Gnomon

The gnomon (Greek gnomon ( γνώμων ): the shadow pointer ) is a known even before the ancient astronomical instrument in the form of a vertically inserted into the bottom of the wooden rod. He served primarily as a gnomon for sundials. From there, the development went up to the occasional use of an obelisk as a gnomon. The sun shadow of its peak is observed to determine astronomical sizes.

The description of the projection of the sun by Nodus ( shadow -throwing point or pinhole ) is an object of the gnomonic, the doctrine of the sundial.

Application of the gnomon

In ancient times, the gnomon to determine the latitude of a place, the north direction of the equinoxes ( the equinoxes ), the solstices ( solstices ) and the ecliptic was used. For this, the gnomon was usually as simple bar (usually of wood ), rarely executed as Obelisk or as a special building. Allen gnomons together is the special design of the tip: For whose shadow will be sharp and so is accurate to read, it is pointed formed or provided with a small ball ( Nodus ). A variant with durchlochter disc at the top to produce a light spot is already known from Ancient China.

After the gnomon a central projection of the celestial sphere is called on a plane gnomonic projection. With it, the shadow of the nodus point can be calculated for each location and the sun and be constructed on the dial a two-dimensional curve network. On the lines, all of which are conic sections, can be read off both the day and the season.

History of the gnomon

In the beginning, probably only the length of the shadow from the gnomon was, the man could be yourself, read and interpreted. An astronomical instrument with gnomon may have been a wise lunch. This was measured using a mounted on the floor in meridian direction scale the midday shadow length.

About this very early step in different cultures (including Ancient China ), little is known. On a Babylonian clay tablet dating from about 2300 BC, the shadow of a gnomon lengths are given at different times.

Among the Chinese, the gnomon to have been an important astronomical instrument since earliest times. In one of the oldest books on mathematics, the Zhoubi suanjing, is in the eleventh century BC living Duke of Zhou, Zhou Gong Dan, his court officials Shang Gao mathematical tasks, including the conversion of the length of the shadow of the gnomon in the sun. Chinese astronomers have used the gnomon at least until the early Yuan Dynasty and developed further (see Gaocheng Observatory ). According to Herodotus (ca. 485-425 BC), the Greeks have adopted the principle of the gnomon by the Babylonians.

Eventually this became a full-fledged Sundial By equipping a lunch Weiser with an hourly scale. Texts and finds of sundials there from ancient Egypt. However, the ancient Egyptian shadow clock and a wall sundial simultaneously used were not suitable, the daylight hours display correctly in every season. Both watches used a horizontal gnomon, an edge a, a bar the other. This sundials type was again used in the Middle Ages (see kanoniale sundial ). From sundials from the fourth century BC in Greece reported Vitruvius ( see main article sundial ).

Eratosthenes of Cyrene turned 225 BC measurements with gnomons to, from which he calculated the circumference of the earth to about 252,000 stadia. He noted that the meridian altitude of the sun in Alexandria different from that in Syene ( Aswan ) by about 7.2 °. This angle and the known distance of about 5,000 stages between the two cities rather lying on the same longitude, he received a result that is the actual value of 40 024 kilometers ( about 240,000 stadia ) very close

Mathematical foundations for the use of the gnomon

Projection of the sun on a dial

The image of the sun through a point is a central projection. It is because of their development in the context of Gnomonik also called Gnomonic projection. The projection center is located in the center of the sky ( equal to the center of the earth). The simplification to move the center of projection on the earth's surface in the tip of a gnomon, is permitted for the task, since the sun is so far away that the parallax is negligible due to the Earth's radius. The figure shows a projection Gnomonic with Gnomon -true and the horizontal projection, the surface of the dial, a sundial, for example (horizontal sundial ). All great circles as the celestial equator and the meridian passing through the site are mapped in the gnomonic projection as straight lines. Since the hour circles of the sun are too great circles, they are imaged on the face than a pencil of lines ( h line), which converges in the intersection point of the polar axis on the screen. The tropics - are represented as hyperbolic. Thus it is seen that the shadow of the Gnomonspitze Equinox ( equinox ) from sunrise to sunset runs on a straight line and it intersects the straight hours. At the solstice, he moves on a hyperbola and intersects over the day also the hour lines.

