It is possible to represent an angle (fraction of a turn) in Euclidean 3-space as a 2-dimensional object rather than as a simple ratio between two lengths. This 2-dimensional object can be viewed mathematically as a value or quantity. Because we can represent direction as a quantity this way, it must be possible to construct a geometry that uses this quantity as a metric, as opposed to using length as a metric.

We don’t know exactly how this is done yet because the algebra hasn’t been worked out sufficiently. We do know that the area under the curve drawn by this 2-dimensional representation is a mathematical quantity.

This section contains preliminary drafts of ideas that are still under development. More material will be furnished on these subjects as it is accumulated.