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THERMO Spoken Here! ~ J. Pohl © ~ 2018 | www.ThermoSpokenHere.com (A4380-044) |

Analytic Geometry has provided capable tools for description of a BODY in motion in space. To describe physical space (called 3-space by some) requires specification of three dimensions. A fourth dimension, time, is needed when events being both spacially and temporally dependent.

Steps required to prescribe a coordinate space include:

**(i)** Selection an "origin" (some say "a point in space") must be made. Within the space of the event (observed or imagined), a point must be chosen (in the yet undefined space) to be the "origin" or center location. An "origin" (fortuitously chosen) can be a convenience in understanding regarding the BODY/event future.

**(ii)** At the chosen origin, three mutually-perpendicular straight lines are imagined to extend. These lines, called "coordinates" are (by convention) named **X**, (or the "X-coordinate"), **Y**, and **Z**. These upper-case letters, their orientations, denote, each their respective coordinate. Coordinates are lines. In addition, (by convention here) the axes are numerated using as notation, the lower cast letters, **"x"**, **"y"** and **"z"**.

To be clear: A BODY located at the origin has numerated position: 0,0,0. Meaning the numerated values of coordinates are (lower-case letters): **x** = 0, **y** = 0, and **z** = 0

**(iii)** In our beginning-level usages, only two of the three axes are used. At our learner's level only two dimensions, only planar considereations, are needed. The cartesian coordinates, **X** and **Y**, (designating a horizontal plane) are chosen for motion of any BODY being independent of gravity. **X** and **t** are the coordinates of linear motion of a BODY in time. Should gravity force be relevant, coordinates **Z and t** would be used (our convention is Earth reference, with "z positive upward."

Value, Slope and Curvature are the information about a Curve at

a point on the curve
More Later - This work is in progress."

Methods of physics and math (about reality simplified to be a BODY) can predict future aspects of a BODY/events quantitatively. The "things," for a BODY (or any other model of physical reality) are its **properties** and its **characteristics**. Features of matter itself, that change are called properties. The BODY has one property which is constant - its mass. The vector quantities, position, velocity and acceleration are called characteristics.

Consider a hypothetical property notated as, **F**, which changes only as does time. That property is written symbolically as: **F(t)**. For us, any observation of some **F(t)** over time must begin at (the beginning of its

observation) **x = x ^{*}**:

A basic idea of calculus is that a function, **F(t)**, has three
characteristics at any specified value of **t**, say **x = x ^{*}**.
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