märts 14, 2008

Pii päev




Kristjan Jaak sündis matemaatiliselt põneval kuupäeval, vähemalt ameerika kirjaviisis kirjutatuna: 3.14.1801
Veel põnevam on see, et samale kuupäevale oskasid oma sünnid sättida nii Albert Einstein (1879) kui ka poola matemaatik Waclaw Sierpinski.
20 aastat tagasi, 1988 tähistati aga esimest korda tõsiselt pii päeva San Franciscos.
Idee algatajaks oli füüsik Larry Shaw.
Ameerikas on tavaks saanud sellel päeva korraldada võistlusi pii auks ja hüvanguks pii numbrikohtade meeldejätmisel.
See võiks ka meil saada väärikaks traditsiooniks! Mitte midagi ei keela ära ühel ja samal päeval pidada nii oma ilusa keele päeva, kui ka sellele ilusale ja põnevale matemaatilisele konstandile pühendatud pidu.

Hakatuseks toon veel kord ära (Ramanujanile pühendatud kirjutises on see juba olemas) pii esimesed 767 numbrikohta, kuni Feynmani punktini.

π = 3.

1415926535897932384626433832795028841971693993751058209749445923 0781640628620899862803482534211706798214808651328230664709384460 9550582231725359408128481117450284102701938521105559644622948954 9303819644288109756659334461284756482337867831652712019091456485 6692346034861045432664821339360726024914127372458700660631558817 4881520920962829254091715364367892590360011330530548820466521384 1469519415116094330572703657595919530921861173819326117931051185 4807446237996274956735188575272489122793818301194912983367336244 0656643086021394946395224737190702179860943702770539217176293176 7523846748184676694051320005681271452635608277857713427577896091 7363717872146844090122495343014654958537105079227968925892354201 995611212902196086403441815981362977477130996051870721134999999

Nii et üllatusena ei ole Feynmani punkt mingi kvantmehhaaniline koht universumis, vaid koht pii numbrite jadas, kus esimest korda esineb KUUS üheksat.
Tõenäosusteooria järgi peaks see olema pi algusest üsna kaugel, tegelikult aga tulevad need üheksad 762-ndast numbrikohast kuni 767-nda komakohani.
Feynman olla selle kohta visanud nalja ühel loengul, märkides,
et pii-d meelde jätta ei olegi nii raske, piisab esimesest 762 st komakohast,
et edasi öelda üheksa, üheksa, üheksa, üheksa, üheksa, üheksa ja nii edasi...

Kuidas aga seda numbrirodu kergemini meelde jätta?

Igal rahval, välja arvatud eestlased, on selleks olemas teatud salmid ja lausungid, mis memoriseerimist kergendavad:

Piirdume inglastega ja albaanlastega:

Inglise füüsikatudengeil on käibel selline fraas:

How I need a drink, alcoholic in nature, after the heavy lectures involving quantum mechanics!

(pärast kõvat kvantmehaanika loengut vajan hädasti jooki, kuna olen olemuselet alkohoolik).

Albaanlased on pii jaoks välja mõelnud sellise fraasi:

Kur e shoh e mesoj sigurisht

(kui ma seda näen, jätan selle kindlasti meelde).

Seni ületamatuks saavutuseks pean luuletust "Near a Raven", Edgar Allan Poe Kaarna (Raven) auks kirjutatud 1995 Mike Keith poolt.
Vähe sellest, et iga sõna kodeerib ühte pii märki, kuni 740-nda komakohani - see luuletus üritab sarnaneda ka Kaarnaga üldmeeleolus ja värsistuseski!

Kui sõna pikkus on 10 märki, tähistab see 0-i, pikemad sõnad märgivad ära 2 komakohta.

Poe, E.
Near a Raven

Midnights so dreary, tired and weary.
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap - the weirdest tap!
An ominous vibrating sound disturbing my chamber's antedoor.
"This", I whispered quietly, "I ignore".

Perfectly, the intellect remembers: the ghostly fires, a glittering ember.
Inflamed by lightning's outbursts, windows cast penumbras upon this floor.
Sorrowful, as one mistreated, unhappy thoughts I heeded:
That inimitable lesson in elegance - Lenore -
Is delighting, exciting...nevermore.

Ominously, curtains parted (my serenity outsmarted),
And fear overcame my being - the fear of "forevermore".
Fearful foreboding abided, selfish sentiment confided,
As I said, "Methinks mysterious traveler knocks afore.
A man is visiting, of age threescore."

Taking little time, briskly addressing something: "Sir," (robustly)
"Tell what source originates clamorous noise afore?
Disturbing sleep unkindly, is it you a-tapping, so slyly?
Why, devil incarnate!--" Here completely unveiled I my antedoor--
Just darkness, I ascertained - nothing more.

While surrounded by darkness then, I persevered to clearly comprehend.
I perceived the weirdest dream...of everlasting "nevermores".
Quite, quite, quick nocturnal doubts fled - such relief! - as my intellect said,
(Desiring, imagining still) that perchance the apparition was uttering a whispered "Lenore".
This only, as evermore.

Silently, I reinforced, remaining anxious, quite scared, afraid,
While intrusive tap did then come thrice - O, so stronger than sounded afore.
"Surely" (said silently) "it was the banging, clanging window lattice."
Glancing out, I quaked, upset by horrors hereinbefore,
Perceiving: a "nevermore".

Completely disturbed, I said, "Utter, please, what prevails ahead.
Repose, relief, cessation, or but more dreary 'nevermores'?"
The bird intruded thence - O, irritation ever since! -
Then sat on Pallas' pallid bust, watching me (I sat not, therefore),
And stated "nevermores".

