By George K. Francis
Goals to motivate mathematicians to demonstrate their paintings and to assist artists comprehend the tips expressed through such drawings. This booklet explains the photo layout of illustrations from Thurston's international of low-dimensional geometry and topology. It provides the foundations of linear and aerial standpoint from the point of view of projective geometry.
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Extra resources for A Topological Picturebook
Obviously, the other leg A-Z of the right triangle is a sightline perpendicular to SP, and hence Z is the desired zenith. CHAPTER 3 47 PICTURES IN PERSPECTIVE _-------,1 o 1 Z.
Originally, it took ten dedicated minutes in the dead of night on PLATO's Cyber73/CDC6500 timeshared mainframe. It was the convenience of the PLATO system and the uncommonly supportive personal environment that got me started in programming there rather than on a proper graphics setup. My computer novitiate thus was similar to what awaits current beginners in micro-computing. I developed a hybrid approach where the computer furnishes the underlay for a pen drawing. It still serves me well in the micro-computer world of reduced resolution and marginal printing quality.
Hiding the invisible cusp of each swallowtail produces a different line pattern, 2(13). Note how the longer of Stillwell's contours in 2(21) continues beyond the cusp points, hinting at a shading scheme, 2(23). The convention works well for characteristic views of the Klein bottle 2(22), Boy surface 2(31), Morin surface 2(32) and Roman surface 2(33). You should "mold" these line drawings by shading with a pencil, "pushing back" the regions near the cusps as outlined by Stillwell's curls. TRIPRONG.
A Topological Picturebook by George K. Francis