“pie” - a new “very large number”

7/21/2019 PIE - a new Very Large Number

1/10

WN@K H`w T`ry Jkra` Hufi`r

khe Fusnhas bh Nhdnhnty

iy Irkej`y Qkjm`rKprnj ;0, 97;0


2/10

Ucns pkp`r ns kibut v`ry jkra` hufi`rs (TJHs) nh tc` s`hs` bd hufi`rs tckt kr` snahndnokhtjy

jkra`r tckh tcbs` brenhkrnjy usè nh `v`ryeky jnd`, jnm` nh snfpj` obuhtnha br nh fbh`tkry

trkhskotnbhs. TJHs bdt`h boour nh dn`jes suoc ks fktc`fktnos, obsfbjbay, oryptbarkpcy, `to.

_bf`tnf`s p`bpj` r`d`r tb hufi`rs ks i`nha "kstrbhbfnokjjy jkra`"= cbw`v`r, nt ns `ksy tb

fktc`fktnokjjy e`dnh` hufi`rs tckt kr` fuoc jkra`r `v`h tckh tcbs` usè nh kstrbhbfy

@xkfpj`s bd TJHs (kpprbxnfkt`) e`sornikij` nh snfpj` t`rfshufi`r bd cufkhs jnvnha nh Nhenk br Ocnhk

;7>hufi`r bd iks` pknrs nh tc` cufkh EHK a`hbf`

;7;7hufi`r bd cufkhs jnvnha bh @krtc

;7;7hufi`r bd ikot`rnk nh tc` cufkh fbutc

;7;7ka` bd tc` Phnv`rs` nh y`krs (ks p`r Ina Ikha fbe`j)

;7;;hufi`r bd tbtkj Cbfb-skpn`hs tckt ckv` `v`r jnvè bh @krtc

;7;;hufi`r bd hùrbhs nh tc` cufkh irknh

;7;;hufi`r bd iks` pknrs nh EHK a`hbf` bd tc` fbst obfpj`x pjkhts / khnfkjs

;7;;sp`è bd jnact nh k vkouuf, nh fnjjnf`t`rs-p`r-sòbhe.

;7;;enstkho` korbss bis`rvkij` Phnv`rs` nh jnact-y`krs

;7;;hufi`r bd akjkxn`s nh tc` bis`rvkij` Phnv`rs`

;7;;hufi`r bd uhnqu` wì pka`s nhe`xè iy Abbaj`

;7;9hufi`r bd stkrs nh tc` kv`rka` akjkxy

;7;?hufi`r bd ourr`htjy-mhbwh enants bd `

;7;?hufi`r bd ikot`rnk bh tc` surdko` bd tc` cufkh ibey

;7;?enstkho` bd k jnact-y`kr, nh mnjbf`t`rs / fnj`s

;7;?enstkho` tb h`kr`st stkr Kjpck O`htkurn, nh mnjbf`t`rs / fnj`s

;7;?hufi`r bd ourr`htjy-mhbwh enants bd (Wn)

;7;?kfbuht bd tc` hktnbhkj eìt bd tc` Phntè _tkt`s, nh ebjjkrs

;7;?hufi`r bd ints bh k obfput`r ckre ensm

;7;5hufi`r bd o`jjs nh tc` cufkh ibey

;7;5hufi`r bd hùrbhkj obhhòtnbhs nh tc` cufkh irknh

;7;5fkss bd kv`rka` fbuhtknh bh @krtc, nh mnjbarkfs


3/10

;7;5ka` bd tc` Phnv`rs` nh cburs (ks p`r Ina Ikha fbe`j)

;7;0hufi`r bd syhkps`s nh tc` cufkh irknh

;7;4hufi`r bd khts bh @krtc kjnv` kt khy bh` tnf`

;7;4tnf` dbr _bjkr _yst`f tb brint Fnjmy Qky Akjkxy, nh sòbhes

;7;4enstkho` tb h`kr`st stkr Kjpck O`htkurn, nh f`t`rs / d``t

;7;4enstkho` bd k jnact-y`kr, nh f`t`rs / d``t

;7;1ka` bd tc` Phnv`rs` nh sòbhes (ks p`r Ina Ikha fbe`j)

