12.1 A 3D coordinate system
- Author:
- Stephen Vallette
- Topic:
- Coordinates, Equations
Today we
- extend our understanding of Cartesian coordinates,
- re-introduce notations for points, lines, and planes,
- extend our distance formula,
- extend formulas for lines, planes, and some circular 3D surfaces.
We begin by "assigning" a point's location in by measuring in two dimensions (directions): and .
We can describe these directions into quadrants (1, 2, 3, and 4) by categorizing the numbers of each axis into negative, 0, and positive numbers.
Next we apply these ideas to a universe in which we've added one new set of axes.
(Or, in which we've added a new coordinate.)
We "assigning" a point's location in by measuring in three dimensions (directions): , and .
We can describe these directions into quadrants octants (1, 2, 3, 4, 5, 6, 7, and 8) by again categorizing the numbers of each axis into negative, 0, and positive numbers.