header Notes Collection

10 Mark 1993, Germany

in Krause book Number: 38с
Years of issue: 01.10.1993
Edition: --
Signatures: Bundesbank Präsident: Hans Tietmeyer (1993-1999), Vizepräsident: Johann Wilhelm Gaddum (1993-1998)
Serie: Fourth Series
Specimen of: 02.01.1989
Material: Cotton fiber
Size (mm): 130 х 65
Printer: Bundesdruckerei GmbH, Berlin

* All pictures marked magnify are increased partially by magnifying glass, the remaining open in full size by clicking on the image.

** The word "Specimen" is present only on some of electronic pictures, in accordance with banknote images publication rules of appropriate banks.

10 Mark 1993




The Copy of Portrait of Johann Carl Friedrich Gauss (by Gottlieb Biermann), Oil on wood, 1887.


10 Mark 1993

Johann Carl Friedrich Gauß Johann Carl Friedrich GaußThe engraving on banknote is made in mirror view after the copy of the portrait of Johann Carl Friedrich Gauss by German painter Gottlieb Biermann. Today the copy belongs to the University of GÖttingen, where Gauss war a professor, and original painting belongs to the Pulkovo observatory in Russia (for which it was ordered to Jensen).

Christian Albrecht Jensen (26 June 1792 – 13 July 1870) was a Danish portrait painter who was active during the Golden Age of Danish Painting in the first half of the XIX century. Painting more than 400 portraits over the course of his career, he depicted most of the leading figures of the Danish Golden Age, including the writer Hans Christian Andersen, the painter Christoffer Wilhelm Eckersberg, the sculptor Bertel Thorvaldsen, the physicist Hans Christian Ørsted and the theologian N. F. S. Grundtvig.

Although Jensen experienced considerable commercial success, he received little official appreciation from the artistic establishment of his day. In particular, the art historian and critic Niels Lauritz Høyen criticized his style, finding his paintings "unfinished".

Gottlieb Biermann (October 13, 1824 in Berlin - October 18, 1908) was a German portrait, genre and historical painter.

Johann Carl Friedrich Gauss (April 30, 1777 - February 23, 1855) was a German mathematician, astronomer, and physicist. Although Gauss made many contributions to science and to the understanding of the nature of electricity and magnetism, his true passion was mathematics. He referred to math as the "queen of sciences" and his influence on the field of mathematics was extraordinary. Gauss was, for example, the first mathematician to prove the fundamental theorem of algebra, and he proved it four different ways over the course of his lifetime. Gauss is widely celebrated as one of the greatest mathematicians in history.

Gauss was born in Brunswick, Germany into a working class family. His parents had little or no formal education, but their son went to school at age seven and immediately distinguished himself as a math prodigy who could compute complex mathematical solutions in his head. He learned German and Latin and received a scholarship from the Duke of Brunswick to attend an academy where he studied astronomy, math, and geometry.

On his own as a teenager he began to discover advanced mathematic principles, and in 1795 - at the age of 18 - Gauss became the first person to prove the Law of Quadratic Reciprocity, a theory of math that allows us to determine whether quadratic equations can be solved. The same year he entered Göttingen University.

While at the university, he made one of his most important discoveries. Using a ruler and compass, he constructed a regular 17-sided polygon or heptadecagon. While investigating the underlying theory behind this construction, Gauss revealed an important connection between algebra and geometrical shapes that successfully finalized work first begun by classical Greek mathematicians. Gauss thus changed the world of modern mathematics, while also adding to research begun by 16th century French philosopher and mathematician Renee Descartes.

After three years at the university, Gauss left without earning a diploma, and returned to Brunswick. Gauss completed a doctorate degree by submitting a thesis about algebra through the University of Helmstedt.

In 1801, Gauss wrote a paper that attempted to predict the orbital path of the dwarf planet or asteroid Ceres, which was newly discovered at the time. His conclusions were radically different from those submitted by other experts in the field of astronomy, but turned out to be the most accurate. To calculate the trajectory of Ceres, Gauss used the method of "least squares" which he had discovered but had not yet revealed to others. His least squares method was officially published in 1809, was widely embraced, and is used today by all branches of science to control and minimize the effect of measurement errors.

In 1805, Gauss married Johanna Ostoff, and in 1807 they moved to Gottingen from Brunswick, where he became the director of the Gottingen Observatory. Gauss was very happy at that time in his life. They had three children, but soon tragedy struck and left him grief stricken. In 1808, Gauss’ father died; in 1809, Gauss’ new wife died; and Johanna’s death was followed immediately by the death of Gauss’ second son. Gauss suffered from depression following this chain of events but later remarried and had three children with Minna Waldeck.

In 1818, Gauss began work that led to research in the field of differential geometry and the writing of significant theories related to the nature of curves and curvature. He published over 70 papers over the next 12 years, including one that won the Copenhagen University Prize.

In 1831, Gauss began to collaborate with Wilhelm Weber, a physicist. Gauss and Weber did extensive research into the nature of electricity and magnetism, creating a simple telegraph machine and discovering Kirchhoff's laws, a set of rules that apply to electrical circuits. The two men also developed the magnometer and the electrodynamometer, instruments that measured electric current and voltage. They also created innovative systems of units for electricity and magnetism. The term "gauss" came to describe a unit of magnetic flux density or magnetic induction.

Also in 1831, Gauss's second wife died after a long illness. He continued to live with his daughter, who took care of Gauss for the rest of his life.

Johann Carl Friedrich Gauss died February 23, 1855, in Göttingen, Germany. (www.rare-earth-magnets.com)

On background are:

Johann Carl Friedrich GaußNormal distribution by Gauss.

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of random variables is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.

The normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as Cauchy's, Student's, and logistic). The terms Gaussian function and Gaussian bell curve are also ambiguous because they sometimes refer to multiples of the normal distribution that cannot be directly interpreted in terms of probabilities.

The probability density of the normal distribution is:

f(x \; | \; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi} } \; e^{ -\frac{(x-\mu)^2}{2\sigma^2} }

Here, \mu is the mean or expectation of the distribution (and also its median and mode). The parameter \sigma is its standard deviation with its variance then \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.

If \mu = 0 and \sigma = 1, the distribution is called the standard normal distribution or the unit normal distribution denoted by N(0,1) and a random variable with that distribution is a standard normal deviate.

The normal distribution is the only absolutely continuous distribution whose cumulants beyond the first two (i.e., other than the mean and variance) are zero. It is also the continuous distribution with the maximum entropy for a specified mean and variance.

The normal distribution is a subclass of the elliptical distributions. The normal distribution is symmetric about its mean, and is non-zero over the entire real line. As such it may not be a suitable model for variables that are inherently positive or strongly skewed, such as the weight of a person or the price of a share. Such variables may be better described by other distributions, such as the log-normal distribution or the Pareto distribution.

The value of the normal distribution is practically zero when the value x lies more than a few standard deviations away from the mean. Therefore, it may not be an appropriate model when one expects a significant fraction of outliers—values that lie many standard deviations away from the mean—and least squares and other statistical inference methods that are optimal for normally distributed variables often become highly unreliable when applied to such data. In those cases, a more heavy-tailed distribution should be assumed and the appropriate robust statistical inference methods applied.

The Gaussian distribution belongs to the family of stable distributions which are the attractors of sums of independent, identically distributed distributions whether or not the mean or variance is finite. Except for the Gaussian which is a limiting case, all stable distributions have heavy tails and infinite variance. It is one of the few distributions that are stable and that have probability density functions that can be expressed analytically, the others being the Cauchy distribution and the Lévy distribution.

Johann Carl Friedrich GaußThe view on historic buildings in Göttingen, where Gauss worked as professor.

On foreground is the old auditorium Maximum (built from 1826 till 1865).

The University of Göttingen (German: Georg-August-Universität Göttingen, GAU), known informally as Georgia Augusta, is a public comprehensive research university in the city of Göttingen, Germany. Founded in 1734 by George II, King of Great Britain and Elector of Hanover, and starting classes in 1737, the university is the oldest in the state of Lower Saxony and the largest in student enrollment, which stands at around 26,000. The university is highly renowned and respected both in Germany and throughout the world. This reputation has thus shaped Göttingen into a university city with a high student and faculty population.

Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The River Leine runs through the town.

Johann Carl Friedrich GaußOn background are the mathematics symbols.

Lower, left, are the Braille symbols for visually impaired.

Denominations in numerals are lower and on right side, in words on right side (vertically).


10 Mark 1993

heliotropeVizeheliotrop of Gauss. (Sextant No. 420 by Edward Troughton). Brass, glass, gold, mahogany box, 31 x 31 x 15 cmю (before 1801). With handwritten inscription: "Property of Hofraths Gauss". Today is in University of Göttingen, First Physical Institute.

For its angular measurements Gauss used, developed in 1788, sextant by the founding member of the Royal Astronomical Society Edward Troughton (1753-1835). Later he provided with it with an additional mirror and called Vizeheliotrop.

The heliotrope is an instrument that uses a mirror to reflect sunlight over great distances to mark the positions of participants in a land survey. The heliotrope was invented in 1821 by the German mathematician Carl Friedrich Gauss. The word "heliotrope" is taken from the Greek: helios (Greek: Ἥλιος), meaning "sun", and tropos (Greek: τρόπος), meaning "turn". It is a fitting name for an instrument which can be turned to reflect the sun toward a given point.

