Mathematical Physics - Quantum-Relativity (qr)

The Gaussian-School of Higher-Arithmetic (1831, updated 2022); tutorial #4-a.

The cypher "one" (1) with no polarity specification, is NOT a number, it's a circle.

Author's  comment:

The so called “number” minus-one (-1) must be interpreted as inverse-one (-1), that is direct-one (+1) times a rotation of one quadrant of polarity-rotation twice in series. As inverse-one is generated by a process of multiplication by a single quadrant of polarity-rotation twice in series, the number inverse-one has an obvious square-root. This was first shown to be the case by Hero of Alexandria in the 1st century AD, but it seems that (with the possible exception of Hero himself) only JCF Gauss and myself ever paid enough attention to the logic of rotational polarity inversion. However, Gauss could never deal with this misunderstanding on his own because he was fixated upon the radian unit of rotation. That is why you are now learning the 2022 breakthrough formalized version of the original 1831 Gaussian language of numerical polarity.

This sketch gives a graphical clarification of the words in my previous paragraph.