Born as Johannes Muller, Regiomontanus was born on June 6, 1436 in Konigsberg, Bavaria (not to be confused with the Konigsberg in what was East Prussia and is now Kalingrad). As was the custom at the time Johannes Muller used a latinicized pseudonym for his writings. The Latin name for Konigsberg is Regio Monte and from this Muller derived Regiomontanus. The son of a miller, Regiomontanus was educated at home until the age of 11. In 1447 he entered the University of Leipzig to study dialectics. Attracted by its reputation for mathematics, in 1450 he entered the University of Vienna where he studied mathematics under Georg von Puerbach. He completed his baccalaureate in 1452. He was unable to earn his Master's Degree until 1457, as university regulations required recipients to be 21.
In 1547 he was appointed to the faculty of the University of Vienna, where he taught classes on perspective, Euclid and Virgil's Bucolics. He also collaborated with his former teacher Puerbach, doing astronomical observations. His primary interest was reading old manuscripts, of which he made copies. He also collaborated with Peurbach on an a abridgment of Ptolemy's Almagest. On his deathbed Peurbach urged his student to finish the work, which he did and although it was finished in 1462, it was not published until 1496. This work used the trigonometric functions sine and cosine and included a table of natural sines.
After the death of his teacher Regiomontanus traveled to Rome with his new patron Cardinal Bessarion. Regiomontanus spent the years from 1461 to 1465 as a member of the Cardinal's household. During this time he continued his studies, learning Greek from the Cardinal and using the Cardinal's library of Greek classics. Realizing the need for a systemic book on trigonometry, Regiomontanus completed De triangulis omnimodis (On Triangles of All Kinds) in 1464. This is the earliest systemic exposition on trigonometry, both planar and spherical, although portions of the sections on spherical trigonometry were taken, without attribution, from the twelfth century work of Jabir ibn Afla.
In 1471 Regiomontanus settled in Nuremberg, where he established an observatory and printing press. In Nuremberg he wrote three books on astronomy and he also created a mechanical eagle for Emperor Maximilian, which flapped its wings and was considered one of the marvels of the age. In 1475 Regiomontanus returned to Rome. He had been invited by Pope Sixtus IV, who wanted Regiomontanus' advice in reforming the calendar. The trip to Rome would prove fatal. Some commentators claim that Regiomontanus was poisoned. Others say that he died in the outbreak of plague that followed the flood of the Tiber in January 1476.
Regiomontanus died on July 6, 1476.
Ball, Walter William Rouse; A Short Account of the History of Mathematics; Macmillan and Company Ltd.; 1908
O'Conner, J.J. and Robertson, E.F.;"Johan Muller Regiomontanus" at www-history.mcs.st-andrews.ac.uk
Regiomontanus wikipedia entry