William Shanks
Encyclopedia
William Shanks was a British
amateur
mathematician
.
Shanks is famous for his calculation of π
to 707 places, accomplished in 1873, which, however, was only correct up to the first 527 places. This error was highlighted in 1944 by D. F. Ferguson (using a mechanical desk calculator).
Shanks earned his living by owning a boarding school
at Houghton-le-Spring
, which left him enough time to spend on his hobby of calculating mathematical constants. His routine was as follows: he would calculate new digits all morning; and then he would spend all afternoon checking his morning's work. To calculate π, Shanks used Machin's formula
:
Shanks' approximation was the longest expansion of π until the advent of the electronic digital computer
about one century later.
Shanks also calculated e and the Euler–Mascheroni constant
γ to many decimal places. He published a table of prime
s up to 60 000 and found the natural logarithm
s of 2, 3, 5 and 10 to 137 places.
Shanks died in Houghton-le-Spring in summer 1882, aged 70, and was buried at the local Hillside Cemetery on June 17th 1882.
United Kingdom of Great Britain and Ireland
The United Kingdom of Great Britain and Ireland was the formal name of the United Kingdom during the period when what is now the Republic of Ireland formed a part of it....
amateur
Amateur
An amateur is generally considered a person attached to a particular pursuit, study, or science, without pay and often without formal training....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
Shanks is famous for his calculation of π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
to 707 places, accomplished in 1873, which, however, was only correct up to the first 527 places. This error was highlighted in 1944 by D. F. Ferguson (using a mechanical desk calculator).
Shanks earned his living by owning a boarding school
Boarding school
A boarding school is a school where some or all pupils study and live during the school year with their fellow students and possibly teachers and/or administrators. The word 'boarding' is used in the sense of "bed and board," i.e., lodging and meals...
at Houghton-le-Spring
Houghton-le-Spring
Houghton-le-Spring is part of the City of Sunderland in the county of Tyne and Wear, North East England that has its recorded origins in Norman times. It is situated almost equidistant between the cathedral city of Durham 7 miles to the south-west and the centre of the City of Sunderland about 6...
, which left him enough time to spend on his hobby of calculating mathematical constants. His routine was as follows: he would calculate new digits all morning; and then he would spend all afternoon checking his morning's work. To calculate π, Shanks used Machin's formula
John Machin
John Machin, , a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.Machin's formula is:...
:
Shanks' approximation was the longest expansion of π until the advent of the electronic digital computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
about one century later.
Shanks also calculated e and the Euler–Mascheroni constant
Euler–Mascheroni constant
The Euler–Mascheroni constant is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter ....
γ to many decimal places. He published a table of prime
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s up to 60 000 and found the natural logarithm
Natural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
s of 2, 3, 5 and 10 to 137 places.
Shanks died in Houghton-le-Spring in summer 1882, aged 70, and was buried at the local Hillside Cemetery on June 17th 1882.
See also
- section "Numerical approximations" of the article on π
- Chronology of computation of π