*Space, space everywhere; not a single point is known*. The first primitive humans must have found the awareness of *space* very perplexing (imagine being thrown into a *space* about which you know nothing). Modern humans have become a lot less nervous about *space* because they now know a lot about *space*. For example, they are able to determine the coordinates and characteristics of spaces on earth and some spaces beyond earth. *Geometry* is the key knowledge that allowed humans to successfully journey from a point in time when no single point in *Space* was known in the context of a coordinate system, to a time when almost all points in *Space* are known.

What is geometry? Partitions of *Space* abound, so it is not surprising that there are various geometries (Eulidean, Non-Euclidian, Affine, Projective, Spherical, Inversive, etc) and as a result, several definitions of *geometry*. Nonetheless, there is a commonality about what geometry does: *it represents a space and the possible transformations in the space*. The representation is usually depicted by one or more number lines. The number of *number lines* indicate the *dimension* (usually denoted by the letter *n*) of the space. For example, there is the Euclidean line (a 1-dimensional Euclidean space where n =1); the Euclidean plane (a 2-dimensional Euclidean space where n=2) and the 3-dimensional Euclidean space (where n = 3). The properties of the space that are unaltered by any of the possible transformations in the space constitute its geometric properties. For example, in the Euclidean space, the possible transformations preserve *lengths*.

The *containership* property of space is common to all geometries. In fact, *geometries* exist for the purpose of analyzing and effecting *containerships* and the possible *transformations* of the *containerships*.

The number lines that depict *geometries*; the *containership* of the spaces the geometries represent; and the possible transformations in the spaces are expressions of Pj Problems. Consequently, *geometries* are expressions of Pj Problems

## For Knowledge Sake, One Code (S_{i}P_{j}A_{jk}) For All Knowledge
TECTechnics Overview