header Notes Collection

10 Franken 1990, Switzerland

in Krause book Number: 53h
Years of issue: 1990
Edition: 60 000 000
Signatures: Le président du Conseil: Herr Peter Gerber, Un membre de la Direction générale: Herr Hans Meyer
Serie: Series VI
Specimen of: 05.11.1979
Material: Cotton fiber
Size (mm): 137 х 66
Printer: Orell Füssli, Zürich

* 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 Franken 1990




Leonhard Euler.


10 Franken 1990

Leonhard EulerThe engraving on banknote based after the portrait by Jakob Emanuel Handmann, made in 1753. Today is in Kunstmuseum, in Basel.

Leonhard Euler (15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.

Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest mathematicians to have ever lived. He is also one of the most prolific mathematicians; his collected works fill 60 to 80 quarto volumes. He spent most of his adult life in St. Petersburg, Russia, and in Berlin, then the capital of Prussia.

A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."

Euler worked in almost all areas of mathematics, such as geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes. Euler's name is associated with a large number of topics.

Euler is the only mathematician to have two numbers named after him: the important Euler's Number in calculus, e, approximately equal to 2.71828, and the Euler–Mascheroni constant γ (gamma) sometimes referred to as just "Euler's constant", approximately equal to 0.57721. It is not known whether γ is rational or irrational.

A large, three-dimensional numeral "10" is displayed at the top center of the note, inside the area of the background. Its shadow is printed in orange-brown or red-brown ink while the number is a light in color, and the designs on the background underneath are visible through the "10". The caption "Leonhard Euler" is printed in blue below the large numeral, and below that is "1707-1783", signifying the lifespan of Euler. Printed in an upward direction in purple at the bottom center of the note is the German value "ZEHN FRANKEN", and written to the right of it in a similar manner, but with blue and red ink, is the Romansh value "DIESCH FRANCS". Directly outside of the area with the background, near the left of the large "10", is a small, touch-perceptible red/orange dot that can be used by the visually-impaired for identifying the value of the note. Printed vertically and upward in orange or red ink at the left edge of the obverse is the German bank title "SCHWEIZERISCHE NATIONALBANK". Accompanying it to the right is the Romansh "BANCA NAZIUNALA SVIZRA", written in the same manner.

Leonhard EulerTo the left of portrait is a partially green and orange background consisting of Euler diagrams captioned with "A", "B", and "C". One of the "C" items is white in color.

An Euler diagram is a diagrammatic means of representing sets and their relationships. The first use of "Eulerian circles" is commonly attributed to Swiss mathematician Leonhard Euler (1707–1783). They are closely related to Venn diagrams.

Venn and Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s. Since then, they have also been adopted by other curriculum fields such as reading.

In a logical setting, one can use model theoretic semantics to interpret Euler diagrams, within a universe of discourse. In the examples above, the Euler diagram depicts that the sets Animal and Mineral are disjoint since the corresponding curves are disjoint, and also that the set Four Legs is a subset of the set of Animals. The Venn diagram, which uses the same categories of Animal, Mineral, and Four Legs, does not encapsulate these relationships. Traditionally the emptiness of a set in Venn diagrams is depicted by shading in the region. Euler diagrams represent emptiness either by shading or by the absence of a region.

Leonhard EulerOften a set of well-formedness conditions are imposed; these are topological or geometric constraints imposed on the structure of the diagram. For example, connectedness of zones might be enforced, or concurrency of curves or multiple points might be banned, as might tangential intersection of curves. In the diagram to the right, examples of small Venn diagrams are transformed into Euler diagrams by sequences of transformations; some of the intermediate diagrams have concurrency of curves. However, this sort of transformation of a Venn diagram with shading into an Euler diagram without shading is not always possible. There are examples of Euler diagrams with 9 sets that are not drawable using simple closed curves without the creation of unwanted zones since they would have to have non-planar dual graphs.

Leonhard EulerLower are showed the Euler angles.

The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them. Euler angles are also used to describe the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or φ, θ, ψ.

Euler angles represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate system. For instance, a first rotation about z by an angle α, a second rotation about x by an angle β, and a last rotation again about z, by an angle γ. These rotations start from a known standard orientation. In physics, this standard initial orientation is typically represented by a motionless (fixed, global, or world) coordinate system; in linear algebra, by a standard basis.

Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system (extrinsic rotations) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation (intrinsic rotations). The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Without considering the possibility of using two different conventions for the definition of the rotation axes (intrinsic or extrinsic), there exist twelve possible sequences of rotation axes, divided in two groups:

Proper Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y)

Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z).

Tait–Bryan angles are also called Cardan angles; nautical angles; heading, elevation, and bank; or yaw, pitch, and roll. Sometimes, both kinds of sequences are called "Euler angles". In that case, the sequences of the first group are called proper or classic Euler angles.

On the top is short silver cross, as Swiss emblem. The cross reminds us that Switzerland's sovereignty is inviolable. For many centuries, the logo has remained virtually unchanged.


10 Franken 1990


Printed horizontally in red ink at the top of the reverse is the French bank title "BANQUE NATIONALE SUISSE", and written in the same format on a line below is the Italian "BANCA NAZIONALE SVIZZERA", followed by a small Swiss cross identical in appearance to the cross presented on the obverse.

Directly below the Italian title is a blank area in which a watermark becomes visible.

The signatures of the President of the Bank Council and a member of the Board of Directors are featured in orange/red in the order listed below the blank area, the former captioned above by the French "Le président du Conseil" ("The President of the Council") and the latter accompanied by "Un membre de la Direction générale" ("A member of the Board of Directors"). Both of these captions are printed on two lines, the first separated between "president" and "du" and the second between "la" and "Direction".

Below all of the aforementioned elements is a colored area in which the prominent features of the reverse are located.

Leonhard EulerThis area, decorated at portions with several wavy lines, features a large illustration of a water turbine that was initially sketched by Leonhard Euler, signifying Euler's contributions to fluid physics.

The Euler’s pump and turbine equations are most fundamental equations in the field of turbo-machinery. These equations govern the power, efficiencies and other factors that contribute in the design of Turbo-machines thus making them very important. With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined. As the name suggests these equations were formulated by Leonhard Euler in the eighteenth century. These equations can be derived from the moment of momentum equation when applied for a pump or a turbine.

Euler’s pump and turbine equations can be used to predict the impact of changing the impeller geometry on the head. Qualitative estimations can be made from the impeller geometry about the performance of the turbine/pump. For the design of an aero-engines and the designing of power plants, the equations assume prime significance. Thus for the design aspect of turbines and pumps, the Euler equations are extremely useful.

Next to the turbine, and even superimposing parts of it, is a depiction of a ray diagram with an object in front of five converging lenses and the object's resultant image. Such a depiction represents Euler's work with optics.

Leonhard EulerThroughout his years in Berlin and beyond, Euler was deeply occupied with geometric optics. His memoirs and books on this topic, including the monumental three-volume Dioptrics (E367, E386, E404), written mostly while still in Berlin, fill no fewer than seven volumes in his "Opera omnia". A central theme and motivation of this work was the improvement of optical instruments like telescopes and microscopes, notably ways of eliminating chromatic and spherical aberration through intricate systems of lenses and interspaced fluids. (Leonhard Euler: His Life, the Man, and His Works)

Leonhard EulerFeatured in the center of the reverse, superimposing the turbine but covered partially by the ray diagram, is a representation of a model drawn by Euler of the solar system, showing the planets of Mercury (not accompanied by a symbol on the note), Venus (♀), Earth (♁), Mars (♂), Jupiter (♃), and Saturn (♄), as well as Halley's Comet, in their respective orbits around the sun. Also displayed in the illustration is the Moon (☾) orbiting around Earth, the four known moons of Jupiter during Euler's lifetime – Io, Europa, Ganymede, and Callisto – traveling around the planet, and the five known moons of Saturn of Euler's time – Tethys, Dione, Rhea, Titan, and Iapetus – circling Saturn. Erroneously, a fifth moon is shown in Jupiter's orbits. In between the orbits of Mars and Jupiter is a white oval, which corresponds to the location of the white "C" item on the note's obverse.

Presumably, the white spot in the Euler solar system is predicted by him asteroid 2002 Euler.

2002 Euler, provisional designation 1973 QQ1, is an asteroid from the asteroid belt, about 17 kilometers in diameter. It was discovered on August 29, 1973, by Russian astronomer Tamara Smirnova at the Crimean Astrophysical Observatory in Nauchnyj. The asteroid's low-eccentric, only slightly inclined orbit has a period of 3 years and 9 month with a semi-major axis of 2.4 AU. It rotates around its axis every 6 hours. Its geometric albedo of 0.084 has been measured by the Infrared Astronomical Satellite (IRAS).

