The gnomon was an L-shaped movable sundial used for astronomical studies. It operated by resting on one leg so that the other pointed vertically upward. By measuring the length and direction of the sun's shadow, information about the time of day, season, latitude, obliquity of the ecliptic, etc. could be obtained. In particular, if the shadow falls directly on the horizontal leg at noon (when the shadow is shortest), that leg is pointing north. The gnomon was therefore a sort of calendar, compass, and clock combined into one simple and easy-to-construct instrument (Shanks 1993, p. 123) that has been termed "the Babylonian shadow clock" by Merzbach and Boyer (1991, p. 49).
The original of word "gnomon" is variously described as being related to the word for "knowing" (Merzbach and Boyer 1991, p. 49) or as deriving from the Greek word meaning carpenter's square (an L-shaped tool with its two sides at right angles; Joyce).
When drawn as a square grid of dots, successive square numbers are formed from the sequence 
, with each odd
number forming an L-shaped pattern resembling a gnomon with equal arm lengths
placed around two sides of the preceding square pattern. As a result, the term "gnomon"
came to be attached to the odd numbers themselves (Merzbach and Boyer 1991, p. 49);
i.e., gnomonic numbers.
Euclid used the term "gnomon" to describe the a geometric figure obtained by removing one quarter of a parallelogram. His
use of the word therefore does not require that the sides of a gnomon be at right
angles. In particular, Book II, Definition 2 states, "And in any parallelogrammic
area let any one whatever of the parallelograms about its diameter with the two complements
be called a gnomon" (Joyce, Densmore 2002, p. 37). Euclid denoted gnomons
by referring to arcs of circles around the inner gnomon vertex, so the gnomon illustrated
above was denoted 
(Joyce), though perhaps a clearer way to refer to it would be via the coordinates
of their vertices 
(or just 
).
