Coordinate foundations · Laboratory 01
Cartesian Coordinate Laboratory
One space. Every direction.
A right-handed Cartesian coordinate system with X, Y, and Z axes meeting at the origin. The default view shows eight octants, three translucent coordinate planes, and a quarter-inch grid. Use the labeled controls to change the view. Coordinate planes are boundaries of octants, not part of their interiors.
Built in the open
This laboratory is taking shape.
This working preview begins with the space itself: coordinates, planes, octants, and different ways of looking. Next, we will connect this space to algebra and an inspectable mathematical design sequence.
Preview 0.1September 22, 2026
Understanding the coordinate space
Three axes, one origin. X, Y, and Z are perpendicular. Each coordinate measures a signed distance along its axis. The three coordinate planes separate space into eight octants.
A plane is a boundary. On the XY plane, z = 0. A point such as (2, 1, 0) is in the first quadrant of that plane, on the boundary between octants I and V. It is not inside either octant.
Orthographic and perspective. Orthographic projection keeps parallel lines parallel. A tilted view still foreshortens lengths; the XY view looks directly onto the XY plane. Perspective adds depth through apparent size.
Units and extent. One inch is exactly 25.4 millimeters or 2.54 centimeters. The grid shows model measurements, not physical inches on your screen. Axes extend indefinitely; the controls select a finite portion to display.
Octant convention. Here I–IV lie above the XY plane, beginning at (+,+,+) and following the usual XY quadrant order. V–VIII repeat that order below it. The sign triples are always shown because octant numbering conventions can vary.