A Dictionary of Real Numbers by Jonathan Borwein

By Jonathan Borwein

How will we realize that the quantity . 93371663 . . . is really 2 IoglQ(e + 7r)/2 ? Gauss saw that the number one. 85407467 . . . is (essentially) a rational price of an elliptic integral-an remark that used to be serious within the improvement of 19th century research. How will 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, most likely, exceptional perception and a prodigious reminiscence? a part of the reply, we are hoping, lies during this quantity. This booklet is dependent like a opposite phone book, or extra safely, like a opposite guide of distinctive functionality values. it's a record of simply over 100,000 eight-digit genuine numbers within the period [0,1) that come up because the first 8 digits of distinct values of normal capabilities. it really is designed for individuals, like ourselves, who come across numerous numbers computationally and wish 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. notwithstanding, the possibilities of an 8 digit quantity agreeing with a small rational, say with numerator and denominator under twenty-five, is small. hence the checklist is comprised essentially of designated functionality reviews at a number of algebraic and straightforward transcendental values. the precise numbers integrated are defined lower than. each one access contains the 1st 8 digits after the decimal element of the quantity in question.

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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!

5/3 0395 4627 lOX : 5Ā«(3)/6 0395 6055 rt : (1,7,1,9) 0395 6923 sq : 4/2/3 - v'3/2 03957858 sq : 5(1/7r)/8 0395 8738 sinh: 10/11 0395 9282 3/5 + exp(e) 03959536 ell : 4e/3 - 37r/4 0395 9651In(2/5) + exp(7r) 0396 0065 ( : 1/ {fif. /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!

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