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Path Curves in the Plane (1)We add a Dimension Stepping a point along a line produces linear measures. This is One Dimensional, as it is confined to a line.. Next, we step a line (red) across a plane (blue), as we want to use two such stepping lines to track a point as it steps across a plane. That track must represent the combination of two linear measures. This is Two Dimensional, as it is confined to a plane. 


Where for the steps on a line we used
now, for the steps of a line on the plane, we use


We move a red line, first lifting it in a plane (gray) through one of the directing lines ('up', or u) until it encounters the intermediate plane, then returning it along another plane (pale gray) through the other directing line ('down', or d). All this can work only if the red line and the directing lines all pass through the meeting point of the three coloured planes. 
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