Gnomon

A gnomon ([ˈnoʊmɒn], from Greek γνώμων, gnōmōn, literally: "one that knows or examines") is the part of a sundial that casts a shadow. The term has come to be used for a variety of purposes in mathematics and other fields.

A painted stick from 2300 BCE found in China is the oldest known gnomon.Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Greeks.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.

Hero of Alexandria defined a gnomon as that which, when added 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.

Perforated gnomons projecting a pinhole image of the sun were described in the Chinese Zhoubi Suanjing writings (1046 BCE—256 BCE with material added until circa 220 CE). The location of the bright circle can be measured to tell the time of day and year. In Arab and European cultures its invention was much later attributed to Egyptian astronomer and mathematician Ibn Yunus around 1000 CE. Italian astronomer, mathematician and cosmographer Paolo Toscanelli is associated with the 1475 placement of a bronze plate with a round hole in the dome of the Cathedral of Santa Maria del Fiore in Florence to project an image of the sun on the cathedral's floor. With markings on the floor it tells the exact time of each midday (reportedly to within half a second) as well as the date of the summer solstice. Italian mathematician, engineer, astronomer and geographer Leonardo Ximenes reconstructed the gnomon according to his new measurements in 1756.

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