By Jonathan Borwein

How can we realize that the quantity . 93371663 . . . is de facto 2 IoglQ(e + 7r)/2 ? Gauss saw that the #1. 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 come to a decision that this sort of quantity is admittedly a unique worth of a well-recognized functionality with no the instruments Gauss had at his disposal, that have been, most likely, extra special perception and a prodigious reminiscence? a part of the reply, we are hoping, lies during this quantity. This e-book is based like a opposite phone book, or extra effectively, like a opposite instruction manual of precise 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 particular values of usual services. it's designed for individuals, like ourselves, who come upon numerous numbers computationally and need to grasp if those numbers have a few basic shape. this isn't a very well-defined endeavor-every eight-digit quantity is rational and this isn't attention-grabbing. even though, the possibilities of an 8 digit quantity agreeing with a small rational, say with numerator and denominator below twenty-five, is small. hence the record is comprised basically of particular functionality reviews at numerous algebraic and easy transcendental values. the precise numbers integrated are defined less than. each one access involves the 1st 8 digits after the decimal aspect of the quantity in question.

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Extra info for A Dictionary of Real Numbers

Sample text

FiI 0567 6970 eu : 4 - 4V5/3 0562 4372 V5 + exp{3/4) 05678554 II! /2/4 - 3/3/4 0562 6823 J 2 : 13/19 0568 2553 2'" : 3 + 3e/2 05627289 II! /2/2 0563 2557 II! /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!

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! /19/2 0557 2809 sq : 2 - V5 05573065 eu : 6{1/7I")/5 05573997 II!

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!