Let's Play NumberWang

Jesus Wept · 23-04-2008 11:25AM

Hermy · 23-04-2008 12:07PM

1. [a in triangle] = a[3] = a^a
* n[3] = n^n
* n[3]2 = n[3][3] = n[3]^n[3] = (n^n)^(n^n)
* n[3]3 = n[3]2[3] = n[3]2^n[3]2 = ((n^n)^(n^n))^((n^n)^(n^n))
* n[3]4 = n[3]3[3] = n[3]3^n[3]3 = (((n^n)^(n^n))^((n^n)^(n^n)))^(((n^n)^(n^n))^((n^n)^(n^n)))
* n[3]k = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2k terms]
* 2[3] = 2^2 = 4
* 2[3]2 = 2[3]^2[3] = 4^4 = 256
* 2[3]3 = 2[3]2^22[3] = 256^256 = 10616.509...
* 2[3]4 = 2[3]3^23[3] = 10616.509...^10616.509... = 10616.509... x 10616.509... = 1010619.3...
* 2[3]5 = 2[3]4^2[3]4 = 1010619.3...^1010619.3...
* etc..
* 3[3] = 3^3 = 27
* 3[3]2 = 3[3]^3[3] = 27^27 = 443426488243037769948249630619149892803 = 1038.646...
* 3[3]3 = 3[3]2^3[3]2 = 1038.646...^1038.646... = 101040.23...
* etc...
* 4[3] = 4^4 = 2[3]^2[3] = 2[3][3] = 2[3]2
* 4[3]2 = 4[3][3] = 2[3]2[3] = 2[3]3
* 4[3]3 = 4[3]2[3] = 2[3]3[3] = 2[3]4
* 4[3]k = 2[3]k+1
2. [a in square] = a[4] = a[3]a
* n[4] = n[3]n = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2n terms]
* 2[4] = 2[3]2 = 256
* 2[4]2 = 2[4][4] = 256[4] = 256[3]256
* 2[4]3 = 2[4]2[4] = 256[3]256[4] = 256[3]256[3]256[3]256
* etc...
* 3[4] = 3[3]3 = 3[3]2^3[3]2 = (27^27)^(27^27)
* 3[4]2 = 3[3]3[4] = (3[3]2^3[3]2)[4] = ((27^27)^(27^27))[4]
= ((27^27)^(27^27))[3](27^27)^(27^27)
* etc...
* 4[4] = 4[3]4 = 2[3]5
* etc...
3. [a in pentagon] = a[5] = a[4]a
* 2[5] = Steinhaus' Mega = 2[4]2 = 2[3]2[4] = (2^2)[3][4] = (4^4)[4] = 256[3]256
* A polygon with 2[5] sides is a Megagon. It looks pretty circular if drawn!
* 2[5]2 = 2[5][5] = 2[4]2 = 256[3]256[5]
* 3[5] = 3[4]3 = ((27^27)^(27^27))[3](27^27)^(27^27)[4]
* 10[5] = Steinhaus' Megiston = 10[4]10
* etc..
4. a[6] = a[5]a
1. 2[6] = 2[5]2 = 256[3]256[5]
2. 3[6] = 3[5]3 = 3[5][5]2 = ((27^27)^(27^27))[3](27^27)^(27^27)[4][5]2
5. in general, a[k+1] = a[k]a

Jesus Wept · 23-04-2008 12:45PM

THAT'S NUMBERWANG!!!11!

Capt'n Midnight · 23-04-2008 08:04PM

2.718281828459045235360287471352662497757247093699959574966967627724\
07663035354759457138217852516642742746639193200305992181741359662904\
35729003342952605956307381323286279434907632338298807531952510190115\
73834187930702154089149934884167509244761460668082264800168477411853\
74234544243710753907774499206955170276183860626133138458300075204493\
38265602976067371132007093287091274437470472306969772093101416928368\
19025515108657463772111252389784425056953696770785449969967946864454\
90598793163688923009879312773617821542499922957635148220826989519366\
80331825288693984964651058209392398294887933203625094431173012381970\
68416140397019837679320683282376464804295311802328782509819455815301\
75671736133206981125099618188159304169035159888851934580727386673858\
94228792284998920868058257492796104841984443634632449684875602336248\
27041978623209002160990235304369941849146314093431738143640546253152\
09618369088870701676839642437814059271456354906130310720851038375051\
01157477041718986106873969655212671546889570350354

Hermy · 23-04-2008 10:08PM

Apparently that's numberwang.

Jesus Wept · 24-04-2008 04:12PM

Basq · 24-04-2008 04:23PM

That's wanger-numb!

Jesus Wept · 24-04-2008 04:43PM

1

Jesus Wept · 24-04-2008 04:46PM

Jesus Wept · 24-04-2008 04:47PM

Jesus Wept · 24-04-2008 04:48PM

Jesus Wept · 24-04-2008 04:50PM

42-18445269.jpg?size=572&uid=%7B330B1749-7FA1-407A-A36E-A5CB974E2599%7D

Basq · 24-04-2008 04:52PM

That's one-ber wang!

challengemaster · 24-04-2008 04:59PM

... 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196
4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273
724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609

Jesus Wept · 24-04-2008 05:25PM

Jesus Wept · 24-04-2008 07:01PM

Capt'n Midnight · 25-04-2008 12:11AM

2.718281828459045235360287471352662497757247093699959574966967627724\
07663035354759457138217852516642742746639193200305992181741359662904\
35729003342952605956307381323286279434907632338298807531952510190115\
73834187930702154089149934884167509244761460668082264800168477411853\
74234544243710753907774499206955170276183860626133138458300075204493\
38265602976067371132007093287091274437470472306969772093101416928368\
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90598793163688923009879312773617821542499922957635148220826989519366\
80331825288693984964651058209392398294887933203625094431173012381970\
68416140397019837679320683282376464804295311802328782509819455815301\
75671736133206981125099618188159304169035159888851934580727386673858\
94228792284998920868058257492796104841984443634632449684875602336248\
27041978623209002160990235304369941849146314093431738143640546253152\
09618369088870701676839642437814059271456354906130310720851038375051\
01157477041718986106873969655212671546889570350354021234078498193343\
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