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The Dalzell-Integral reads:

$$0<\int_0^1\frac{x^4(1-x)^4}{1+x^2}dx=\frac{22}{7}-\pi$$

It proves that $\pi<\frac{22}{7}$.

See also Wikipedia. It was introduced by D.P.Dalzell in 1944 (see Wikipedia).

My question: Who was D.P. Dalzell? Any information on him or her?

L. Milla
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1 Answers1

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In the Paul J. Nahin's book Inside Interesting Integrals, p. 24, it is said

The author of the 1944 paper that first published this gem was D. P. Dalzell, a curious fellow who is mostly a ghost in the history of mathematics. All of the modern references to Dalzell’s integral make no mention of the man, himself, even though he wrote a number of high quality mathematical papers and had an excellent reputation among mathematicians. Dalzell didn’t help his cause by his habit of always using his initials. In fact, he was Donald Percy Dalzell (1898–1988), who graduated in 1921 from St. John’s College, Cambridge, in mathematics and mechanical sciences. He received an MA degree in 1926, and his career was not as a mathematician but rather as a chartered engineer (a term used in England for a masters level professional engineer). He worked for a number of years for the Standard Telephones and Cables Company in London, and had two patents on electrical communication cables. The only known photograph of him is the one on the MacTutor math web-site (taken at the 1930 Edinburgh Mathematical Society Colloquium at St. Andrews).

Andrew
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