Following on from the success of yesterday's post which achieved much, another post intimately related in theme to the preceding will follow. Again we are in the realm of the mysterious and esoteric, this time in the infinite form of the square root of two, probably(according to Wikipedia) the first known irrational number.
The discovery of the irrational numbers is usually attributed to the Pythagorean, Hippasus of Metapontum, who produced a proof of the irrationality of the square root of 2, or two. According to one legend, Pythagoras believed in the absoluteness of numbers, and could not accept the existence of irrational numbers. He could not disprove their existence through logic, but his beliefs would not accept their existence and so he sentenced Hippasus to death by drowning. Other legends report that Hippasus was drowned by fanatical Pythagoreans or merely expelled from their circle.
The irrational defence of the falsely imagined rational. Anyway, quite a large number of the opening numbers of the square root of two follow:
1.4142135623730950488016887242096980785696718753769480731766797379907324784621 07038850387534327641572735013846230912297024924836055850737212644121497099935831 41322266592750559275579995050115278206057147010955997160597027453459686201472851 74186408891986095523292304843087143214508397626036279952514079896872533965463318 08829640620615258352395054745750287759961729835575220337531857011354374603408498 84716038689997069900481503054402779031645424782306849293691862158057846311159666 87130130156185689872372352885092648612494977154218334204285686060146824720771435 85487415565706967765372022648544701585880162075847492265722600208558446652145839 88939443709265918003113882464681570826301005948587040031864803421948972782906410 45072636881313739855256117322040245091227700226941127573627280495738108967504018 36986836845072579936472906076299694138047565482372899718032680247442062926912485 90521810044598421505911202494413417285314781058036033710773091828693147101711116 83916581726889419758716582152128229518488472089694633862891562882765952635140542
If this has whetted your appetite, all of the first million of the square root of two's digits can be enjoyed at your lesure here, and remember this is but a prologue to an infinity of digits which one could literally spend one's lifetime reading. And who could argue that it would be a wasted life?
Incidentally, now might be the time for a confession. This is supposed to be mathematics at its height, and yet I find these numbers to be, if not dull, a little monotonous in their effect. Which isn't to suggest the fault is any but mine own.
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4 comments:
This is a glimpse into a rarefied intellectual world in whose existence I had not dared to believe.
I never suspected there were so many numbers.
Are you sure you're not really a fascist?
Is it by intent that the internal structure of your finely wrought sentences mysteriously echo the contrapuntal harmonies of the great music of the Baroque period?
Your words as opposed to Elberry's, whoom I suspect to be a counter-revolutionary.
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