Heliotropes were used in surveys from Gauss's survey in Germany in 1821 through the late 1980s, when GPS measurements replaced the use of the heliotrope in long distance surveys. Colonel Sir George Everest introduced the use of heliotropes into the Great Trigonometric Survey in India around 1831, and the US Coast and Geographic Survey used heliotropes to survey the United States. The Indian specification for heliotropes was updated in 1981, and the American military specification for heliotropes (MIL-H-20194E) was retired on 8 December 1995.

Surveyors used the heliotrope as a specialized form of survey target; it was employed during large triangulation surveys where, because of the great distance between stations (usually twenty miles or more), a regular target would be indistinct or invisible. Heliotropes were often used as survey targets at ranges of over 100 miles. In California, in 1878, a heliotrope on Mount Saint Helena was surveyed by B.A. Colonna of the USCGS from Mount Shasta, a distance of 192 miles (309 km.).

The heliotrope was limited to use on sunny days and was further limited (in regions of high temperatures) to mornings and afternoons when atmospheric aberration least affected the instrument-man's line of sight. The heliotrope operator was called a "heliotroper" or "flasher" and would sometimes employ a second mirror for communicating with the instrument station through heliography, a signalling system using impulsed reflecting surfaces. The inventor of the heliograph, a similar instrument specialized for signaling, was inspired by observing the use of heliotropes in the survey of India.

Left of Vizeheliotrop is the seal of German Bundesbank.

TriangulationIn lower right corner is a section of the triangle network, carried out by Gauss triangulation of the Kingdom of Hanover, in, among other things, this instrument (Vizeheliotrop) was used.

In 1818 Gauss, putting his calculation skills to practical use, carried out a geodesic survey of the Kingdom of Hanover, linking up with previous Danish surveys. To aid the survey, Gauss invented the heliotrope, an instrument that uses a mirror to reflect sunlight over great distances, to measure positions.

The diagram shows the settlements: Neuwerk (Insel), Wangerooge, Langwarden, Jever, Varel, Garlste, Bremen, Lehe (Bremerhaven), Brillit, Steinberg (Gemeinde Langwedel), Zeven, Litberg, Hamburg, Hohenhorn, Wilsede, Falkenberg, Elmhorst.

In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly (trilateration). The point can then be fixed as the third point of a triangle with one known side and two known angles.

Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work of Willebrord Snell in 1615-1617, who showed how a point could be located from the angles subtended from three known points, but measured at the new unknown point rather than the previously fixed points, a problem called resectioning. Surveying error is minimized if a mesh of triangles at the largest appropriate scale is established first. Points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying until the rise of global navigation satellite systems in the 1980s.

Denominations in numerals are lower and on left side, in words on left side (vertically).


The signatures on banknote belong to:

Johann Wilhelm GaddumJohann Wilhelm Gaddum (18 June 1930).

Hans TietmeyerHans Tietmeyer (18 August 1931).

Reinhold GerstetterDesigner - Reinhold Gerstetter.

Reinhold Gerstetter (October 18, 1945 in Leonberg in Baden-Württemberg) is a German graphic artist and designer. The most famous work in Germany is the last series of DM banknotes, which he designed, as well as the revision of the second Euro Series, the so-called "Euro-Series".

Gerstetter studied graphic design at the State Academy of Fine Arts in Stuttgart and later worked in advertising in London, Berlin and Haifa. From 1979 to 2002 he worked for the Bundesdruckerei. There he designed as a chief designer behördliches graphic design, stamps and banknotes (including for Israel, Bolivia and Peru). 1987 Gerst Etters design was chosen as the basis for the fourth and final series of banknotes of the German mark, which was from 1990 to early 2002 in circulation. A short time later, he also won the design competition of the Banco de España, which published four banknote values ​​from 1992, based on Gerst Etters designs. Although his designs submitted for the first series of banknotes of the common currency were not selected euro by the jury for the implementation, however, he was entrusted with the revision of the second series of euro banknotes that came into circulation as of May 2013.

His daughter, Avitall, is Germany's first female Jewish cantor.

Fourth Series of DM.

On March 19, 1981, the members of the Central Bank Council of the Deutsche Bundesbank decided to issue a new banknote series. She had become necessary due to technological progress, by the falsification of the old notes had become ever easier. Also a new series for the automatic payment transactions would be more appropriate. It took almost ten years, until the first two banknote values ​​were put into circulation on 1 October 1990 levels. This was around the 100- and 200-mark note. The latter denomination was introduced in this series of banknotes.

When designing the bank notes and the selection of the design elements were a lot of decisions to make. As early as the preliminary to the new series portraits were determined as the main subject. It should "be chosen brilliant portraits of personalities of German history in the fields of art, literature, music, economics, science and technology". In addition, the rear in conjunction should be about the person depicted on the front. Further, the primary colors of the note values ​​should remain unchanged and the word banknote stand on every bill in Gothic script.

People Picker.

