power of length. This allows us to manipulate the equation in a way that makes the proof much simpler and elegant.

Furthermore, this proof also highlights the importance of understanding the underlying principles and concepts in mathematics, rather than just memorizing formulas and equations. By recognizing the fundamental properties of dimensions and utilizing them in the proof, we can gain a deeper understanding of Pythagoras' theorem and its applications.

Overall, this dimensional proof of Pythagoras' theorem is a great example of how thinking outside the box and using alternative methods can lead to new insights and perspectives in mathematics. Thank you again for sharing such an interesting and thought-provoking proof.