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Johann Faulhaber (5 May 1580 – 10 September 1635) was a German
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SLUB Dresden
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Johann Faulhaber
in VD17 * {{DEFAULTSORT:Faulhaber, Johann 1580 births 1635 deaths 16th-century German mathematicians 17th-century German mathematicians Rosicrucians 17th-century German writers 17th-century German male writers
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
.
Born in Ulm
Ulm () is a city in the German state of Baden-Württemberg, situated on the river Danube on the border with Bavaria. The city, which has an estimated population of more than 126,000 (2018), forms an urban district of its own (german: link=no, ...
, Faulhaber was a trained weaver who later took the role of a surveyor of the city of Ulm. He collaborated with Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
and Ludolph van Ceulen
Ludolph van Ceulen (, ; 28 January 1540 – 31 December 1610) was a German-Dutch mathematician from Hildesheim. He emigrated to the Netherlands.
Biography
Van Ceulen moved to Delft most likely in 1576 to teach fencing and mathematics and in 159 ...
. Besides his work on the fortifications of cities (notably Basel
, french: link=no, Bâlois(e), it, Basilese
, neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münchenstein (BL), Muttenz (BL), Reinach (BL), Riehen (BS ...
and Frankfurt
Frankfurt, officially Frankfurt am Main (; Hessian: , "Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on its na ...
), Faulhaber built water wheel
A water wheel is a machine for converting the energy of flowing or falling water into useful forms of power, often in a watermill. A water wheel consists of a wheel (usually constructed from wood or metal), with a number of blades or buckets ...
s in his home town and geometrical instruments for the military. Faulhaber made the first publication of Henry Briggs's Logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...
in Germany. He is also credited with the first printed solution of equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
.Date,name,ratio,cents: from equal temperament monochord tables p55-p78; J. Murray Barbour ''Tuning and Temperament'', Michigan State University Press 1951 He died in Ulm.
Faulhaber's major contribution was in calculating the sums of powers of integers. Jacob Bernoulli
Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Le ...
makes references to Faulhaber in his ''Ars Conjectandi''.
Works
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See also
*Faulhaber's formula
In mathematics, Faulhaber's formula, named after the early 17th century mathematician Johann Faulhaber, expresses the sum of the ''p''-th powers of the first ''n'' positive integers
:\sum_^n k^p = 1^p + 2^p + 3^p + \cdots + n^p
as a (''p''&nb ...
References
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External links
Johann Faulhaber
in VD17 * {{DEFAULTSORT:Faulhaber, Johann 1580 births 1635 deaths 16th-century German mathematicians 17th-century German mathematicians Rosicrucians 17th-century German writers 17th-century German male writers