Editing Gnomon

{{Short description|Part of a sundial that casts a shadow}}
{{other uses}}
{{Moresources|date=August 2023}}
[[File:Sundial Taganrog.jpg|thumb|right|The gnomon is the [[triangular]] blade in this sundial.]]

A '''gnomon''' ({{IPAc-en|ˈ|n|oʊ|ˌ|m|ɒ|n|,_|-|m|ə|n}}; {{etymology|grc|''{{wikt-lang|grc|γνώμων}}'' ({{grc-transl|γνώμων}})|one that knows or examines}})<ref>{{LSJ|gnw/mwn|γνώμων|ref}}.</ref><ref>{{OEtymD|gnomon}}</ref> is the part of a [[sundial]] that casts a [[shadow]]. The term is used for a variety of purposes in mathematics and other fields, typically to measure directions, position, or time.

==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}}

==Pinhole gnomons==
[[File:Osservazione del solstizio 21.06.12, fi, 20.JPG|thumb|The gnomon projection on the floor of the Santa Maria del Fiore Cathedral during the solstice on 21 June 2012]]
Perforated gnomons projecting a pinhole image of the Sun whose location can be measured to tell the time of day and year were described in the Chinese ''[[Zhoubi Suanjing]]'', possibly dating as early as the early [[Zhou dynasty|Zhou]] (11th century BC) but surviving only in forms dating to the [[Eastern Han dynasty|Eastern Han]] (3rd century).<ref>{{cite book|url=https://books.google.com/books?id=CyssAQAAIAAJ&q=%22pierced+gnomon%22|title=The Asiatic Review|year=1969}}</ref> 

In the Middle East and Europe, it was separately credited to the Egyptian astronomer and mathematician [[Ibn Yunus]] around AD 1000.<ref>{{cite book|url=https://books.google.com/books?id=msaqctAH8OkC&q=perforated&pg=PA6|title=Sundials: History, Theory, and Practice|last=Rohr|first=René R.J.|year=2012|publisher=Courier Corporation |isbn=9780486151700}}</ref> The 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.<ref>{{cite news|first=Rufus|last=Suter|year=1964|title=Leonardo Ximenes and the Gnomon at the Cathedral of Florence|jstor=227759}}</ref>

==Orientation==
[[File:Gnomon normalized.jpg|thumb|right|Gnomon situated on the wall of a building facing Tiradentes Square, [[Curitiba]], Brazil]]
{{further|Polar alignment}}

In the [[Northern Hemisphere]], the shadow-casting edge of a sundial gnomon is normally oriented so that it points due [[true north|northward]] and is [[Parallel (geometry)|parallel]] to the rotational axis of [[Earth]]. That is, it is [[polar alignment|inclined]] to the northern horizon at an [[angle]] that equals the [[latitude]] of the sundial's location. At present, such a gnomon should thus point almost precisely at [[Polaris]], as this is within 1° of the north [[celestial pole]].

On some sundials, the gnomon is vertical. These were usually used in former times for observing the [[altitude]] of the [[Sun]], especially when on the [[meridian (geography)|meridian]].

=== Style ===
The ''style'' is the part of the gnomon that casts the shadow. This can change as the Sun moves. For example, the upper west edge of the gnomon might be the style in the morning and the upper east edge might be the style in the afternoon.

==Modern uses==
Gnomons have been used in space missions to the Moon and Mars. The gnomon used by the [[Apollo program|Apollo]] astronauts was a gimballed stadia rod mounted on a tripod. While the rod's shadow indicated the direction of the Sun, the grayscale paints of varying reflectivity and the red, green and blue patches facilitated proper photography on the surface on the Moon.<ref>{{cite web | url = https://airandspace.si.edu/collection-objects/gnomon-lunar-apollo/nasm_A19810890000 | title = Gnomon, Lunar, Apollo | publisher = The Smithsonian Institution, National Air and Space Museum | access-date = 6 February 2024}}</ref> [[MarsDial]]s have been used on [[Mars Exploration Rover]]s.

==In computer graphics==
[[File:3DGraphicsGnomon.png|thumb|right|A gnomon in computer graphics]]
A three-dimensional gnomon is commonly used in [[computer-aided design|CAD]] and [[computer graphics]] as an aid to positioning objects in the [[virtual world]]. By convention, the ''x''-axis direction is colored red, the ''y''-axis green and the ''z''-axis blue. 

==In popular culture==
The [[Gnomon of Saint-Sulpice]] inside the Parisian church, [[Saint-Sulpice (Paris)|Église Saint-Sulpice]], built to assist in determining the date of [[Easter]], was fictionalized as a "[[Rose Line]]" in the novel ''[[The Da Vinci Code]]''.<ref>[[Sharan Newman]], ''The Real History Behind The Da Vinci Code'' (Berkley Publishing Group, 2005, p. 268).</ref>

==Footnotes==
{{reflist}}

==References==
*[[Midhat J. Gazalé|Gazalé, Midhat J.]] ''Gnomons, from Pharaohs to Fractals'', Princeton University Press, Princeton, 1999. {{ISBN|0-691-00514-1}}.
*{{Citation|first=Thomas Little|last=Heath|author-link= T. L. Heath|title=A History of Greek Mathematics
|publisher=Dover publications|year=1981|isbn=9780486240732}} (first published 1921).
*[[Diogenes Laërtius|Laërtius, Diogenes]], ''The Lives and Opinions of Eminent Philosophers'', trans. C.D. Yonge. London: Henry G. Bohn, 1853.
*Mayall, R. Newton; [[Margaret W. Mayall|Mayall, Margaret W.]], ''Sundials: Their Construction and Use'', Dover Publications, Inc., 1994, {{ISBN|0-486-41146-X}}
*Waugh, Albert E., ''Sundials: Their Theory and Construction'', Dover Publications, Inc., 1973, {{ISBN|0-486-22947-5}}.

{{Commons category|Gnomons}}
{{Wiktionary}}
{{Greek astronomy}}

[[Category:Ancient Greek astronomy]]
[[Category:Astronomical instruments]]
[[Category:Chinese inventions]]
[[Category:Greek inventions]]
[[Category:Hellenistic engineering]]
[[Category:Sundials]]