Biography

(1815

1904)

1846

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1861

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7

18

1871

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9

14

1881

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π / 4 = 4 tan ⁡ − 1 ( 1 5 ) − tan ⁡ − 1 ( 1 239 ) \pi/4 = 4 \tan^{-1}(\large\frac{1}{5}

ormalsize ) - \tan^{-1}(\large\frac{1}{239}

ormalsize ) π / 4 = 4 tan − 1 ( 5 1 ​ ) − tan − 1 ( 2 3 9 1 ​ )

1706

100

e e e

60

000

2

3

5

10

137

2 12 m + 1 2^{12m+1} 2 1 2 m + 1

m = 1 , 2 , 3 , . . . , 60 m = 1, 2, 3, ..., 60 m = 1 , 2 , 3 , . . . , 6 0

1944

π / 4 = 3 tan ⁡ − 1 ( 1 4 ) + tan ⁡ − 1 ( 1 20 ) + tan ⁡ − 1 ( 1 1985 ) \pi/4 = 3 \tan^{-1}(\large\frac{1}{4}

ormalsize ) + \tan^{-1}(\large\frac{1}{20}

ormalsize ) + \tan^{-1}(\large\frac{1}{1985}

ormalsize ) π / 4 = 3 tan − 1 ( 4 1 ​ ) + tan − 1 ( 2 0 1 ​ ) + tan − 1 ( 1 9 8 5 1 ​ ) .

528

th

707

707

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9644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412

7372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160

9433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949

1298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051

3200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892

354201996

1882

17

married Jane Elizabeth Pringlein London in. Inhe moved to Houghton-le-Spring, a small town in the coal-mining area of County Durham. We get more information about him from the census.Inhe was living at Quality Hill, Houghton-le-Spring, with his wife, his widowed mother-in-law Sarah Pringle, and a servant Jane Calbreath. Ten years later, in, he was living at a Private Boarding School in Nesham Place, Houghton-le-Spring, with his wife, mother-in-law, William Routledgean English teacher, Ann Olivercook, Alice Oliverhousemaidand eleven pupils aged betweenand. Inhe was still living at the school with his wife, Jane Monkcook, Catherine Pottshousemaidand eleven pupils aged betweenand. Inhe was still living at Nesham Place, with his wife and Jane Shawdomestic servantShanks used his leisure hours working on mathematics, particularly on calculating the decimal expansion of π. He was influenced to undertake this task by William Rutherford from Edinburgh.InShanks published a book entitled. In the same year William Rutherford gavedecimal places in the expansion of π and, later in the same year, Shanks, in a collaboration with Rutherford, gaveplaces. This was a busy year for Shanks, for also inhe gavedecimal places in the expansion of π which had been independently checked as correct to the firstof those places. At this point Shanks rested in his calculations of the decimal expansion of π, but he continued to write mathematical works. BetweenandShanks published nine mathematical memoirs in theof the Royal Society of London Shanks is famed for his calculation of π toplaces in, which, unfortunately, was only correct for the firstplaces. Despite these errors he did manage to correct some errors in the expansion of toplaces which he had given twenty years earlier. The method Shanks used in his calculation was based on the formulawhich had been discovered by Machin inand used by him to correctly calculate todecimal places.Shanks also calculatedand Euler 's constant γ to a great many decimal places. He published a table of primes up to, found the natural logarithms ofandtoplaces, and the values offorInD F Ferguson calculated π using the formulaHe found that his value disagreed with that of Shanks in theplace. Ferguson discovered that Shanks had omitted two terms which caused his error. Of course calculating π toplaces is now a trivial matter using a computer algebra package such as Maple. Shanks spent many long tedious days calculating; he would calculate new digits all morning and then he would spend all afternoon checking his morning's work. Now at a press of a button we getplaces:Shanks died in Juneand was buried at Houghton Hillside Cemetery onJune.