Editing Gnomon (section)

==History==
{{Moresources|section|date=August 2023}}
[[File:gnomon.svg|thumb|A gnomon as in Euclid book II]]
[[File:Chiocciola30s9m.gif|thumb|Invariant snail in the subtraction of gnomons (Hero's definition)<ref>{{cite web |url=http://www.maecla.it/tartapelago/museo/gnomoni/index.htm |title=gnomon collection |last=Pietrocola |first=Giorgio |date=2005 |website=Maecla |access-date=2020-06-28 }}</ref>]]
A painted stick dating from 2300 BC that was excavated at the archeological site of [[Taosi]] is the oldest gnomon known in China.<ref>{{Cite book|chapter=Gnomons in Ancient China|last=Li|first=Geng|publisher=Springer New York|year=2014|isbn=978-1-4614-6141-8|editor-last=Ruggles|editor-first=Clive|publication-date=July 7, 2014|page=2095|title=Handbook of Archaeoastronomy and Ethnoastronomy}}</ref> 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.{{fact|date=August 2023}} 

According to the collection of Zhou Chinese poetic anthologies ''[[Classic of Poetry]]'', one of the distant ancestors of [[King Wen of Zhou|King Wen of the Zhou dynasty]] used to measure gnomon shadow lengths to determine the orientation around the 14th century BC.<ref>{{cite book|bibcode=2015hae..book.2095L|title=Handbook of Archaeoastronomy and Ethnoastronomy|first=Geng|last=Li|chapter=Gnomons in Ancient China |date=9 July 2017|pages=2095–2104|publisher=Springer |location=New York, NY |via=NASA ADS|doi=10.1007/978-1-4614-6141-8_219|isbn=978-1-4614-6140-1 }}</ref><ref>{{Cite book|chapter=Gnomons in Ancient China|last=Li|first=Geng|publisher=Springer New York|year=2014|isbn=978-1-4614-6141-8|editor-last=Ruggles|editor-first=Clive|publication-date=July 7, 2014|pages=2095–2096|title=Handbook of Archaeoastronomy and Ethnoastronomy}}</ref>
The ancient Greek philosopher [[Anaximander#Gnomon|Anaximander]] (610–546 BC) is credited with introducing this [[Babylonia]]n instrument to the Ancient Greeks.<ref>The 2nd-century Chinese book ''[[Nine Chapters on the Mathematical Art]]'' claims gnomons were used by the [[Duke of Zhou]] (11th century BC). [http://classicpersuasion.org/pw/diogenes/dlanaximander.htm Laërtius, Diogenes. "Life of Anaximander".] {{Webarchive|url=https://web.archive.org/web/20170426191654/http://classicpersuasion.org/pw/diogenes/dlanaximander.htm |date=2017-04-26 }}</ref> 

The ancient Greek mathematician and astronomer [[Oenopides#Geometry|Oenopides]] used the phrase ''drawn gnomon-wise'' to describe a line drawn perpendicular to another.<ref name="Heath_78-79">Heath (1981) pp. 78-79</ref> 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's Elements|Euclid]] extended the term to the plane figure formed by removing a [[similarity (geometry)|similar]] [[parallelogram]] from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive [[Figurate number#Gnomon|figurate numbers]], including square and triangular numbers.{{fact|date=August 2023}} 

=== Definition of Hero of Alexandria ===
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]].{{fact|date=August 2023}} 

===Vitruvius===
[[Marcus Vitruvius Pollio|Vitruvius]] mentions the gnomon as "{{lang|la|gnonomice}}" in the first sentence of chapter 3 in volume 1 of his book ''[[Vitruvius#De architectura|De Architectura]]''. That Latin term "{{lang|la|gnonomice}}" leaves room for interpretation. Despite its similarity to "{{lang|grc|γνωμονικός}}" (or its feminine form "{{lang|grc|γνωμονική}}"), it appears unlikely that Vitruvius refers to judgement on the one hand or to the design of sundials on the other. It appears to be more appropriate to assume that he refers to geometry, a science upon which gnomons rely heavily. In those days, calculations were carried out geometrically, in contrast to the algebraic methods in use today. Thus, it seems that he indirectly refers to mathematics and [[geodesy]].{{fact|date=August 2023}}