;7;>hufi`r bd nhsòts bh @krtc kjnv` kt khy bh` tnf`

;7;>enstkho` tb sup`rankht stkr I`t`jaùs`, nh f`t`rs / d``t

;7;>enstkho` tb Kherbfèk Akjkxy (h`kr`st fklbr akjkxy), nh mf / fnj`s

;7;>enstkho` bd k jnact-y`kr, nh fnjjnf`t`rs

;7;>fkss bd kv`rka` kst`rbne, nh mnjbarkfs

;7;>khsw`r tb tc` wc`kt khe oc`ssibkre prbij`f 6 945

;7;>hufi`r bd endd`r`ht pbsntnbhs bd k ?x?x? Yuinm's Oui`

;7;>hufi`r bd wkys tb `ht`r tc` HOKK Fkroc Fkeh`ss 43-t`kf irkom`t

;7;>hufi`r bd obfput`r trkhsnstbrs prbeuoè wbrjewne` nh 9773

;797ka` bd tc` Phnv`rs` nh fnjjnsòbhes (ks p`r Ina Ikha fbe`j)

;797enstkho` tb o`ht`r bd Fnjmy Qky Akjkxy, nh f`t`rs / d``t

;79;hufi`r bd tbtkj arknhs bd skhe bh @krtcs i`koc`s

;79;fkss bd @krtcs bo`khs, nh mnjbarkfs

;79;hufi`r bd obfput`r trkhsnstbrs ourr`htjy `xnstnha wbrjewne`

;799hufi`r bd pbssnij` >> _uebmu arnes

;79?fkss bd tc` Fbbh, nh mnjbarkfs

;79?hufi`r bd stkrs nh tc` bis`rvkij` Phnv`rs`

;795enstkho` korbss bis`rvkij` Phnv`rs` nh mnjbf`t`rs /fnj`s

;795hufi`r bd ktbfs nh ;9 arkfs bd okribh-;9, Kvbakerb obhstkht

;790fkss bd tc` @krtc, nh mnjbarkfs

;791fkss bd Lupnt`r, nh mnjbarkfs

;791enstkho` korbss bis`rvkij` Phnv`rs` nh f`t`rs / d``t

;793hufi`r bd ktbfs nh tc` cufkh ibey


4/10

;793hufi`r bd uhnqu` ckhes nh ;7-pjky`r akf` bd U`xks Cbje'`f Wbm`r

;793hufi`r bd pbssnij` jàkj pbsntnbhs nh Y`v`rsn / Btc`jjb

;7?7fkss bd tc` _uh, nh mnjbarkfs

;7?7enstkho` korbss bis`rvkij` Phnv`rs` nh fnjjnf`t`rs

;7?;hufi`r bd ikot`rnkj o`jjs bh @krtc

;7?4rktnb bd tc` `jòtrbfkah`tno tb tc` arkvntktnbhkj dbro`s i`tw``h twb prbtbhs

;7?3hufi`r bd Nht`rh`t keer`ss`s or`ktkij` uhe`r tc` NWv4 keer`ssnha syst`f

;7?3hufi`r bd endd`r`ht pbssnij` `horyptnbh-m`ys nh tc` K@_ ;93-int m`y spko`

;75;tc` j`kst obffbh fujtnpj` bd `v`ry nhtà`r drbf ; tb ;77

;759k iklnjjnbh, wcnoc ns kfbha tc` Cbjn`st bd hufi`rs

;754hufi`r bd endd`r`ht pbsntnbhs bd k 5x5x5 Yuinm's Y`v`ha` Oui`

;751hufi`r bd pbssnij` jàkj pbsntnbhs nh oc`ss

;70?fkss (bd brenhkry fktt`r) bd tc` bis`rvkij` Phnv`rs`, nh mnjbarkfs

;703hufi`r bd pbssnij` uhnqu` obfpj`t` akf`s bd Y`v`rsn / Btc`jjb

;703hufi`r bd endd`r`ht pbssnij` `horyptnbh-m`ys nh tc` K@_ ;>9-int m`y spko`

;74;ka` bd tc` Phnv`rs` nh Wjkhom-tnf`-nht`rvkjs (ks p`r Ina Ikha fbe`j)

