500 Kroner 1972, Norway
| in Krause book | Number: 34f |
| Years of issue: | 1972 |
| Edition: | 6 964 000 (all years) |
| Signatures: | Direksjonens Formann: Knut Getz Wold (in office 1970-1985), Hovedkasserer: Bernt-Arne Ødegaard |
| Serie: | Fourth Series |
| Specimen of: | 1948 |
| Material: | Cotton fiber |
| Size (mm): | 216 x 127 |
| Printer: | Norges Bank, Oslo (till 2008) |
* All pictures marked 
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.
Description
Watermark:
Niels Henrik Abel.
Avers:
The engraving on banknote is made after the only contemporary portrait of Niels Henrik Abel, painted by Johan Gørbitz in 1826. Copyright: Universitetet i Oslo.
Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for over 350 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. Through the great works from Abel's hand he was known to the world's mathematicians; he made his discoveries while living in poverty and died at the age of 26 from tuberculosis.
Most of his work was done in six or seven years of his working life. Regarding Abel, the French mathematician Charles Hermite said: "Abel has left mathematicians enough to keep them busy for five hundred years." Another French mathematician, Adrien-Marie Legendre, said: "quelle tête celle du jeune Norvégien!" ("what a head the young Norwegian has!").
The Abel Prize in mathematics, originally proposed in 1899 to complement the Nobel Prizes, is named in his honour.
In the theory of series the name of Abel are several important theorems. Abel thoroughly investigated the convergence of the series, and at the highest level of rigor. His criteria for rigor were tougher than even Cauchy. He, for example, argued that the sum of the power number inside the circle of convergence is continuous, while Gauss and Cauchy considered this fact to be self-evident. Cauchy, however, published (1821) the proof of an even more general theorem: "The sum of any convergent series of continuous functions is continuous," but Abel in 1826 gave a counterexample to show that this theorem is incorrect:
{\displaystyle f(x)=\sin x-{\frac {1}{2}}\sin 2x+{\frac {1}{3}}\sin 3x-{\frac {1}{4}}\sin 4x\cdots } f(x)=\sin x-{\frac {1}{2}}\sin 2x+{\frac {1}{3}}\sin 3x-{\frac {1}{4}}\sin 4x\cdots
This function is periodic (with a period of {\ displaystyle 2 \ pi} 2 \ pi). In the interval {\ displaystyle - \ pi In the theory of special, especially elliptic and abelian functions, Abel was a recognized founding leader along with Jacobi. He was the first to define elliptic functions as functions inverse to elliptic integrals, extended their definitions to the general complex case and deeply investigated their properties. Abel's most important theorem on integrals of algebraic functions was published only posthumously. Legendre called this discovery "a monument to non-hands" for Abel. At the top is the coat of arms of Norway. The banknote depicts 2 horses, as holders of the coat of arms. I have not found such a version of the coat of arms of Norway anywhere. I suppose that this is a sketch of the coat of arms, made by the designer specifically for the banknote. A golden lion on a red shield was adopted in or before the early part of the XIII century. In the late part of the same century, a silver axe was added. In continuous use since then, the coat of arms is one of the oldest state coats of arms in the world. The official blazon is: Gules, a lion rampant or, crowned or and bearing an axe with blade argent. Among the state coats of arms that are still in use today, the Coat of Arms of Norway is among the oldest in Europe and even world-wide. It is known since the early XIII century, when it served as the coat of arms of the kings of the Sverre dynasty. It is told that Sverre, who was King between 1184 and 1202, had a lion in his coat of arms. This coat of arms appears in 1225, when it was used by Earl Skule Bårdsson, who had relations to the royal family. A coat of arms with a lion was also used by Haakon the Young Haakonson, who was King between 1240 and 1257. This was in 1250. Haakon the Young's father, King Haakon the Old Haakonson, had a lion in his seal. This lion, however, does not appear in a coat of arms, but in the shape of a small lion which lies between the King's feet. This might be the same lion that Earl Skule and Haakon the Young used in their seals. On the other hand, lions were a frequently used symbol of kings and royal power. Snorre Sturlason claims that a golden lion on a red background was used already in 1103 by King Magnus III, the son of King Olav III. In 1894, historian Gustav Storm concluded that this is ahistorical. Storm explained that the claimed lion in King Magnus's coat of arms is unknown both in the older Saga literature and in other