*Adam M.
Costello*
## The AMC Logo

### Meaning and Usage

The AMC logo can appear in a two-dimensional form (above left), a
three-dimensional form (above center), or an approximated hand-drawn
form (e.g. above right). I created the logo to refer to myself, and to
indicate my ownership, authorship, or endorsement of objects and works
bearing the logo.

Therefore, unauthorized use of the AMC logo can constitute
impersonation, forgery, and fraud. When in doubt, get my permission.

### History

I first fashioned a crude precursor to the AMC logo in 7th grade
woodshop (late 1983 or early 1984). I refined the 2-D logo into its
final form in 9th grade (late 1985). I designed the 3-D logo during my
freshman year of college (late 1989). Because the model is so simple, I
was able to render the gray levels by hand.

### Properties

In the 2-D version, all eight strokes, including the diagonal ones,
are exactly one unit wide. Most of the vertices lie on unit lattice
points, and none of them need more than ^{1}/_{12} unit
resolution. The geometry is based on the 3-4-5 right triangle.

The 3-D version uses the same outline as the 2-D version, but adds
additional interior vertices, for which ^{1}/_{12}
unit resolution is still sufficient. The model has all the protruding
surfaces intersect the background plane at 45 degree angles, and the
light rays all perpendicular to the leftmost protruding surface, so
there are no shadows. I neglect the effect of light scattering off one
surface and hitting another. The gray levels turn out to be exactly 0%,
10%, 20%, 36%, 64%, sqrt(^{1}/_{2}) (approximately 71%),
80%, 90%, and 100%. But I usually tint the whole thing toward blue.