Regiomontanus (latinized "Königsberger," but confusingly not referring to today's Kaliningrad, but to a small town in Bavaria) was a geometer and astronomer, known in his time for the following:
Publishing an abridged version of Ptolemy's Almagest (together with his predecessor in Vienna, Peuerbach), which included his own model of the motion of Mercury and Venus, and his own observations. Copernicus cites Peuerbachs and Regiomonatus, recalculating their observations to obtain a value of Earth's obliquity.
A treatise on trigonometry, proving results both for spherical and planar triangles, also providing the best trigonometric tables of his time. He formalized the use of sines, cosines and tangents, instead of chords (like we'd see in Hipparchus or Ptolemy, or even later Copernicus).
Founding an observatory in Nürnberg together with Bernhard Walther, which observed systematically the positions of planets for 30 years. This was the first permanent observatory north of the alps (with other important scientific institutions in the Islamic world, notably Ulugh Begh's observatory in Samarkand). Is is also the first observatory to use a mechanical clock (though only for a few observations), and it produced the best planetary observations prior to Tycho Brahe. Notably, they were the first to measure and publish the ecliptic latitudes of planets. Also, the quality of the observing conditions is provided. Copernicus uses the observations of Mercury by Walther and Regiomontanus (and a later pupil, Schöner)
The Ephemerides (1474), which tabelated the position of the moon and planets daily for 32 years ahead. This allowed for a method of longitude determination, using the position of the Moon as a clock. Is is said that Columbus used these Ephemerides for navigation.
Regiomontanus was called to Rome in 1485 to work on reforming the Julian calendar. However, he died in 1486 -- and some speculate he was poisoned by his enemies -- though it appears to me that most scholars wouldn't say so. In any case, we would have to wait almost a century for the Gregorian reform in 1583.
In 1509, Walther sold the house with the observatory to none other than Albrecht Dürer.
A mesmerising Durer engraving, full of mysterious mathematical connection: the original is exhibited in Regiomontanus' house in Nurmberg.
In Germanisches museum in Nurmberg.
Frontpiece of Jan Hevelius' star atlas Firmamentum Sobiescianum (dedicated to Jan III. Sobieski, best known for defeating the Ottomans in Vienna -- the constellation Scutum is named after his shield) , where several new constellations were introduced (Lynx, Vulpecula, Lacerta, Sextans, ...). On the left side of Urania, we see Waltherus standing besides Tycho, and on the right side, Regiomontanus standing besides Copernicus. It appears to me that the figures on the left side are known for observations and catalogues, whereas the figures on the right side are primarily known for mathematical astronomy. Maybe that's why Hevelius himself is coming from the left?