By Jonathan Borwein

ISBN-10: 1461585104

ISBN-13: 9781461585107

ISBN-10: 1461585120

ISBN-13: 9781461585121

How can we realize that the quantity . 93371663 . . . is basically 2 IoglQ(e + 7r)/2 ? Gauss saw that the number one. 85407467 . . . is (essentially) a rational worth of an elliptic integral-an statement that used to be serious within the improvement of 19th century research. How can we make a decision that any such quantity is absolutely a unique price of a well-known functionality with out the instruments Gauss had at his disposal, that have been, possibly, extraordinary perception and a prodigious reminiscence? a part of the reply, we are hoping, lies during this quantity. This ebook is based like a opposite phone book, or extra adequately, like a opposite instruction manual of designated functionality values. it's a record of simply over 100,000 eight-digit actual numbers within the period [0,1) that come up because the first 8 digits of targeted values of regular capabilities. it truly is designed for individuals, like ourselves, who come upon quite a few numbers computationally and wish to understand if those numbers have a few uncomplicated shape. this isn't a very well-defined endeavor-every eight-digit quantity is rational and this isn't attention-grabbing. even though, the probabilities of an 8 digit quantity agreeing with a small rational, say with numerator and denominator under twenty-five, is small. therefore the record is comprised essentially of specific functionality reviews at a variety of algebraic and easy transcendental values. the precise numbers integrated are defined under. each one access includes the 1st 8 digits after the decimal aspect of the quantity in question.

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**Extra resources for A Dictionary of Real Numbers**

**Sample text**

3/3 04899751 IJ! /3/4 04903883 In( y'2) - exp(1/3) 0490 4339 IJ! /3/2)-1/3 0491 1972 IJ! /3 + 3v'5/4 0492 1818 2X : In 2/10 04923355 sr : /2/4 + 4/5 0492 3431 eu : In(ln 2) 0492 4623 J 1 : In(e/3) 0492 5509 rt : (9,1,-6,3) 0492 5801 Ei : 9/25 0492 5924 eu : e/3 - 37r / 4 0492 6062 rt : (8,2,-9,-2) 0492 7853 lOX : P42 04928002 er : 51n 2/3 04930614 In : (e/3)1/2 0493 0700 J2 : 2/5/7 0493 2594 sr : 1O~/3 04934417 (: (5/3)3 0493 4783 Ei : 2~/7 04935475 at : 1/4 + 2/5/3 0493 6777 rt : (9,2,-4,4) 0493 7336 rt : (8,1,-7,-3) 0493 8271 sq : 2/9 0493 8728 rt : (6,6,-9,8) 04938948 IJ!

2/4 - 3/3 0563495710'" : 7In2/10 05689874 11O : 2(/5/3 05635126 e'" : 5(e + 71")/6 05690262 rt : (3,7,-5,5) 0563 5297 rt : (4,1,3,-9) 0569 0769 rt : (1,7,0,-9) 0569 1237 12 : 3e/2 + 471" 0563 5917 S7l" : 1/4 + /3 05636265 rt : (3,5,1,7) 05691682 II!

2/7 0392 1304 ell : 1/3 + e/4 03922065 sq: 21n2/7 0392 2956 ell : e/8 0392 3048 id : 3v'3/5 03924252 In(2/5) x exp(4/5) 0392 5545 ell : 2 + e 0392 5922 2x : 1/18 0392 6101 In: 2ij3/3 0392 7134 eX : 3/2 + 4V5 0392 0393 0393 0393 0393 0393 0393 0393 0393 0393 0394 8335 In(5) - exp(1/2) 1942 at : 3 - 3v'3/4 3398 sr : 6in 2 5034 J2 : (2e)-1/3 5761 2x : 1/2 + 27r /3 6681 lOX : 4e/3 - 7r 6937 in : 97r /10 7701 J: (/27r)-2 7732 rt : (1,5,0,1) 9825 eX : exp( ij3/3) 1778 J: (27r)-3 03943684 2x : 7e/4 03944761 flO : 3/2 + 3V5 0394 4944 Jo : 6e/7 0394 7882 In(4/5) + exp( v'3) 0394 8057 In : 3 - 3e/4 03948441 Ei: 1/ {fif.

### A Dictionary of Real Numbers by Jonathan Borwein

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