Bemused by raven's dissonance, my soul exclaimed, "I seek intelligence;
Explain thy purpose, or soon cease intoning forlorn 'nevermores'!"
"Nevermores", winged corvus proclaimed - thusly was a raven named?
Actually maintain a surname, upon Pluvious seashore?
I heard an oppressive "nevermore".

My sentiments extremely pained, to perceive an utterance so plain,
Most interested, mystified, a meaning I hoped for.
"Surely," said the raven's watcher, "separate discourse is wiser.
Therefore, liberation I'll obtain, retreating heretofore -
Eliminating all the 'nevermores' ".

Still, the detestable raven just remained, unmoving, on sculptured bust.
Always saying "never" (by a red chamber's door).
A poor, tender heartache maven - a sorrowful bird - a raven!
O, I wished thoroughly, forthwith, that he'd fly heretofore.
Still sitting, he recited "nevermores".

The raven's dirge induced alarm - "nevermore" quite wearisome.
I meditated: "Might its utterances summarize of a calamity before?"
O, a sadness was manifest - a sorrowful cry of unrest;
"O," I thought sincerely, "it's a melancholy great - furthermore,
Removing doubt, this explains 'nevermores' ".

Seizing just that moment to sit - closely, carefully, advancing beside it,
Sinking down, intrigued, where velvet cushion lay afore.
A creature, midnight-black, watched there - it studied my soul, unawares.
Wherefore, explanations my insight entreated for.
Silently, I pondered the "nevermores".

"Disentangle, nefarious bird! Disengage - I am disturbed!"
Intently its eye burned, raising the cry within my core.
"That delectable Lenore - whose velvet pillow this was, heretofore,
Departed thence, unsettling my consciousness therefore.
She's returning - that maiden - aye, nevermore."

Since, to me, that thought was madness, I renounced continuing sadness.
Continuing on, I soundly, adamantly forswore:
"Wretch," (addressing blackbird only) "fly swiftly - emancipate me!"
"Respite, respite, detestable raven - and discharge me, I implore!"
A ghostly answer of: "nevermore".

" 'Tis a prophet? Wraith? Strange devil? Or the ultimate evil?"
"Answer, tempter-sent creature!", I inquired, like before.
"Forlorn, though firmly undaunted, with 'nevermores' quite indoctrinated,
Is everything depressing, generating great sorrow evermore?
I am subdued!", I then swore.

In answer, the raven turned - relentless distress it spurned.
"Comfort, surcease, quiet, silence!" - pleaded I for.
"Will my (abusive raven!) sorrows persist unabated?
Nevermore Lenore respondeth?", adamantly I encored.
The appeal was ignored.

"O, satanic inferno's denizen -- go!", I said boldly, standing then.
"Take henceforth loathsome "nevermores" - O, to an ugly Plutonian shore!
Let nary one expression, O bird, remain still here, replacing mirth.
Promptly leave and retreat!", I resolutely swore.
Blackbird's riposte: "nevermore".

So he sitteth, observing always, perching ominously on these doorways.
Squatting on the stony bust so untroubled, O therefore.
Suffering stark raven's conversings, so I am condemned, subserving,
To a nightmare cursed, containing miseries galore.
Thus henceforth, I'll rise (from a darkness, a grave) -- nevermore!

Lõpuks üleskutse programeerijaile: äkki viitsiks keegi kodeerida ja siis netti üles riputada pii memoriseerimise kontrolliks mingisuguse miksikese pealt tuntud pranglimisega analoogilise vidina. Siis saaksid parimad mälumängurid ennast testida, kas nad jõuavad kohani,
kus saaksid uhkelt öelda.

üheksa, üheksa, üheksa, üheksa, üheksa, üheksa, ja nii edasi....

Ise olen ajapuudusest (loe laiskusest) selle tänaseks tähtpäevaks tegemata jätnud.

Ja üleskutse poeetidele:kirjutada midagi "Near a Raven"-le ligilähedast kaunis eesti keeles, jäädvustades oma nime nii eesti keele kui pii ajalukku.
Kauneim oleks, kui see osaliseltki saaks teoks veel tänase tähtsa päeva jooksul?

Lõpuks Pii neile, kes rohkem meelde jätta ei viitsi.

Kõikides praktilistest situatsioonides piisab ümbermõõdu saamiseks sellest, kui korrutada dimeeter KOLMEGA (ka Piibel ja Talmud on sama usku).

Edasijõudnud kasutagu murdu 22/7 ja eriti nutikad 355/113, hiinlastele hästi tuntut lähendit.

LINGID:

1. Pii päevast:

http://www.exploratorium.edu/pi/

2. Memoriseerimie nõksudest:

http://www.freewebs.com/howtomemorizepi/

3. Pii poeesiast

a) Mike Keithi pikk luuletus
"Near a Raven "...

http://users.aol.com/s6sj7gt/mikerav.htm

tema kodulehekülg, kus veel mõnda huvitavat leida, incl raamatud

http://users.aol.com/s6sj7gt/mikehome.htm#toc

vrdl. Poe originaalpoeemiga

http://www.heise.de/ix/raven/Literature/Lore/TheRaven.html

"Kaarna" Eestikeelsed tõlked on olemas, kuid netist ma neid ei leidnud. Otsige, raamatuogust leiate!

b) Muid luuletusi

http://www.eveandersson.com/pi/poetry/

c,d ... Jätkake ise googlega pi poems teemal.

4. Pii kohta ühte kui teist huvitavat ja harivat

a)

http://personal.bgsu.edu/~carother/pi/Pi1.html

b) http://www.mobot.org/education/megsl/pi.html

ja nii edasi ja nii edasi.

5. Feynmani punkt:

http://mathworld.wolfram.com/FeynmanPoint.html


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1 Comments:

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märts 19, 2008 4:31 AM  

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