Ten Decimals of π Are Sufficient To Give the Circumference of the Earth To the Fraction of an Inch

Simon Newcomb? John Casey? George McC. Robson? Apocryphal?

Dear Quote Investigator: The number π is a fundamental mathematical constant which equals the ratio of a circle’s circumference to its diameter. Trillions of digits of the decimal expansion of π have been calculated using electronic computers and innovative algorithms. Yet, this precision is not needed in the realm of practical measurement. Simon Newcomb, the prominent astronomer and mathematician, once said something like this:

Ten decimal places of π are sufficient to give the circumference of the earth to a fraction of an inch.

Would you please help me to find a citation?

Quote Investigator: In 1881 Simon Newcomb published “Elements of Geometry” which was based on the foundational tome by Euclid. Here is a passage discussing the calculation of π. The word “computer” refers to a human calculator. Emphasis added to excerpts by QI: 1

This number π is of such fundamental importance in geometry that mathematicians have devoted great attention to its calculation. . . . Dase, a German computer, carried the calculation to 200 places of decimals. The following are the first 36 figures of his result:

3.141 592 653 589 793 238 462 643 383 279 502 884.

The result is here carried far beyond all the wants of mathematics. Ten decimals are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful microscope.

The emphasized text above differs slightly from the modern quotation because it does not repeat the term π.

Below are additional selected citations in chronological order.

Continue reading Ten Decimals of π Are Sufficient To Give the Circumference of the Earth To the Fraction of an Inch

Notes:

  1. 1881, Elements of Geometry by Simon Newcomb (Professor of Mathematics, United States Navy), Book VI: Regular Polygons and the Circle, Problem VII, Quote Page 235, Henry Holt and Company, New York. (Google Books Full View) link