;743hufi`r bd wkys tb bre`r tc` okres nh k 09-okre eòm

;715hufi`r bd endd`r`ht pbsntnbhs bd k 0x0x0 Yuinm's Wrbd`ssbrsOui`

;711hufi`r bd endd`r`ht pbssnij` `horyptnbh-m`ys nh tc` K@_ 904-int m`y spko`

;737hufi`r bd ktbfs nh tc` bis`rvkij` Phnv`rs`

;73?vbjuf` bd tc` bis`rvkij` Phnv`rs`, nh jnt`rs

;7>4hufi`r bd tbtkj obfinhktnbhs bd 57-ockrkot`r pksswbres

;7;77k abbabj, t`rf obnhè nh ;>97 iy fktc`fktnonkh @ewkre Mksh`r

;7;77eòky tnf` nh y`krs dbr k sup`rfkssnv` ijkom-cbj` bd rbuacjy ; akjkxy-fkss

;7;;4hufi`r bd endd`r`ht pbsntnbhs bd k 4x4x4 Yuinm's T-Oui`-4

;7;9?hufi`r bd pbssnij` uhnqu` obfpj`t` akf`s bd oc`ss

;7;47hufi`r bd endd`r`ht pbsntnbhs bd k 1x1x1 Yuinm's T-Oui`-1

;7;3;hufi`r bd wkys tb krrkha` tc` tnj`s nh @hajnsc _orkiij` bh k ;0x;0 ibkre

;7;30hufi`r bd Wjkhom-vbjuf`s nh tc` bis`rvkij` Phnv`rs`

;7?40hufi`r bd pbssnij` uhnqu` obfpj`t` akf`s bd Ab


5/10

Hbw tckt w`v` jnstè fbst bd tc` TJHs wcnoc kr` e`sornikij` nh snfpj` t`rfs, w` okh iành tb

tkjm kibut `v`h jkra`r hufi`rs khe tc` kpprbkoc tbwkres nhdnhnty

;7?40 (k ; dbjjbwè iy ?40 7s) ns k jkra` `hbuac hufi`r tb `xpr`ss tc` ka` bd tc` Phnv`rs` nh

tc` sfkjj`st tnf`-uhnts w` ckv`, tb `xpr`ss tc` snz` bd tc` Phnv`rs` nh tc` sfkjj`st enstkho`-uhnts

w` ckv`, khe tb `xpr`ss tc` tbtkj pbssnij` p`rfutktnbhs bd tc` fbst obfpj`x akf`s khe `horyptnbhkjabrntcfs tckt cufkhs ckv` nhv`htè tb ekt`. Uc`r`dbr`, fbst p`bpj` wnjj o`rtknhjy h`v`r ckv` k

h`è dbr khy hufi`rs jkra`r tckh tckt, khe jnm`jy wnjj h`v`r `v`h _@@ khy hufi`rs jkra`r tckh

tckt.

Cbw`v`r, tc`r` kr` nhdnhnt`jy-fkhy hufi`rs jkra`r tckh ;7?40, khe tc`y okh a`t sb jkra` tckt tc`y

fkm` ;7?40jbbm fnorbsobpno iy obfpkrnsbh

Bh` suoc `xkfpj` ns Arkckf's hufi`r, hkfè kdt`r Ybhkje Arkckf, wcnoc ns kh upp`r ibuhe

bh tc` sbjutnbh tb tc` dbjjbwnha prbij`f nh Ykfs`y tc`bry33,

r`ke`rs bd tc` Fktc`fktnokj Nht`jjna`ho`r vbtè nt "tc` Fbst I`kutnduj Fktc`fktnokj Dbrfujk

@v`r". (Nfpr`ssnv`jy, @uj`r wks r`spbhsnij` dbr tcr`` bd tc` tbp-dnv` dbrfujk` nh tckt pbjj.)

_b, hbw tckt w` ckv` iòbf` fbr` dkfnjnkr wntc tc` obhstkhts Wn khe @, khe w` ckv` s``h tckt

tc`y okh wbrm ckrfbhnbusjy tba`tc`r, N wbuje jnm` tb suaa`st kh nht`r`stnha h`w us` dbr tc`s`

khon`ht, skorè hufi`rs


8/10

Fbst p`bpj` ebht us` tc` obhstkhts Wn br @nh tc`nr eknjy jnv`s kt kjj. Fkhy p`bpj` ckv` h`v`r v`h

c`kre bd tcbs` t`rfs. Uc` d`w p`bpj` wcb eb us` tcbs` obhstkhts, kr` prbikijy dkfnjnkr wntc usnha

k okjoujktbr, khe kjfbst `v`ry okjoujktbr kjr`key cks iuttbhs dbr tc`s` 9 obhstkhts. Dnhkjjy, `v`h nd

k rkr` p`rsbh wkhtè / h`èè tb mhbw tc`s` hufi`rs, tc`y wbuje prbikijy j`krh tc`f ks

?.;5;0>940?0 khe 9.1;393;393, snho` tcbs` truhoktè hufi`rs kr` ojbs` `hbuac tb tc` kotukj

obhstkhts, i`nha wntcnh bh`-injjnbhtc bd tc` tru` vkju`.