Figure shows that the shadow of the plumb Gnomonstabes intersects the straight hours. Would the bar placed on the screen in the intersection point of the polar axis and pointing towards the sky pole, his shadow would like the hours straight line from the intersection point of run radially outwards. Thus, each point of the shadow would show the time correctly. Such a bar called gnomon. He is the sun from one-dimensional.

Antique measurements with the Gnomon

For the geographical localization length and width of a location must be specified. Reference point, the width is the equator. For the length of a reference point must be agreed: Today is the meridian of the observatory of Greenwich. In ancient times, one has chosen a well-known city of Alexandria, for example, as a reference point. From the latter, then the length of which could be determined by determining the direction and distance to the next place. This had to be measured in practice by splitting the track into individual specific direction and longitudinal sections ( traversing ).

Determination of the north and the latitude

To determine the north direction, several circles are drawn around the gnomon ( see Fig.) The sun intersects each circle once in the morning ( V) and once in the afternoon (N). The north direction - or the lunch line - is the bisector of the respective pairs of legs to V and N. The process can be shown to increase accuracy on different days or as in fig with various circles to be repeated. Same procedure, just closer to the meridian, is known in astrometry as Zirkummeridian method.

At the equinox the sun is in the equatorial plane. Then the lunch ( maximum position of the sun ) corresponds to measured ratio shadow length: rod length to the tangent of the latitude. In the literature of antiquity, the width was therefore specified as the equinoctial shadow ratio. The literature reports for

• Alexandria 3 to 5 ( Strabo II, 5, 38)
• Massila (Marseille ) ( Pytheas ) and Byzantion ( Hipparchus ) 120 41.8
• Rome 8 to 9 ( Vitruvius )
• Rhodes 5 to 7 ( Vitruvius )
• Taranto 9 to 11 ( Vitruvius )
• Athens 3 to 4 ( Vitruvius )

The Äquinoktialschatten are, however, difficult to determine. However, the corresponding shadow line lies on the bisector of the two Solstitienschatten. These are very well observable. Thus, the latitude will be winter and averaged from the two observations on the summer solstice.

Since the sun has a relatively large expansion as a light source ( ½ degrees), it does not cast a sharply defined shadows, which complicates the accurate reading. Therefore, a disk with a pinhole or a sphere in order to improve the accuracy of reading has been attached to the Gnomonspitze. The ball still found today on our steeples - but is this tower pommel with cross predominantly a symbol of globe and redemption, which often also serves as a document capsule.

Current research on ancient astro- geodetic measuring instruments justify the assumption that, even with the Greeks for this survey specially made complex measuring instruments were used on the basis of such an improved gnomon, which were constructed in their functional expression similar to that of Fig.

Term use in geometry

In mathematics, especially in the planar geometry, the term refers to the gnomon residual surface between two similar characters. This design was known in Greco- Hellenistic mathematics and described a geometrical figure that results when any similar and similarly situated as cuts of a parallelogram that has a corner with the original parallelogram together.

Gnomon metaphor in the literature on biblical exegesis

In theological literature, the term gnomon found in a famous work of biblical exegesis use in a figurative sense as a metaphor.

In 1742, the Pietist theologian Johann Albrecht Bengel ( 1687-1752 ) published the Latin Gnomon Novi Testamenti, should show an accuracy tried to comment to the New Testament, which unlock the true meaning of the text. This emblematic ( figuratively ) oriented choice of the term "pointer" has boy on his interest in his view chronologically comprehensible, predictable story of salvation towards which it considers to be through him decrypted statements of John's apocalypse should accordingly run like clockwork. Bengel's son Philipp David Burk also used the term in his exegesis of the Psalms.