A Dictionary of Real Numbers by Jonathan Borwein

By Jonathan Borwein

How will we realize that the quantity . 93371663 . . . is admittedly 2 IoglQ(e + 7r)/2 ? Gauss saw that the #1. 85407467 . . . is (essentially) a rational worth of an elliptic integral-an commentary that used to be serious within the improvement of 19th century research. How will we make a decision that this sort of quantity is basically a different worth of a well-recognized functionality with out the instruments Gauss had at his disposal, that have been, possibly, out of the ordinary perception and a prodigious reminiscence? a part of the reply, we are hoping, lies during this quantity. This booklet is established like a opposite phone book, or extra safely, like a opposite instruction manual of exact functionality values. it's a checklist of simply over 100,000 eight-digit actual numbers within the period [0,1) that come up because the first 8 digits of distinctive values of time-honored capabilities. it really is designed for individuals, like ourselves, who stumble upon numerous numbers computationally and need to understand 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. besides the fact that, the probabilities of an 8 digit quantity agreeing with a small rational, say with numerator and denominator under twenty-five, is small. hence the record is comprised basically of specific functionality reviews at numerous algebraic and easy transcendental values. the precise numbers integrated are defined under. each one access involves the 1st 8 digits after the decimal aspect of the quantity in question.

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5 0436 5296 r : 27r /3 0432 3757 t7r : (27r)-1/2 0436 6509 J2 : 3/5 0432 4077 sq : 31n 2/10 0436 7169 sq : 3/4 + e/4 0432 6528 2x : 3 + 3e 0436 8021 II! /5/2 0444 3125 II! /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!

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!

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!

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