Albrecht Dürer (21 May 1471 – 6 April 1528), sometimes spelled in English as Durer or Duerer, was a German painter, printmaker, and theorist of the German Renaissance. Born in Nuremberg, Dürer established his reputation and influence across Europe in his twenties due to his high-quality woodcut prints. He was in contact with the major Italian artists of his time, including Raphael, Giovanni Bellini and Leonardo da Vinci, and from 1512 was patronized by Emperor Maximilian I.
https://en.m.wikipedia.org/wiki/Albrecht_Dürer
In about 1508 Dürer began to collect material for a major work on mathematics and its applications to the arts. This work would never be finished but Dürer did use parts of the material in later published work. He continued to produce art of outstanding quality, and he produced one of his most famous engravings Melancholia in 1514.
It contains the first
magic square
(In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. https://en.m.wikipedia.org/wiki/Magic_square )
to be seen in Europe, cleverly including the date 1514 as two entries in the middle of the bottom row. Also of mathematical interest in Melancholia is the polyhedron in the picture. The faces of the polyhedron appear to consist of two equilateral triangles and six somewhat irregular pentagons.
[…] Dürer had a second reason for this visit to the Netherlands, for he believed that Maximilian’s daughter had a book by Jacopo de Barbari on applications of mathematics to art, and Dürer had long sought the truths which he believed this work contained. On meeting Maximilian’s daughter he offered her the portrait of her father which he had painted, but was distressed to find that she did not want the portrait. She had already given the book by Jacopo de Barbari to another artist so Dürer’s quest was in vain. He did persuade Charles V to restore his pension, however, which was formally agreed on 12 November 1520.
After returning to Nürnberg, Dürer’s health became still worse. He did not slacken his work on either mathematics or painting but most of his effort went into his work Treatise on proportion. Although it was completed in 1523, Dürer realised that it required mathematical knowledge which went well beyond what any reader could be expected to have, so he decided to write a more elementary text. He published this more elementary treatise, in four books, in 1525 publishing the work through his own publishing company.
This treatise, Unterweisung der Messung mit dem Zirkel und Richtscheit, is the first mathematics book published in German (if one discounts an earlier commercial arithmetic book) and places Dürer as one of the most important of the Renaissance mathematicians.
https://mathshistory.st-andrews.ac.uk/Biographies/Durer/
German artist Albrecht Dürer (1471–1528) was interested in the geometry of proportion and perspective. In 1525 he published a treatise called Vnderweysung der Messung mit dem Zirckel vnd Richtscheyt (Measurement calculations with compass and ruler). Another Mathematical Treasure provides images from a 1538 Latin translation.
Dürer’s magic square is a magic square with magic constant 34 used in an engraving entitled Melencolia I by Albrecht Dürer (The British Museum, Burton 1989, Gellert et al. 1989). The engraving shows a disorganized jumble of scientific equipment lying unused while an intellectual sits absorbed in thought. Dürer’s magic square is located in the upper right-hand corner of the engraving. The numbers 15 and 14 appear in the middle of the bottom row, indicating the date of the engraving, 1514.
Dürer’s magic square has the additional property that the sums in any of the four quadrants, as well as the sum of the middle four numbers, are all 34 (Hunter and Madachy 1975, p. 24). It is thus a gnomon magic square. In addition, any pair of numbers symmetrically placed about the center of the square sums to 17, a property making the square even more magical.