Visual Plane
every picture states the point it is correct from
Ladder

Auxiliary — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. true length1.3928 mpoint viewthe edge is one pointtrue shape1.3232 m²one face, three ray directionseach step is a choice of direction, not a construction on the paper

    The view that makes a line a point

    Descriptive geometry's first drill is to look at an edge from a direction perpendicular to it, so it draws at true length, and then along it, so it draws as a point. Both are the same identity — the imaged length is the true length times the sine of the angle to the ray — and the sine holds to 1e-12 across the whole sweep of directions.

    rung 3 · parallel
  2. 90°106°front view · 1.997 m²its own view · 2.900 m²area × 0.6886, the cosineworst corner out by 15.60°

    The true shape of a cut

    A plane through a box makes a hexagon of 2.8996 m². The front view draws it at 1.9966 m² — the true area times the cosine, 0.6886 — and gets its corners wrong as well, the worst by 15.60°, because a foreshortening scales one direction and not the other. The area is recoverable with one number and the angles are not, which is why a section gets a view of its own.

    rung 4 · parallel

All ladders