History of geometry in the context of "Straightedge and compass construction"

Albrecht Dürer (/ˈdjʊərər/ DURE-ər, German: [ˈalbʁɛçt ˈdyːʁɐ]; 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.

Dürer's vast body of work includes engravings, his preferred technique in his later prints, altarpieces, portraits and self-portraits, watercolours and books. The woodcuts series are stylistically more Gothic than the rest of his work, but revolutionised the potential of that medium, while his extraordinary handling of the burin expanded especially the tonal range of his engravings.

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics.

Ancient Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the ancient Greek mathematician Euclid in his Elements, with the great innovation of proving all properties of the space as theorems, by starting from a few fundamental properties, called postulates, which either were considered as evident (for example, there is exactly one straight line passing through two points), or seemed impossible to prove (parallel postulate).

Johannes Trolle Hjelmslev (Danish: [ˈjelˀmsle̝w]; 7 April 1873 – 16 February 1950) was a mathematician from Hørning, Denmark. Hjelmslev worked in geometry and history of geometry. He was the discoverer and eponym of the Hjelmslev transformation, a method for mapping an entire hyperbolic plane into a circle with a finite radius.He was the father of Louis Hjelmslev.

Originally named Johannes Trolle Petersen, he changed his patronymic to the surname Hjelmslev to avoid confusion with Julius Petersen. Some of his results are known under his original name, including the Petersen–Morley theorem.