A committee, consisting of historians Karl Otmar von Aretin, Knut Borchardt and Horst Fuhrmann, was commissioned to define the persons who should appear on the banknotes. The choice was between about 70 to 80 people. Here to "Top Artists" (z. B. Goethe, Schiller, Dürer) has been omitted. Likewise, retired people from whose expellees affiliation was unclear or a provocation in creed or political manner could mean (for example, Martin Luther, Karl Marx) or who had rendered her work mainly abroad, such as Jacques Offenbach.

When selecting the people should pay attention to balance in terms of gender, religion, national origin and work area. It should, if possible, three, but at least be represented two female characters in the series. However, the selection was very limited to female personalities. The aim was to show women who have created an independent work and not in the shade close to them were men (Charlotte von Stein, Charlotte von Kalb). However, such women were very rare until the XIX century. Therefore, the Panel chose to begin with the female figures, so not limitations on the field of activity, origin or confession had to be considered.

One of the requirements for the design was that the people viewed by the observer, the left should look towards banknote center. This meant that the provided portraits for five, ten, twenty, fifty and two hundred-Mark banknotes had to be mirrored. As with the Brothers Grimm two people should be ready to give them the largest banknote was reserved because of the large space requirement. Otherwise, men and women should alternate. The rest of the allocation of person and note value, however, was random and does not constitute a rating of persons.

Actually, Maria Sibylla Merian was earmarked for the 100- and Clara Schumann for the 500-mark note. However, only an artistically inferior etching by Johann Rudolf Schellenberg was for the portrait of Maria Sibylla Merian available, as in the original template doubts about the authenticity arose. Therefore, the Bundesbank held a design competition in order to get a high-quality master of this etching, which was the basis for the portrait on the bill later. Since the 100-DM-note should appear as one of the first, the people were replaced because of these difficulties.

Selection of the winning design.

Bundesdruckerei (represented by Rudolf Gerhardt, who had already designed the bench marks (BBK-II) for West Berlin), Ernst: For the design competition, which ran from 1 January to 30 June 1987, four graphic designers were by the Bundesbank in charge disciples, Johann Müller and Adrian Arthur Senger. According to the judgment of an expert commission consisting of historians, designers and graphic designers as well as a sociologist, corresponded to only one series to the high expectations. However, this reminded too much of the Swiss franc, so that she did not come into question. Thus, it would have been necessary actually a new design competition, which would have delayed the project by at least one year. But since Bundesdruckerei did submit two drafts, which was not accepted by the Bundesbank, was the draft by the then chief graphic designer of Bundesdruckerei, Reinhold Gerstetter, yet unseen in custody of the Bundesbank. After review by the Panel of this design was selected eventually as a basis for the new banknote series. The experts wrote: "The art expert panel is unanimously of the view that the here [...] compiled draft properties largely meet the requirements [...]. The art expert panel may recommend in this sense, the Deutsche Bundesbank, to make the present proposals for the basis of a new banknote series."

Configuration of the front sides.

The to be seen on the front towns pictures were an idea Gerst Etters. In his designs were to be seen in some cases striking modern building of the respective cities. However, the draft of the city of Frankfurt led to the decision to represent only historical buildings. The reason given was that the office towers of Deutsche Bank dominated the design and the Bundesbank should not be suspected to advertise for a private company.

In 1988, it was now necessary to select the appropriate city for each person. The design of the graphic looked for Paul Ehrlich Bad Homburg, his place of death, before. However, his work was held in Berlin and Frankfurt mostly. Frankfurt had Gerstetter however provided for Clara Schumann, who spent her final years there. After deciding on the introduction of the 5-DM-bill with the portrait of Bettina von Arnim was soon clear map to this the city of Berlin. Because each city should appear on the banknotes only once, only came for Paul Ehrlich thus Frankfurt in question. For Clara Schumann, the city of Leipzig was chosen because Leipzig was not just her birth, but because they also had their first successes there later.

Due to the events in the years 1989/1990, the decision for Leipzig proved a stroke of luck; because the banknote series was originally intended only for West Germany and West Berlin. But as the new federal states were represented with a city which also still has a special symbolic meaning: Here is the first Monday demonstrations took place that led to the dissolution of the GDR and the reunification of Germany.

Design of backs.

Reinhold Gerstetter looked for the back of the 1000-Mark certificate as the main subject is a figure from the fairy tale The Star Money before. However, the Brothers Grimm should, despite their extensive collection of fairy tales, can not be reduced to the fairy tale, as they have rendered outstanding services to the issuing of the German dictionary much about the German language. Thus, the dictionary was the main motif, and the Sterntaler "wandered" into the White Field.

Also in the design of the back was done with great attention to detail. So, even the background pattern a reference to the person who is pictured on the front. A penalty for the forgery of bank notes was no longer available in the fourth series.