Visualizing linear functionals Linear form

geometric interpretation of 1-form α stack of hyperplanes of constant value, each corresponding vectors α maps given scalar value shown next along sense of increase.      0 plane through origin.

in finite dimensions, linear functional can visualized in terms of level sets.  in 3 dimensions, level sets of linear functional family of mutually parallel planes; in higher dimensions, parallel hyperplanes.  method of visualizing linear functionals introduced in general relativity texts, such gravitation misner, thorne & wheeler (1973).