Charles T. Gidiney

Charles T. Gidiney
Members of the Official Board of the A.M.E. Zion Church, and Trustees in Trust, 1887-88; "C. T. Gidney" is on the front row, third from the right
Born	(1813-09-05)September 5, 1813 Milton, New York, US
Disappeared	June 4, 1900 (aged 86) Milton, New York, US
Other names	Charles F. Gidiney; Chas T. Gidiney; Charles T. Gideney; Charles T. Gidney; C. T. Gidney; Charles L. Gedney
Ethnicity	African American
Occupation	Laborer; Whitewasher; Class Leader; Sexton
Known for	Untrained mathemathian who discovered a unique algebraic equation to determine the value of π
Home town	Troy, New York, US
Denomination	African Methodist Episcopal Zion Church[1]
Spouse(s)	Thodosia Ball (married March 20, 1837); Harriet A. Gidiney (married 1855 - September 11, 1890)
Children	John T. Gidiney Melicia Johnson

Charles T. Gidiney (September 5, 1813 – June 1900) was an untrained African-American mathematician who made his living as a whitewasher. He became a local celebrity when he claimed to have found an algebraic formula for the value of π. Though his suggestions proved incomplete, he furthered scientific discussions with a formula that has been since used in other studies.^[2]

Personal Life

Gidiney and his wife, Harriet, were members of the African Methodist Episcopal (A.M.E.) Zion Church of Seventh Street in Troy, New York.

Life in documents

Most of Gidiney's life can be found in official records, but unintended modifications to his name may prove research difficult.

1840s

The first document to mention Gidiney (27 years old) is the Federal Census of 1840, who was listed as the head of a household of nine unnamed “free colored people”,^[3] the largest of its kind in the Shaker community of New Lebanon, New York. Gidiney decided to move to Troy around that time, where the abolitionist paper National Watchman was established two years later and where the first Negro State Convention and play Tom Shows, based on the 1852 book Uncle Tom's Cabin, were held.

1850s

A decade later, records stated that Gidiney (37) the “laborer” was born in 1813 New York and likely had a son, John T. Gidiney (11), while in the Third Ward of the City of Troy. The Gidineys lived with two other household members: Anna Hardy (3), the only one from Pennsylvania, and Mary C. Hardy (22).^{[4][lower-alpha 1]} The 1855 census of New York was the first to mention Harriet A. Gidiney (36) of Schoharie County as Gidiney's wife while Gidiney's birthplace was pinpointed at Columbia County, his year of birth in 1815, his residence at the First Ward of the City of Troy, and his job as a whitewasher. Both have lived in Troy for 2 years and Harriet was illiterate.^[5]

1860s

In 1860, Chas T. Gidiney (45), still recorded as born in 1815, but residing in the Seventh Ward this time,^[6] was in proximity of Harriet Tubman, who was on her way to an abolitionist meeting in Boston. A year later, Gidiney shows up in the Troy City directory “as a whitewasher...living at house number 156 Green”^[1] and continued living there up to 1868.^{[lower-alpha 2]} The 1865 census of New York lists the Gidineys still living in the Seventh Ward, each having been married twice with at least one child, and is the only census to have dated Charles' birth back to 1808 instead of 1813 and located Harriet's birthplace to Broome.^[7][8]

Gidiney sent a letter to the mayor of Troy on July 18, 1863 in the wake of the draft riots during the Civil War, where civilians either joined the Union Army or paid $300 in support. Possibly preserved at the Rensselaer County Historical Society, the letter was an appeal to stop the mob, where rioters consisting mostly of Irish-Americans infiltrated the city of Troy from factories to the Troy Daily Times' offices. He writes:

As I learn that you are in town I now inform you of my Grief, and no doubt all the rest of my people are under the same grievances. I have been advised by white gentlemen and ladies for to stay in my house and not to be seen in the streets because it is not safe the Irish mob was going about seeking the coloured peoples lives. Since the mob, I cannot go out to get groceries but there is something thrown at my head, I have been staying in my house for two days. And we are afraid of our lives being destroyed. Therefore I now pray to you for protection so that I may walk the streets undisturbed you know that I cannot live without my daily labor. And when I pass through the streets I heard them say Kill the Nigger, Kill the Nigger, Kill the Nigger. And even yesterday little boys stood before my door at a short distance and my wife stood in her door, and there they stood with clubs and saying Nigger, Nigger, Shaking their clubs at her and etc. I pray you to forthwith put out a proclamation against all such offenses so that we Coloured people may walk the street in perfect Peace and etc.

