Person: Hermann Of Reichenau
Hermann of Reichenau was a German mathematician who important for the transmission of Arabic mathematics, astronomy and scientific instruments into central Europe.
Mathematical Profile (Excerpt):
- The lake has a western arm, west of the city of Konstanz, and in this is situated the island of Reichenau.
- This island, about 5 km long and 1.5 km wide, was the artistic and literary centre of south west Germany during this period and was the site of a famous Benedictine monastery which had been founded there in 724.
- Hermann is called 'the Lame' or 'Contractus' for very good reason.
- Using the biography written by his disciple Berthold, the most important contemporary source about Hermann's life, an approach to a correct diagnosis from a neurologists point of view was the aim of this study.
- By unbiased analysis of the symptoms described by Berthold a neurologic syndrome is worked out: it comprised a flaccid tetraparesis involving the bulbar area.
- Hermann entered the Cloister School at Reichenau, attached to the monastery, on 13 September 1020 and studied there under the Abbot Berno (about 978-1048).
- The monastery was a centre of learning at this time, containing a fine library and a well-equipped workshop.
- Hermann became a monk at the Benedictine Monastery at Reichenau in 1043, later becoming Abbot of the Monastery after the death of Abbot Berno on 7 June 1048.
- Despite his disabilities, being confined to a chair and hardly able to speak, he was a key figure in the transmission of Arabic mathematics, astronomy and scientific instruments from Arabic sources into central Europe.
- His pupil Berthold of Reichenau, from whom we have the details of Hermann's life, does not mention that he could read Arabic and, given the nature of Berthold's writings about his master, it would be highly unlikely that he would not have mentioned this ability if indeed Hermann had been knowledgeable in the Arabic language.
- However, Gerbert of Aurillac, who died ten years before Hermann was born, had learnt much from Arabic sources in Spain and had written several works which, almost certainly, would have found their way to the monastery at Reichenau.
- Hermann introduced three important instruments into central Europe, knowledge of which came from Arabic Spain.
- of an upright cylinder with a conical top terminating in a knob by which it might be turned, with a vertical scale to the right of the cylinder and obliquely curving lines across the face of the cylinder which are to trace the sun's shadow.
- Apparently these instruments were used to determine the latitude as well as to find the hour and the altitude of the sun, or at least they were adapted to determine the hour in different places and latitudes where a traveller might be.
- Some parts of these works may not have been written by Hermann and the most likely author on which they are based must be Gerbert of Aurillac.
- The description of the astrolabe that Hermann gives is for an instrument which is designed to be used at a latitude of forty-eight degrees, which is indeed the latitude of Reichenau.
- These works contain more than just a description of the astrolabe, however, for they also contain star charts (again with data correct for the latitude of Reichenau) and a calculation of the earth's diameter.
- Hermann's contributions to mathematics include a treatise "Qualiter multiplicationes fiant in abbaco" dealing with multiplication and division, although this book is written entirely with Roman numerals.
- It contains the multiples, products, and quotients of the duodecimal fractions.
- A closely similar, and also undescribed, set of tables is, in fact, to be found in a manuscript of English origin written in or about the year 1111 A.D. and now in the library of St John's College, Oxford.
- They are arranged with great economy of space and are handy to use.
- This chart is ruled in double lines of red and green, meeting in one corner in a grotesque drawing of a lion's head.
- Another interesting piece of work by Hermann is on lunar months.
- Around 1040 he wrote "Epistola de quantitate mensis lunaris" which addressed the problem of the lengths of the lunar month.
- It was known that the moon and the sun essentially returned to the same position after a cycle of 19 years.
- Of course, Hermann did not have the decimal notation we have just used in this calculation.
- He had units of time which divided a day into 24 hours, an hour into 40 moments, and a moment into 564 atoms.
- If you do a little arithmetical calculation, you will see that Hermann was exactly right.
- He used this value for the average length of the month to create a new lunar calendar in Abbreviato compoti (1042).
- Hermann also wrote on music, considered as a part of mathematics at this time.
- Crocker begins that article by quoting from Hermann's Opuscula musica.
- Hermann had learnt musical theory from his teacher Berno who, having reformed the Gregorian chant into eight modes called 'tones', was probably the leading music expert in his day.
- This matter of recognition, to be sure, though it may be reduced to a brief statement, is nevertheless extensive and notable in character, since that which is very elegantly indicated in it finds a place among the proper and rightful foundations of the modes.
- And in Hermann's discussion, this major sixth so strongly resembles the hexachord that it seems the two should be identified without hesitation.
- Not only did Hermann write on the theory of music but he also wrote poetry and hymns.
- It is always difficult to be certain that the attribution of works from this early period is correct and, indeed, many scholars doubt whether these hymns have come down to us in the same form as Hermann wrote them.
- There seems little doubt, however, that even if these works have been modified later, they are based on hymns written by Hermann.
- A poem about the eight deadly sins, written for the nuns at Buchau, shows that Hermann had an excellent sense of humour.
- Finally, let us note Hermann's important contributions to history.
- He had requested that his disciple, Berthold of Reichenau, should take wax tablets on which his writings were recorded and have these made into manuscripts.
- Indeed, it is because Berthold faithfully carried out Hermann's request that so much of Hermann's work was preserved.
- Hermann also requested that Berthold continue to record the chronicle which he had taken as far as the year 1054.
Born 18 July 1013, Saulgau, Swabia, Germany. Died 24 September 1054, Reichenau, Germany.
View full biography at MacTutor
Tags relevant for this person:
Astronomy, Origin Germany
Thank you to the contributors under CC BY-SA 4.0!
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive