A gnomon ( /, / , from Greek γνώμων, gnōmōn, literally: "one that knows or examines" ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields.
A painted stick dating from 2300 BC that was excavated at the astronomical site of Taosi is the oldest gnomon known in China.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. The ancient Greek philosopher Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Ancient Greeks. The ancient Greek mathematician and astronomer 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.
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 mentions it 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. Albeit ist 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 sun dials on the other hand. It appears to be more appropriate to assume, that he generally refers to geometry, a science on which gnomons heavily rely upon. In those days, calculations were carried out geometrically which is in stark contrast to the algebraic methods in today's use. Thus, it seems that he indirectly refers to mathematics and geodesy.
Perforated gnomons projecting a pinhole image of the Sun were described in the Chinese Zhoubi Suanjing writings (1046 BCE—256 BC with material added until circa 220 AD).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 AD. 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.
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. 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.
Anaximander was a pre-Socratic Greek philosopher who lived in Miletus, a city of Ionia. He belonged to the Milesian school and learned the teachings of his master Thales. He succeeded Thales and became the second master of that school where he counted Anaximenes and, arguably, Pythagoras amongst his pupils.
Archaeoastronomy is the interdisciplinary or multidisciplinary study of how people in the past "have understood the phenomena in the sky, how they used these phenomena and what role the sky played in their cultures". Clive Ruggles argues it is misleading to consider archaeoastronomy to be the study of ancient astronomy, as modern astronomy is a scientific discipline, while archaeoastronomy considers symbolically rich cultural interpretations of phenomena in the sky by other cultures. It is often twinned with ethnoastronomy, the anthropological study of skywatching in contemporary societies. Archaeoastronomy is also closely associated with historical astronomy, the use of historical records of heavenly events to answer astronomical problems and the history of astronomy, which uses written records to evaluate past astronomical practice.
Thales of Miletus was a Greek mathematician, astronomer and pre-Socratic philosopher from Miletus in Ionia, Asia Minor. He was one of the Seven Sages of Greece. Many, most notably Aristotle, regarded him as the first philosopher in the Greek tradition, and he is otherwise historically recognized as the first individual in Western civilization known to have entertained and engaged in scientific philosophy.
A sundial is a device that tells the time of day when there is sunlight by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate and a gnomon, which casts a shadow onto the dial. As the Sun appears to move across the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude.
An armillary sphere is a model of objects in the sky, consisting of a spherical framework of rings, centred on Earth or the Sun, that represent lines of celestial longitude and latitude and other astronomically important features, such as the ecliptic. As such, it differs from a celestial globe, which is a smooth sphere whose principal purpose is to map the constellations. It was invented separately in ancient Greece and ancient China, with later use in the Islamic world and Medieval Europe.
The four cardinal directions, or cardinal points, are the directions north, east, south, and west, commonly denoted by their initials N, E, S, and W. East and west are perpendicular to north and south, with east being in the clockwise direction of rotation from north and west being directly opposite east. Points between the cardinal directions form the points of the compass.
The scaphe was a sundial said to have been invented by Aristarchus of Samos. There are no original works still in existence by Aristarchus, but the adjacent image is an image of what it might have looked like; only his would have been made of stone. It consisted of a hemispherical bowl which had a vertical gnomon placed inside it, with the top of the gnomon level with the edge of the bowl. Twelve gradations inscribed perpendicular to the hemisphere indicated the hour of the day.
Indian astronomy has a long history stretching from pre-historic to modern times. Some of the earliest roots of Indian astronomy can be dated to the period of Indus Valley Civilization or earlier. Astronomy later developed as a discipline of Vedanga or one of the "auxiliary disciplines" associated with the study of the Vedas, dating 1500 BCE or older. The oldest known text is the Vedanga Jyotisha, dated to 1400–1200 BCE.
Taosi is an archaeological site in Xiangfen County, Shanxi, China. Taosi is considered to be part of the late phase of the Longshan culture in southern Shanxi, also known as the Taosi phase.
Gnomonics is the study of the design, construction and use of sundials.
Kokino is a Bronze Age archaeological site in the Republic of North Macedonia, approximately 30 km from the town of Kumanovo, and about 6 km from the Serbian border, in the Staro Nagoričane Municipality. It is situated between about 1010 and 1030 m above sea level on the Tatićev Kamen summit and covers an area of about 90 by 50 meters, overlooking the eponymous hamlet of Kokino.
Greek astronomy is astronomy written in the Greek language in classical antiquity. Greek astronomy is understood to include the ancient Greek, Hellenistic, Greco-Roman, and Late Antiquity eras. It is not limited geographically to Greece or to ethnic Greeks, as the Greek language had become the language of scholarship throughout the Hellenistic world following the conquests of Alexander. This phase of Greek astronomy is also known as Hellenistic astronomy, while the pre-Hellenistic phase is known as Classical Greek astronomy. During the Hellenistic and Roman periods, much of the Greek and non-Greek astronomers working in the Greek tradition studied at the Musaeum and the Library of Alexandria in Ptolemaic Egypt.
The Zhoubi Suanjing is one of the oldest Chinese mathematical texts. "Zhou" refers to the ancient Zhou dynasty ; "Bi" means thigh and according to the book, it refers to the gnomon of the sundial. The book is dedicated to astronomical observation and calculation. "Suan Jing" or "classic of arithmetics" were appended in later time to honor the achievement of the book in mathematics.
Gaocheng Astronomical Observatory, also known as the Dengfeng Observatory, is a World Heritage Site in Duke of Zhou's shrine, Gaocheng Town, near Dengfeng in Henan province, China. This site has a long tradition of astronomical observations, from the time of the Western Zhou up to the early Yuan dynasty. There is also a gnomon used for the Da Yan calendar in 729 AD and the great observatory of the Yuan Dynasty.
Carahunge, also called Zorats Karer, Karahunj, Qarahunj and Carenish, is a prehistoric archaeological site near the town of Sisian in the Syunik Province of Armenia. It is also often referred to in international tourist lore as the "Armenian Stonehenge".
Paris M. Herouni was an Armenian physicist and engineer. He was a member of the Armenian National Academy of Sciences in the fields of radio-physics, radio-engineering, and radio-astronomy and the head of the Antenna Systems chair, which he founded, at the National Polytechnic University of Armenia and Radio Physics Research Institute (RRI). In 1986, he was awarded the USSR State Prize.
The ancient Egyptians were one of the first cultures to widely divide days into generally agreed-upon equal parts, using early timekeeping devices such as sundials, shadow clocks, and merkhets . Obelisks are used by reading the shadow that it makes. The citizens could divide the day into two parts, and then into smaller hours.
The shadow square, also known as an altitude scale, was an instrument used to determine the linear height of an object, in conjunction with the alidade, for angular observations. It was invented by Muhammad ibn Mūsā al-Khwārizmī in 9th-century Baghdad. Shadow squares are often found on the backs of astrolabes.
A sundial is a device that indicates time by using a light spot or shadow cast by the position of the Sun on a reference scale. As the Earth turns on its polar axis, the sun appears to cross the sky from east to west, rising at sun-rise from beneath the horizon to a zenith at mid-day and falling again behind the horizon at sunset. Both the azimuth (direction) and the altitude (height) can be used to create time measuring devices. Sundials have been invented independently in every major culture and became more accurate and sophisticated as the culture developed.
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