Yours most respectably etc.,

Chas. T Gidiney^{[9][lower-alpha 3]}

1870s

In 1870, Gidney^{[lower-alpha 4]} (56) of Rensselaer, about 9 miles away from Troy, lived alone with Harriet (52), a real estate value of $2,000, and a personal estate value of $200. Two years later, the Troy City directory found them at 52 North Third Street and continued to list that information for several more years. Then the 1875 New York census renamed the Gidineys to Charles L. Gedney (62)^{[lower-alpha 5]} and Harretta Gedney (58). The census also added a 17-year-old “daughter”, Melicia Johnson, and a 52-year-old “broader”, William H. Brown, to the household,^[10] which is the only time they appear in records with the Gidiney family. Troy's directory in 1877 listed Gidiney as “Gideney”.^[11]

1880s

Religious activity started to appear in the Gidineys' records around the 1880s. Gidiney had already been a vice president of the “Seventh street Methodist church” for 4 years.^[12] In 1884, Mrs. Harriet Gidiney became “president of the Female Benevolent Society, a society for African American women that met the 'First Tuesday evening of each month.'”^[1] In March 27, 1886, the New York Freeman reported that Charles Gidiney was elected for the board of trustees of the A.M.E. Zion Church of Seventh Street (est. 1830s), which was well known for its archive of literacy and even held some math lectures. For two years after that, the Gidiney couple were recorded as members of the church, including Charles as a “Class Leader”.^[13] During that time, the Gidineys moved to 2168 Sixth Ave, where they stayed for 6 years with a property value of $1,000.

1890s

Harriet Gidiney (72) suddenly died four days after Charles' birthday party (September 5, 1890) and the church held her funeral at 3 p.m. in September 11,^[14] led by Rev. Decker and pastor Rev. Geo. E. Smith. A year later, Gidiney was invited for dinner at the Bingham house on 1632 Sixth Avenue. In the city directories of 1893 and 1895, Gidiney appeared as a sexton, but was also noted as the chairman of the A.M.E. Zion church in 1894.^[15]

1900s

It was eventually around June 1900 when the last details of widowed “Charles F. Gidiney”^{[lower-alpha 6]} were documented on a ward census in Milton, about 30 miles away from Troy. The census also pointed out that neither Gidiney, nor the people in the ward, save for one, had ever attended school,^[16] which was already noted in the news.^[17]

Periodical records

Despite the abundance of newspapers that mentioned Gidiney, he was still little-known among a number of Gidneys and African-American mathematicians. The first paper to ever mention Gidiney is in the Troy Daily Whig of March 30, 1837, when he married Thodosia Ball ten days before, led by Reverend Daniel Vandervere.^[18][19]

Mathematics

On the matter of π

On October 20, 1877, the Troy, New York, Daily Times' Saturday afternoon paper reported that Gidiney “discovered the true and exact ratio between the diameter and circumference of a circle”, known as π today. Two days later, the New York Times republished that article as “A Negro Mathematician's Claim”.

The Troy Times of Saturday says: “A colored man named Gidney, residing on North Third street, below Jacob, claims to have discovered the true and exact ratio between the diameter and circumference of a circle. According to the accepted rule, with the diameter or circumference alone given, the other cannot be exactly told. The ratio is 3.14159 plus, or as commonly used, 3.1416 plus. Mr. Gidney claims that by an algebraic calculation he has discovered the exact ratio, and he has in preparation a book on the subject which he intends shortly to publish. The demonstration of this interesting discovery is now receiving the attention of competent mathematicians, and whether it amounts to anything or not will soon be determined. Mr. Gidney possesses little or no education except in mathematics, and in this branch it is said he is able to solve most difficult problems.”^[17]

So far, no book under Gidiney's writing has been found, giving the impression that he never got to publish it. The New York Times republished another Troy Times article exactly a year after the original article above under "A Colored Man's Solution".

