By Jonathan Borwein

How will 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 commentary that used to be serious within the improvement of 19th century research. How can we make a decision that this kind of quantity is basically a distinct worth of a well-recognized functionality with out the instruments Gauss had at his disposal, which have been, most likely, 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 effectively, like a opposite guide of particular 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 distinct values of customary capabilities. it's designed for individuals, like ourselves, who come upon numerous numbers computationally and wish to understand if those numbers have a few easy 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. hence the record is comprised essentially of exact functionality reviews at a variety of algebraic and easy transcendental values. the precise numbers incorporated are defined less than. each one access includes the 1st 8 digits after the decimal element of the quantity in question.

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Additional resources for A Dictionary of Real Numbers

Example text

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!

5 0422 9559 eu : 1/2 - 2V3 0423 2462 t7r : 7r 2/6 0423 3510 r : v'2 - V3 - V6 04234965 J2 : 1/ln{2e) 04235138 flO :,7f/2/8 04235364 sr : v'2/2 + 2V3 0423 7846 rt : (2,4,-7,-2) 0423 9044 J 2 : 13/22 0424 0759 ( : 4/11 0424 1445 e'" : 15/2 0424 1563 rt : (4,9,-8,5) 0424 1687 0424 1687 II! /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!

3/3 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!