contemporary sources. It is possible that Snorre, who wrote under the instruction of the King, attributed King Sverre's coat of arms to earlier Kings of Norway. Approximately in 1280, either King Magnus VI (dead in 1280) or the guardianship of his son Eric Magnuson let the lion be equipped with a crown of gold and in the foremost paws an axe of silver. The axe was a symbol of Saint Olaf, i.e. King Olaf II, and by inserting it into the coat of arms it was symbolised that the King was the rightful heir and descendant of the "Eternal King of Norway" (Latin: Rex Perpetuus Norvegiae). Along the lower edge of the banknote is Norwegian pattern. Denomination in numerals and in words is centered. Regarding the paintings, on the reverse of the banknote, I wrote to the Norwegian Bank. On March 25, 2020, a response was received from the Bank of Norway engraver and banknote designer Arild Yttri. Here is what he replied: "...Thanks for your mail and interesting questions. During the work with main motifs for the NOK IV series the 500 back created some problems. The first draft sketch by another artist was rejected and the committee/jury turned to Reidar Aulie and asked him if he could make a proposal. The theme was Norwegian livelihoods and 500 should cover the Industry. Aulies sketch shows a hydropower plant, at the time one of Norways most important industries. After Aulie showed the proposal to the committee there were several adjustments to the sketch - for example the, to two guys didn’t look as typical Norwegians and the sketch were re designed several times". I want to make my little annotation - in my opinion, the two guys in the figure on the left do not look typical Norwegians :), despite the sketch being adjusted at that time. I am very grateful to Arild Juttri for the detailed answer. I have only one add. I put the only photo that I found on the net. The old wooden house in the photo, near the waterfall, is very similar to the one depicted by Reidar Aulie. Many thanks to Olga from the Orenburg region, Russia for the thought of the wooden house. By the way, Arild Yuttri was also right - the workers unload the goods at the factory which looks like "modern" sawmill... On banknote are the industries that operate on hydropower! On banknote is the watermill in Hellesylt, Norway, which is located at: Hellesyltfossen, 6218 Stranda-Hellesylt. A watermill or water mill is a mill that uses hydropower. It is a structure that uses a water wheel or water turbine to drive a mechanical process such as milling (grinding), rolling, or hammering. Such processes are needed in the production of many material goods, including flour, lumber, paper, textiles, and many metal products. These watermills may comprise gristmills, sawmills, paper mills, textile mills, hammermills, trip hammering mills, rolling mills, wire drawing mills. One major way to classify watermills is by wheel orientation (vertical or horizontal), one powered by a vertical waterwheel through a gear mechanism, and the other equipped with a horizontal waterwheel without such a mechanism. The former type can be further divided, depending on where the water hits the wheel paddles, into undershot, overshot, breastshot and pitchback (backshot or reverse shot) waterwheel mills. Another way to classify water mills is by an essential trait about their location: tide mills use the movement of the tide; ship mills are water mills onboard (and constituting) a ship. Watermills impact the river dynamics of the watercourses where they are installed. During the time watermills operate channels tend to sedimentate, particularly backwater. Also in the backwater area, inundation events and sedimentation of adjacent floodplains increase. Over time however these effects are cancelled by river banks becoming higher. Where mills have been removed, river incision increases and channels deepen. Denomination in numeral and in words is at the lower left corner of banknote. Invalid from 13.07.1999. Work on this banknote series began before the Second World War. In 1930, an artistic competition was held to design a new banknote series, but the war put a stop to its realisation. Since none of the winning designs were deemed suitable, the architect Arnstein Arneberg was engaged as an artistic collaborator. The series was to feature portraits of prominent Norwegians from the recent past on the obverse, with illustrations of the most important industries on the reverse. The engravings for the 10-krone and 100-krone banknotes were done before the war by the firm Thomas de la Rue in London, while the other banknotes in the series were engraved by Henry Welde, a graphic designer at Norges Bank's Printing Works.
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