Now, take two different circles. Let the letter w represent the diameter and the letter x the circumference of one circle; and the letter y the diameter and the letter z the circumference of the second circle. From this, we form the proportion w:x::y:z. Reducing this, we find that wx=yz, and these products must always be equal. Thus we see that if we take any two different circles, and multiply the diameter of the first by the [circumference] of the second, and the circumference of the first by the diameter of the second, these products will be exactly equal. In illustration of this Mr. Gidiney takes two circles; the diameter of the first he considers 113 feet, and the diameter of the second 7. By a long series of ingeniously-constructed equations he finds the exact circumferences of these circles to the 348 5*12 and 21 7*12 respectively, or 113:348 5*12 : : 7:21 7*12. Reduce this, and 2,438 11*12 = 2,438 11*12. In solving this and kindred problems, Mr. Gidiney uses over 1,350 different equations, all of which prove themselves correct from beginning to end. Another, as 7:21 7*12 : : 7 5*37:22. Multiplying the means and the extremes to-gether, their products will be exactly equal. Thus 7 5*37x21 7*12=7x22, or 154 equals 154.^[20]

Various newspapers shared the news over time in different ways, including

• Indianapolis Sentinel (Indiana) – October 24, 1877
• Jersey Journal (New Jersey) – October 29, 1877
• Weekly Louisianian (New Orleans) – November 3, 1877
• The Troy Evening Standard (New York) – October 2, 1878^{[lower-alpha 7]}

The Historic Magazine and Notes and Queries compared Gidiney's result from this article (3.15135+) with others' finds and was not one of the twenty who got the first 13 digits correct.^[22] Nevertheless, an uneducated person reaching this close to the answer of π is rare.

• The Chicago Tribune (Illinois) – October 26, 1878^[23]
• The Valley Republican (Kinsley, Kansas) – November 2, 1878^[24]
• Arkansas City Weekly Traveler (Kansas) – November 6, 1878^[25]
• Belleville Telescope (Kansas) – November 7, 1878^[26]
• The Osage City Free Press (Kansas) – November 8, 1878^[27]
• St. Albans Daily Messenger (Vermont) – March 1, 1879
• The Rome Sentinel (New York) - March 4, 1879

C. T. Gidiney,^{[lower-alpha 8]} of Troy, N.Y., a poor man more than sixty years old, announces that he has discovered the ratio between the diameter and circumference of a circle, and that it is worked out by laws immutable. Jealous of his discovery[,] he is guarding it until he can secure the protection of the law to prevent others from wresting it from him.^[28]

• The Athens Messenger (Ohio) – March 6, 1879^[29]
• State Journal (Harrisburg) – July 26, 1884

Other publications

On February 11, 1843, Gidiney published a formula to extract the fourth root under “A Concise Formula to Extract the Fourth Root: Example” in The New York State Mechanic, a Journal of the Manual Arts, Trades, and Manufactures. Interestingly, he writes from New Lebanon Springs, also about 30 miles away from Troy.

RULE.–Separate the given number into periods, of four figures each, by putting a point over the unit figure, and every fourth figure from the place of units to the left, and if there be decimals, to the right hand. Find the greatest biquadrate in the left hand period, and place its root in the quotient. Subtract the biquadrate thus found from the said period, and to the remainder bring down the next period, calling this the dividend. Multiply the cube of the quotient by 4000, calling it the imperfect divisor. Find how often the imperfect divisor may be had in the dividend, and place the result in the quotient. Then multiply the square of the former quotient by the last quotient figure, and that product by 600, calling it the first triple product, and place it under the imperfect divisor; then multiply the square of the last quotient figure by the former quotient, and that product by 40, calling it the second triple product, and place it under the first triple product; then cube the last quotient figure, and place it under the second triple product, and the sum of these four called a perfect divisor. Multiply the perfect divisor by the last quotient figure, calling the product the subtractend. Place this regularly under the dividend, and subtract, bring down the next period for a new dividend. Then to find another imperfect divisor, (instead of cubing the quotient and multiplying it by 4000,) add to the last perfect the first triple product, and twice the second triple product, and three times the cube of the last quotient figure, placing three cyphers to the right hand of their sum. Then proceed as above directed, remembering at every period brought down to find your imperfect divisor, according to the above direction.^[30]

Other mentions

The Troy Daily Times put his name in a “list of letters remaining in the Troy Post Office, May 16, 1853,”^[31] placed his real estate under two city tax sales in 1872^[32][33] and a county tax sale in 1876.^[34] The paper also posted Gidiney's ad for whitewashing under the Miscellaneous section in May 11, 1885.^[35] The property of Gidiney's wife, located in the Third Assessors' District, was also posted in county tax sales: one in 1893 for $22.47^[36] and in 1901 for $9.40.^[37]

Notes

References