Gnomon

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For other uses, see Gnomon (disambiguation).
The gnomon is the triangular blade in this sundial

A gnomon ([ˈnoʊmɒn], from Greek γνώμων, gnōmōn, literally: "one that knows or examines"[1][2]) is the part of a sundial that casts a shadow. The term has come to be used for a variety of purposes in mathematics and other fields.

History[edit]

A gnomon as in Euclid book II

A painted stick from 2300 BCE found in China is the oldest known gnomon.[3] Anaximander (610–546 BC) is credited with introducing this Babylonian instrument to the Greeks.[4] Oenopides used the phrase drawn gnomon-wise to describe a line drawn perpendicular to another.[5] 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.

Hero of Alexandria defined a gnomon as that which, when added 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.

Pinhole gnomons[edit]

The gnomon projection on the floor of the Santa Maria del Fiore Cathedral during the solstice on 21.06.2012

Perforated gnomons projecting a pinhole image of the sun were described in the Chinese Zhoubi Suanjing writings (1046 BCE—256 BCE with material added until circa 220 CE).[6] 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 CE.[7] 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.[8]

Orientation[edit]

Gnomon situated on the wall of a building facing Tiradentes Square, Curitiba, Brazil
A gnomon in computer graphics

In the northern hemisphere, the shadow-casting edge of a sundial gnomon is normally oriented so that it points north and is parallel to the rotation axis of the Earth. That is, it is inclined to the horizontal 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 a degree 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.

In popular culture[edit]

  • In the book The Tower at the End of the World by Brad Strickland, a giant tower and thin stairs turn out to be the gnomon of a giant sundial. The island the tower is found on is often called "Gnomon Island".

External links[edit]

Media related to Gnomons at Wikimedia Commons

Footnotes[edit]

  1. ^ γνώμων. Liddell, Henry George; Scott, Robert; A Greek–English Lexicon at the Perseus Project.
  2. ^ "gnomon". Online Etymology Dictionary. 
  3. ^ http://adsabs.harvard.edu/abs/2015hae..book.2095L
  4. ^ 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".
  5. ^ Heath (1981) pp. 78-79
  6. ^ The Asiatic Review. 1969. 
  7. ^ Rohr, René R.J. (2012). Sundials: History, Theory, and Practice. 
  8. ^ Suter, Rufus (1964). "Leonardo Ximenes and the Gnomon at the Cathedral of Florence". 
  9. ^ Sharan Newman, The Real History Behind The Da Vinci Code (Berkley Publishing Group, 2005, p. 268).

References[edit]