Gnomon

Agnomon(/ˈnoʊˌmɒn,-mən/;fromAncient Greekγνώμων(gnṓmōn)'one that knows or examines')^[1]^[2]is the part of asundialthat casts ashadow.The term is used for a variety of purposes in mathematics and other fields.

History[edit]

Invariant snail in the subtraction of gnomons (Hero's definition)^[3]

A painted stick dating from 2300 BC that was excavated at the archeological site ofTaosiis the oldest gnomon known in China.^[4]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.^{[citation needed]}

According to the collection of Zhou Chinese poetic anthologiesClassic of Poetry,one of the distant ancestors ofKing Wen of the Zhou dynastyused to measure gnomon shadow lengths to determine the orientation around the 14th century BC.^[5]^[6] The ancient Greek philosopherAnaximander(610–546 BC) is credited with introducing thisBabylonianinstrument to the Ancient Greeks.^[7]

The ancient Greek mathematician and astronomerOenopidesused the phrasedrawn gnomon-wiseto describe a line drawn perpendicular to another.^[8]Later, the term was used for anL-shaped instrument like asteel squareused to draw right angles. This shape may explain its use to describe a shape formed by cutting a smaller square from a larger one.Euclidextended the term to the plane figure formed by removing asimilar parallelogramfrom a corner of a larger parallelogram. Indeed, the gnomon is the increment between two successivefigurate numbers,including square and triangular numbers.^{[citation needed]}

Definition of Hero of Alexandria[edit]

The ancient Greek mathematician and engineerHero of Alexandriadefined 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 senseTheon of Smyrnaused it to describe a number which added to apolygonal numberproduces the next one of the same type. The most common use in this sense is an odd integer especially when seen as afigurate numberbetweensquare numbers.^{[citation needed]}

Vitruvius[edit]

Vitruviusmentions the gnomon as "gnonomice"in the first sentence of chapter 3 in volume 1 of his bookDe 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 andgeodesy.^{[citation needed]}

Pinhole gnomons[edit]

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 ChineseZhoubi Suanjing,possibly dating as early as the earlyZhou(11th century BC) but surviving only in forms dating to theEastern Han(3rd century).^[9]

In the Middle East and Europe, it was separately credited to the Egyptian astronomer and mathematicianIbn Yunusaround AD 1000.^[10]The Italian astronomer, mathematician and cosmographerPaolo Toscanelliis 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 geographerLeonardo Ximenesreconstructed the gnomon according to his new measurements in 1756.^[11]

Orientation[edit]

In theNorthern Hemisphere,the shadow-casting edge of a sundial gnomon is normally oriented so that it points duenorthwardand isparallelto the rotational axis ofEarth.That is, it isinclinedto the northern horizon at ananglethat equals thelatitudeof the sundial's location. At present, such a gnomon should thus point almost precisely atPolaris,as this is within 1° of the northcelestial pole.

On some sundials, the gnomon is vertical. These were usually used in former times for observing thealtitudeof theSun,especially when on themeridian.

style[edit]

Thestyleis 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[edit]

Gnomons have been used in space missions to the Moon and Mars. The gnomon used by theApolloastronauts 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.^[12]MarsDialshave been used onMars Exploration Rovers.

In computer graphics[edit]

A three-dimensional gnomon is commonly used inCADandcomputer graphicsas an aid to positioning objects in thevirtual world.By convention, thex-axis direction is colored red, they-axis green and thez-axis blue.

In popular culture[edit]

TheGnomon of Saint-Sulpiceinside the Parisian church,Église Saint-Sulpice,built to assist in determining the date ofEaster,was fictionalized as a "Rose Line"in the novelThe Da Vinci Code.^[13]

Footnotes[edit]

^γνώμων.Liddell, Henry George;Scott, Robert;A Greek–English Lexiconat thePerseus Project.
^Harper, Douglas."gnomon".Online Etymology Dictionary.
^Pietrocola, Giorgio (2005)."gnomon collection".Maecla.Retrieved2020-06-28.
^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 bookNine Chapters on the Mathematical Artclaims gnomons were used by theDuke of Zhou(11th century BC).Laërtius, Diogenes. "Life of Anaximander".Archived2017-04-26 at theWayback Machine
^Heath (1981) pp. 78-79
^The Asiatic Review.1969.
^Rohr, René 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.
^"Gnomon, Lunar, Apollo".The Smithsonian Institution, National Air and Space Museum.Retrieved6 February2024.
^Sharan Newman,The Real History Behind The Da Vinci Code(Berkley Publishing Group, 2005, p. 268).

References[edit]

Gazalé, 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).
Laërtius, 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.

[1] γνώμων.Liddell, Henry George;Scott, Robert;A Greek–English Lexiconat thePerseus Project.

[2] Harper, Douglas."gnomon".Online Etymology Dictionary.

[3] Pietrocola, Giorgio (2005)."gnomon collection".Maecla.Retrieved2020-06-28.

[4] 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.

[5] 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.

[6] 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.

[7] The 2nd-century Chinese bookNine Chapters on the Mathematical Artclaims gnomons were used by theDuke of Zhou(11th century BC).Laërtius, Diogenes. "Life of Anaximander".Archived2017-04-26 at theWayback Machine

[Heath_78-79-8] Heath (1981) pp. 78-79

[9] The Asiatic Review.1969.

[10] Rohr, René R.J. (2012).Sundials: History, Theory, and Practice.ISBN 9780486151700.

[11] Suter, Rufus (1964). "Leonardo Ximenes and the Gnomon at the Cathedral of Florence".JSTOR 227759.

[12] "Gnomon, Lunar, Apollo".The Smithsonian Institution, National Air and Space Museum.Retrieved6 February2024.

[13] Sharan Newman,The Real History Behind The Da Vinci Code(Berkley Publishing Group, 2005, p. 268).

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v t e Ancient Greek astronomy
Astronomers	Aglaonice Agrippa Anaximander Andronicus Apollonius Aratus Aristarchus Aristyllus Attalus Autolycus Bion Callippus Cleomedes Cleostratus Conon Eratosthenes Euctemon Eudoxus Geminus Heraclides Hicetas Hipparchus Hippocrates of Chios Hypsicles Menelaus Meton Oenopides Philip of Opus Philolaus Posidonius Ptolemy Pytheas Seleucus Sosigenes of Alexandria Sosigenes the Peripatetic Strabo Thales Theodosius Theon of Alexandria Theon of Smyrna Timocharis
Works	Almagest(Ptolemy) Catasterismi(Eratosthenes) On Sizes and Distances(Hipparchus) On the Sizes and Distances(Aristarchus) On the Heavens(Aristotle)
Instruments	Antikythera mechanism Armillary sphere Astrolabe Dioptra Equatorial ring Gnomon Mural instrument Triquetrum
Concepts	Callippic cycle Celestial spheres Circle of latitude Counter-Earth Deferent and epicycle Equant Geocentrism Heliocentrism Hipparchic cycle Inferior and superior planets Metonic cycle Octaeteris Solstice Spherical Earth Sublunary sphere Zodiac
Influences	Babylonian astronomy Egyptian astronomy
Influenced	Medieval European science Indian astronomy Medieval Islamic astronomy