Uc` r`ksbh hbibey okr`s tbb fuoc kibut tc` iklnjjnbhs (;759s) bd enants kdt`r tc` dnrst ebz`h-br-sb

enants bd Wn khe @, ns tckt tc` `xtrk enants iành tb fkm` j`ss khe j`ss endd`r`ho` tbwkres tc` bv`rkjj

hufi`r, khe tc`y iòbf` sbf`wckt nrr`j`vkht ks tc`y *obhv`ra`* tbwkres k snhaj` pbnht. Hbibey

r`kjjy okr`s wckt tc` 143tcenant bd Wn ns, (nts >) iòkus` wc`h wbuje ybu `v`r h`è tb i` koourkt`

tb tckt fkhy enants22 Oj`krjy, ?.;5;4 ns ojbs` `hbuac. Ynact2

Q`jj, c`r`s wc`r` w` okh fkm` tcnhas fuoc fbr` nht`r`stnha. Uc` Phnv`rs` andtè us wntc tc`s`

fkanokj skorè hufi`rs bd Wn khe @, khe N i`jn`v` tc`r` okh i` fbr` wkys tckt w` kr` f`kht tb

us` tc`f. N prbpbs` tckt w` okh snfpjy r`fbv` tc` eònfkj pbnht drbf `koc bd tc`s` obhstkhts,

khe dnhkjjy us` tc`f ks tc` trujy pbw`rduj, nhdnhnt`jy jkra` hufi`rs tckt tc`y kr`!!

Wj`ks` kjjbw f` tb `xpjknh

Dnrst, w` wnjj tr`kt pn khe `ks hbrfkj eònfkj obhstkhts, khe fujtnpjy tc`f tba`tc`r. (_`` tkij`

i`jbw) Uc` fbr` enants w` `ht`r dbr bur nrrktnbhkj & trkhso`he`htkj hufi`rs, tc` fbr` koourkt`

tc` r`sujtnha prbeuot a`ts. Cbw`v`r, ks ybu okh s``, tc` prbeuot obhv`ra`s dknrjy qunomjy tbwkres

tc` tru` r`sujt, fkmnha keentnbhkj enants sbf`wckt uhhò`sskry... Qc`h usè ks hbrfkj eònfkj

obhstkhts, ]pn x `Vcks kh bivnbus snhaj` khsw`r.

?.;5 x 9.1; 6 3.07>5

?.;5;0 x 9.1;39 6 3.0?>990?

?.;5;0>9 x 9.1;393; 6 3.0?>19>35?

?.;5;0>940 x 9.1;393;39 6 3.0?>1?5;34?5749

?.;5;0>940?0 x 9.1;393;3935 6 3.0?>1?599995?>>

?.;5;0>940?03> x 9.1;393;39350> 6 3.0?>1?599941;91

?.;5;0>940?03>1> x 9.1;393;39350>75 6 3.0?>1?599941?05

pn x ` 6 3.0?>1?599941?04


9/10

Cbw`v`r, nd w` snfpjy r`fbv` tcbs` tnhy jnttj` eònfkj-pbnhts nh pn khe `, khe tr`kt tc`f ks

nhor`ksnhajy-jkra`r nhtà`rs hkfè WNkhe@, tc`h tcnhas a`t fuoc fbr` nht`r`stnha(_``

tkij` i`jbw) N tcnhm bd tcns prbo`ss ks ]WN x @ 6WN@VHbw, tc` hufi`r bd enants w` `ht`r dbr

bur nrrktnbhkj & trkhso`he`htkj obhstkhtskotukjjy kjt`rs cbw jkra` tc` hufi`rs kr`, khe or`kt`s

`htnr`jy endd`r`ht fujtnpjnoktnbh prbij`fs. _b, nhst`ke bd a`ttnha k eònfkj prbeuot tckt

*obhv`ra`s* tbwkres k snhaj` pbnht, wc`r` `xtrk enants snfpjy f`kh fbr` koourkt` khe okh`v`htukjjy i` nahbrè, tcns h`w WN@hufi`r kotukjjy *env`ra`s* `xpbh`htnkjjy tbwkres

Nhdnhnty!! Ucns f`khs tc` hufi`r bd enants khe tc` snz`s bd tc` hufi`rs h`è tb i` tkm`h qunt`

s`rnbusjy!!

Kjsb, hbw tckt w` kr` r`fbvnha tc` eònfkj pbnhts khe tr`ktnha tc`s` ks vkrnbus-snzè nhtà`rs,

tc` r`sujtnha prbeuot eb`s hbt `v`h hò`sskrnjy ckv` khy s`t pktt`rh bd enants!!

