A gnomon (/ˈnoʊˌmɒn,-mən/; from Ancient Greekγνώμων (gnṓmōn) 'one that knows or examines')[1][2] is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields.
The gnomon is the triangular blade in this sundial.
invariant snail in the subtraction of gnomons (Hero's definition)[3]
A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the oldest gnomon known in China.[4] The gnomon was widely used in ancient China from the second century 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.[5][6] The ancient Greek philosopher Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Ancient Greeks.[7] The ancient Greek mathematician and astronomer Oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another.[8] 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 similarparallelogram from a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successive figurate numbers, including square and triangular numbers.
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.
Vitruvius
Vitruvius mentions the gnomon as "gnonomice" in the first sentence of chapter 3 in volume 1 of his famous book De Architectura. That Latin term "gnonomice" leaves room for interpretation. Despite its similarity to "γνωμονικός" (or its feminine form "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 stark contrast to the algebraic methods in use today. Thus, it seems that he indirectly refers to mathematics and geodesy.
Pinhole gnomons
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 (11th century BC) but surviving only in forms dating to the Eastern Han (3rd century).[9] In the Middle East and Europe, it was separately credited to the Egyptian astronomer and mathematician Ibn Yunus around AD 1000.[10] 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.[11]
Orientation
Gnomon situated on the wall of a building facing Tiradentes Square, Curitiba, Brazil
In the Northern Hemisphere, the shadow-casting edge of a sundial gnomon is normally oriented so that it points due northward and is parallel to the rotational axis of Earth. That is, it is 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. 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.
In computer graphics
A three-dimensional gnomon is commonly used in 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. NASA astronauts used a gnomon as a photographic tool to indicate local vertical and to display a color chart when they were working on the Moon's surface.
^Pietrocola, Giorgio (2005). "gnomon collection". Maecla. Retrieved 2020-06-28.
^Li, Geng (2014). "Gnomons in Ancient China". In Ruggles, Clive (ed.). Handbook of Archaeoastronomy and Ethnoastronomy. Springer New York (published July 7, 2014). p. 2095. ISBN978-1-4614-6141-8.
^Li, Geng (9 July 2017). "Gnomons in Ancient China". Handbook of Archaeoastronomy and Ethnoastronomy. New York, NY: Springer. pp. 2095–2104. Bibcode:2015hae..book.2095L. doi:10.1007/978-1-4614-6141-8_219. ISBN978-1-4614-6140-1 – via NASA ADS.
^Li, Geng (2014). "Gnomons in Ancient China". In Ruggles, Clive (ed.). Handbook of Archaeoastronomy and Ethnoastronomy. Springer New York (published July 7, 2014). pp. 2095–2096. ISBN978-1-4614-6141-8.
Waugh, Albert E., Sundials: Their Theory and Construction, Dover Publications, Inc., 1973, ISBN0-486-22947-5.
Wikimedia Commons has media related to Gnomons.
Look up gnomon in Wiktionary, the free dictionary.
