Gnomon

A gnomon (ˈnoʊˌmɒn,_-mən; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields. A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the oldest gnomon known in China. The gnomon was widely used in ancient China from the second millennium BC onward in order to determine the changes in seasons, orientation, and geographical latitude. The ancient Chinese used shadow measurements for creating calendars that are mentioned in several ancient texts. According to the collection of Zhou Chinese poetic anthologies Classic of Poetry, one of the distant ancestors of King Wen of the Zhou dynasty used to measure gnomon shadow lengths to determine the orientation around the 14th century BC. The ancient Greek philosopher Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Ancient Greeks. The ancient Greek mathematician and astronomer Oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another. Later, the term was used for an L-shaped instrument like a steel square used to draw right angles. This shape may explain its use to describe a shape formed by cutting a smaller square from a larger one. Euclid extended the term to the plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive figurate numbers, including square and triangular numbers. The ancient Greek mathematician and engineer Hero of Alexandria defined a gnomon as that which, when added or subtracted to an entity (number or shape), makes a new entity similar to the starting entity. In this sense Theon of Smyrna used it to describe a number which added to a polygonal number produces the next one of the same type. The most common use in this sense is an odd integer especially when seen as a figurate number between square numbers. Vitruvius mentions the gnomon as "gnonomice" in the first sentence of chapter 3 in volume 1 of his book De Architectura.