Pi, número irracional
Pi = 3,141592535897932384626433832795028841971693993751058...,
Para a maioria dos cálculos simples é comum aproximar π por 3,14.
Uma boa parte das calculadoras científicas de 8 dígitos aproxima π 3,1415927.
Na ciência, é comum usar com 52 casas decimais.
Para cálculos ainda mais precisos, pode-se obter aproximações de π através de algoritmos computacionais (Shigeru Kondo e Alexander Yee apresentaram, em 2011, Pi com 10.000.000.000.000 casas decimais).
Pi = 3,141592535897932384626433832795028841971693993751058...,
Para a maioria dos cálculos simples é comum aproximar π por 3,14.
Uma boa parte das calculadoras científicas de 8 dígitos aproxima π 3,1415927.
Na ciência, é comum usar com 52 casas decimais.
Para cálculos ainda mais precisos, pode-se obter aproximações de π através de algoritmos computacionais (Shigeru Kondo e Alexander Yee apresentaram, em 2011, Pi com 10.000.000.000.000 casas decimais).
Poe, Edgar Allan (1809-1849): Near a Raven
Escritor e poeta americano. Criou um poema mnemónico para o valor de Pi, com 740 casas decimais:
Poe (3), E.(1)
Escritor e poeta americano. Criou um poema mnemónico para o valor de Pi, com 740 casas decimais:
Poe (3), E.(1)
Near(4) a(1) Raven(5)
Midnights (9) so (2) dreary (6), tired (5) and (3) weary(5).
Silently (8) pondering(9) volumes(7) extolling (9) all (3) by (2) –now (3) obsolete(8) lore(4).
During (6) my (2) rather (6) long (4) nap (3) - the (3) weirdest (8) tap! (3)
An (2) ominous (7) vibrating (9) sound (5) disturbing (0) my (2) chamber's (8) antedoor.(8)
"This"(4), I (1) whispered (9) quietly (7), "I (1) ignore" (6).
Silently (8) pondering(9) volumes(7) extolling (9) all (3) by (2) –now (3) obsolete(8) lore(4).
During (6) my (2) rather (6) long (4) nap (3) - the (3) weirdest (8) tap! (3)
An (2) ominous (7) vibrating (9) sound (5) disturbing (0) my (2) chamber's (8) antedoor.(8)
"This"(4), I (1) whispered (9) quietly (7), "I (1) ignore" (6).
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.
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."
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.
"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.
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".
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".
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".
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' ".
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".
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' ".
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".
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."
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".
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.
"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.
"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".
"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!
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!
-- Original: E. Poe
-- Redone by measuring circles.
-- Redone by measuring circles.