gnomon

gnomon, device originally meant as an instrument for calculating the time. In its most simple form it seems to have been a rod placed vertically on a plane surface, later upon the surface of a hemisphere.

The term gnomon was at one time substantially synonymous with a vertical line. From this early use it came to represent a figure like a carpenter’s square but usually with equal arms. Seeking to relate numbers to geometric forms, early Greek mathematicians imagined squares as built up of gnomons added to unity. For example, they saw that 1 + 3, 1 + 3 + 5, 1 + 3 + 5 + 7, and so on, are squares and that the odd numbers in a figure like this were related to the geometric gnomon. Such numbers were, therefore, themselves called gnomons. The early idea of a geometric gnomon was extended by Euclid (c. 300 bce) to include a figure consisting of two parallelograms forming an L. Some four centuries later Heron of Alexandria extended the term to mean that which, added to any number or figure, makes the whole similar to that to which it is added. This usage is also found in the writings of Theon of Smyrna in connection with figurate numbers. For example, the pentagonal numbers are 1 + 4, 1 + 4 + 7, 1 + 4 + 7 + 10; the gnomons in this case are 4, 7, 10, etc. They constitute an arithmetical series with a common difference of 3.

The sundial with a gnomon as a vertical needle is said to have been introduced into Greece by Anaximander in 575 bce.