Nh tc` `xkfpj` tkij` kibv`, tc` WNkhe@objufhs kjwkys cke kh `qukj hufi`r bd enants,

wcnoc ns wcy tc` prbeuot objufh *kpp`krs* tb obhv`ra` nh tc` skf` wky ks tc` r`kj ]pn x `V

r`sujt (nahbrnha fkahntue`). Iut w` kr` hbt r`qunrè tb us` kh `qukj hufi`r bd enants!! Q` okhus` cbw`v`r fkhy w` ocbbs`(_`` tkij` i`jbw)

Uc`r`dbr`, tcns h`w WN @hufi`r cks fkhy nht`r`stnha prbp`rtn`s tb ensouss

? x 9 6 4

?; x 91 6 3?1

?;5 x 91; 6 30,7>5

?;,5;0 x 91,;39 6 30?,>99,0?7

?,;5;,0>9 x 9,1;3,93; 6 3,0?>,19>,35?,?09

?;5,;0>,940 x 91;,393,;39 6 30,?>1,?5;,34?,574,977

?;,5;0,>94,0?0 x 91,;39,3;3,935 6 30?,>1?,599,995,?>>,777,777

?,;5;,0>9,40?,03> x 9,1;3,93;,393,50> 6 3,0?>,1?5,999,41;,917,777,777,777

?;5,;0>,940,?03,>1> x 91;,393,;39,350,>75 6 30,?>1,?59,994,1?0,577,777,777,777,777

WN x @ 6 WN@ 22

? x 91 6 3;

?; x 91; 6 3,57;

?; x 91,;39 6 359,459

?;,5;0 x 9,1;3,93; 6 30,?>5,1>1,4;0

?;,5;0 x 91;,393,;39 6 3,0?>,539,??1,0?7

?;,5;0,>94 x 91,;39,3;3,935 6 30?,>1?,571,43;,0>;,777

?;,5;0,>94,0?0 x 9,1;3 6 30,?33,533,?99,;?7

?,;5;,0>9,40?,03> x 9,1;3,93; 6 3,0?>,1?;,4;>,>>7,047,777

WN x @ 6 WN@ 22


10/10

Dnrst, j`ts ocbbs` (kjpck) tb r`pr`s`ht tc` # bd enants bd pn tcktw` `ht`r dbr WN, khe (i`tk) tb

r`pr`s`ht tc` # bd enants bd `tckt w` `ht`r dbr @, khe tc`h ]+-; 6 V wc`r` (akffk) anv`s us

tc` # bd enants bd tc` r`sujtnha prbeuot ]WN x @ 6WN @V. Nd w` pjko` tc`s` # bd enantsvkju`s ks

suisornpts, tc`h w` a`t tc` fbr` koourkt` / c`jpduj / nht`r`stnha `quktnbh< ]WNx @6WN @V

_nho` w` mhbw tcktpn

khe`kr` nrrktnbhkj & trkhso`he`htkj hufi`rs, w` okh sky tckt tc` ebfknhbd pbssnij` r`ksbhkij` vkju`s dbr khe (tc`# bd enants drbf pn khe `tckt w` ocbbs` tb `ht`r ks

WN khe@) ks tc` obuhtnha hufi`rsdrbf bh` tb Nhdnhnty, nh prbp`r hbtktnbh ks< {H | ;}

Uc`r`dbr`, tc` ebfknh bd , okjoujktè drbf ]+-;V, ns kjsb tc` obuhtnha hufi`rsdrbf bh` tb

Nhdnhnty, nh prbp`r hbtktnbh ks< {H | ;}

_b tc` jbw`st pbssnij` vkju` bd WN@boours wc`h ]6;,6;,6;Vdbr ]? x 9 6 4V. Uc` h`xt

jbw`st pbssnij` vkju` bd WN@boours wc`h ]69,6;,69Vdbr ]?; x 9 6 49V. Ucns ns dbjjbwè iy

]6;,69,69Vdbr ]? x 91 6 3;V.

iut wckt *btc`r* vkju`s bd WN@kr` pbssnij`22 Cbw fkhy uhnqu` vkju`s bd WN @kr` pbssnij`22

Ns tc`r` kh `quktnbh tckt wbuje ocòm wc`tc`r k anv`h hufi`r ns nh tc` s`t bd WN @vkju`s br hbt22

Ns tc` fkxnfuf ibuhe bd WN@dnhnt` br Nhdnhnt`22 Qbuje nt i` Obuhtkijy Nhdnhnt` br Phobuhtkijy

Nhdnhnt`22 Qckt wbuje i` tc` okrenhkjnty bd nts Nhdnhnt`-h`ss22

UB I@ OBHUNHP@E.

“pie” - a new “very large number”

Documents