'Matinga's Transposition Law' (Mathematics)

Matinga's Transposition Law

All axes or curves described by an equation will be the same regardless of how the axis is transposed.

Explanatory Examples

Mathematics has reserved the term 'proof' for non-deviating arguments. The discipline is a subset of Physics, as it contains many of the same dimensions - as dependent dimensions, identified as dependent variables in mathematics. Mathematics is programming which is time-based, so it must join Physics whose fundamental dimension is time or quantum evolution. Algebra is the name of the mathematics programming language.

Xerqon, 2026

In algebra we have been using transposition for millennia yet we still have not appreciated that the curves or axes, by another name, should be unchanged when an equation is transposed. When a variable or constant is transposed to the alternative side the equals sign, its value is always preserved, as its sign is negated on the other side of the equals sign, for the wholesale shift.

Observe the image below, for an example of how this is already programmed into some graph plotters, and where it still needs to be applied further - usually with more complex axes. Rather than overwriting axes, the author has changed constants to allow for better visual perspective of the parallel, analogues or similarly, algebraically configured curves.

The image below, was generated from Geogebra.com/calculator

The diagonal axes are parallel as they share the same variable and they a shifted apart by one constant. The curves have also been transposed relative to each other. A similar arrangement exists between the circular axes, which by similar logic should be parallel and complete in its displacement.

© Xerqon ABN 97661410108 2026