January 07, 2023
gnomon, other, uses, disambiguation, gnomon, from, ancient, greek, γνώμων, gnṓmōn, that, knows, examines, part, sundial, that, casts, shadow, term, used, variety, purposes, mathematics, other, fields, gnomon, triangular, blade, this, sundial, contents, history. For other uses see Gnomon disambiguation A gnomon ˈ n oʊ ˌ m ɒ n m e n from Ancient Greek gnwmwn gnṓmōn one that knows or examines 1 2 is the part of a sundial that casts a shadow The term is used for a variety of purposes in mathematics and other fields The gnomon is the triangular blade in this sundial Contents 1 History 1 1 Definition of Hero of Alexandria 1 2 Vitruvius 2 Pinhole gnomons 3 Orientation 4 In computer graphics 5 In popular culture 6 See also 7 Footnotes 8 ReferencesHistory Edit A gnomon as in Euclid book II invariant snail in the subtraction of gnomons Hero s definition 3 A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the oldest gnomon known in China 4 The gnomon was widely used in ancient China from the second century 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 5 6 The ancient Greek philosopher Anaximander 610 546 BC is credited with introducing this Babylonian instrument to the Ancient Greeks 7 The ancient Greek mathematician and astronomer Oenopides used the phrase drawn gnomon wise to describe a line drawn perpendicular to another 8 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 Definition of Hero of Alexandria Edit 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 Edit Vitruvius mentions the gnomon as gnonomice in the first sentence of chapter 3 in volume 1 of his famous book De Architectura That Latin term gnonomice leaves room for interpretation Despite its similarity to gnwmonikos or its feminine form gnwmonikh 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 stark contrast to the algebraic methods in use today Thus it seems that he indirectly refers to mathematics and geodesy Pinhole gnomons Edit 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 11th century BC but surviving only in forms dating to the Eastern Han 3rd century 9 In the Middle East and Europe it was separately credited to the Egyptian astronomer and mathematician Ibn Yunus around AD 1000 10 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 11 Orientation Edit Gnomon situated on the wall of a building facing Tiradentes Square Curitiba Brazil A gnomon in computer graphics Further information Polar alignment In the Northern Hemisphere the shadow casting edge of a sundial gnomon is normally oriented so that it points due northward and is parallel to the rotational axis of Earth That is it is 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 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 In computer graphics EditA three dimensional gnomon is commonly used in 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 NASA astronauts used a gnomon as a photographic tool to indicate local vertical and to display a color chart when they were working on the Moon s surface In popular culture EditThe Gnomon of Saint Sulpice inside the church of Saint Sulpice in Paris France built to assist in determining the date of Easter was fictionalized as a Rose Line in the novel The Da Vinci Code 12 See also EditMarsDial Gnomon sent to planet Mars Footnotes Edit gnwmwn Liddell Henry George Scott Robert A Greek English Lexicon at the Perseus Project Harper Douglas gnomon Online Etymology Dictionary Pietrocola Giorgio 2005 gnomon collection Maecla Retrieved 2020 06 28 Li Geng 2014 Gnomons in Ancient China In Ruggles Clive ed Handbook of Archaeoastronomy and Ethnoastronomy Springer New York published July 7 2014 p 2095 ISBN 978 1 4614 6141 8 Li Geng 9 July 2017 Gnomons in Ancient China Handbook of Archaeoastronomy and Ethnoastronomy New York NY Springer pp 2095 2104 Bibcode 2015hae book 2095L doi 10 1007 978 1 4614 6141 8 219 ISBN 978 1 4614 6140 1 via NASA ADS Li Geng 2014 Gnomons in Ancient China In Ruggles Clive ed Handbook of Archaeoastronomy and Ethnoastronomy Springer New York published July 7 2014 pp 2095 2096 ISBN 978 1 4614 6141 8 The 2nd century Chinese book Nine Chapters on the Mathematical Art claims gnomons were used by the Duke of Zhou 11th century BC Laertius Diogenes Life of Anaximander Archived 2017 04 26 at the Wayback Machine Heath 1981 pp 78 79 The Asiatic Review 1969 Rohr Rene R J 2012 Sundials History Theory and Practice ISBN 9780486151700 Suter Rufus 1964 Leonardo Ximenes and the Gnomon at the Cathedral of Florence JSTOR 227759 Sharan Newman The Real History Behind The Da Vinci Code Berkley Publishing Group 2005 p 268 References EditGazale Midhat J Gnomons from Pharaohs to Fractals Princeton University Press Princeton 1999 ISBN 0 691 00514 1 Heath Thomas Little 1981 A History of Greek Mathematics Dover publications ISBN 9780486240732 first published 1921 Laertius Diogenes The Lives and Opinions of Eminent Philosophers trans C D Yonge London Henry G Bohn 1853 Mayall R Newton 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 Wikimedia Commons has media related to Gnomons Look up gnomon in Wiktionary the free dictionary Retrieved from https en wikipedia org w index php title Gnomon amp oldid 1130315302, wikipedia, wiki, book, books, library,