It was named after Swiss mathematician, physicist and astronomer Leonhard Euler (1707-1783). His contributions to astronomy included two theories for the motion of the Moon. Euler spent much of his time in St. Petersburg and was associated with the Russian Academy of Sciences.

The inclusion of the solar system identifies Euler's contributions to astrology.

There was a branch of contemporary mathematics, which Euler had not worked. He studied mechanics, theory of elasticity, theory of machines, mathematical physics and optics, the theory of the ship, ballistics. In these areas, he performed not only theoretical but also applied research.

Most of the astronomical writings devoted to the topical issues at the time of celestial mechanics and geodesy, spherical, practical and seaworthy astronomy, the theory of tides, astronomical theory of climate, the refraction of light in the Earth's atmosphere, parallax and aberration, the Earth's rotation. In the field of celestial mechanics, Euler made substantial contributions to the theory of perturbed motion. He elaborated the theory of the moon's motion, developing the works of Clairaut and d'Alembert, JL, built on the general principles of the theory of the Moon, admitting study its motion with a very high accuracy. This theory has been introduced into the practice of T. Mayer tabulation, the accuracy of which surprised his contemporaries. Even more perfect theory of the Moon was stated by Euler in his book "Theory of motion of the moon, to interpret the new method ..."

Computational methods proposed for accurate ephemeris of the Moon and planets, were widely used later George. Hill. In the words of Μ. F. Subbotin, they have become a major source of further progress throughout the celestial mechanics. Ample opportunities for application of these methods have arisen with the use of computers. Modern accurate and complete theory of the motion of the Moon was created in 1895-1908 years. E. Brown.

Leonhard EulerAccording to NASA scientists, Euler predicted the appearance of the comet Elenin.

Comet C/2010 X1 (Elenin) is an Oort cloud comet discovered by Russian amateur astronomer Leonid Elenin on December 10, 2010, through remote control of the International Scientific Optical Network's robotic observatory near Mayhill in the U.S. state of New Mexico. The discovery was made using the automated asteroids discovery program CoLiTec. At the time of discovery, the comet had an apparent magnitude of 19.5, making it about 150,000 times fainter than can be seen with the naked eye. The discoverer, Leonid Elenin, originally estimated that the comet nucleus was 3-4 km in diameter, but more recent estimates place the pre-breakup size of the comet at 2 km. Comet Elenin started disintegrating in August 2011, and as of mid-October 2011 was not visible even using large ground-based telescopes.

Video with the arguments of Euler prediction.

The numeral "10" is printed in a large font at the upper right corner of the colored area, the shadow colored red and the remainder showing the designs of the background underneath.

The French value "DIX FRANCS" is printed in a downward direction at the upper left corner of the background, whereas the Italian "DIECI FRANCHI" is inscribed upward at the lower right corner of the note. The serial number is printed once again in blue ink over the image of the water turbine. Written in small, orange or red print at the very bottom of the note, outside of the colored area, is "E + U HIESTAND" followed by "© Banque Nationale Suisse" and "Orell Füssli Arts Graphiques S.A. Zurich". Such text signifies the designs were made by Ernst and Ursula Hiestand and the note is owned by the Swiss National Bank and was printed by Orell Füssli.


A competition was held to determine the designs of the sixth series, and the submissions sent in by artists Ernst (1935-) and Ursula Hiestand (1936-) were selected, although they did not officially win the competition.

The banknote was produced from 1979 to 1992, and was recalled beginning on May 1, 2000. It is expected to be demonetized on May 1, 2020. The note, like the others of the sixth series, is unique in that one side – the obverse – has horizontal orientation while the other – the reverse – has vertical orientation. Also, although Romansh was recognized as a national language in Switzerland in 1938, no banknote series until the sixth series included the language.

There are 2 signatures:


Peter Gerber (08.06.1923 - 11.04.2012). President of the Bank Council from 28.04.1989 till 16.04.1993.


Hans Meyer (20.4.1936 - ). Head of II. Department and vice-president of the Bank since 01.05.1988 till 30.04.1996.