Source: Encyclopedic Dictionary of Mathematics, The Mathematical
Society of Japan (Cambridge, Mass.: MIT Press, 1980);
cited in Maor, E.,
e: The Story of a Number, Princeton NJ: Princeton Univ. Press, 1994, p.
2. Another representation of e, the base of natural logarithms, is as
exponentiation involving only a few digits, namely:
This is due to Brewster, G.W. The Mathematical Gazette, 25-263, 49,
It was cited in Gaither, C. C. and Cavazos-Gaither, A. E.,
Speaking, A Dictionary of Quotations,
For clarity. Note that the exponent for 2 is 5/2 raised to the 2/5.
3. The online calculator at
1.638721270700128 for the sq root of e, and
1.280125490215755 for the sq root of sq root of e if you input
this e approximation: 2.7182818284590452.
4. The fourth root of e, e^0.25, from a TI-81 hand calculator is about
5. In email to the NCTM-L mailing list Han Sah
commented on a property of e, that Martin Gardner wrote of in the context of
"six major discoveries of 1974" (Gardner, M., Scientific American, April
1975), indicating that the article was was an April fool's joke and the
specific statement of interest here, the integer nature of an expression
below (following from the fact that it was said by Gardner to terminate
in an infinite number of nines), was false.
If e(pi*sqrt) isn't actually
integer, it has an interesting property that
Ramanujan knew about.
The "first 12 digits after the decimal point are 9's" (Sah,
http://cq-pan.cqu.edu.au/schools/smad/mc_rc.html, accessed 10/31/03) but not the 13-th.
6. A word mnemonic for e follows.
Take the portrait of Andrew Jackson. There are two things about it. He
was the seventh president of the United States. He was elected in 1828.
He was installed in office in 1828. If you cut it on a diagonal you get
a 45-90-45 triangle.
2.718281828459045 is accurate to a large number of
digits (see 1.).