Month: April 2008

How many roots has Google? I mean integer roots. Some numbers have roots, some not. I think Google has many roots probably. he’s a big number. Probably as many roots as the number One Hundred has divisors. Don’t you think?

Actually One Hundred is Ten times Ten which means primes Two and Five twice. He should have Nine divisors since Three time Three is Nine.
(Three options: each prime should appear either Zero or One or Two times).

Let me check….

One is a divisor –> Ten is a root. [Ten^{One Hundred} is Google]
Two is a divisor –> One Hundred is a root. [One Hundred^Fifty is Google]
Four is a divisor –> Ten Thousand is a root. [Ten Thousand^{Twenty Five} is Google]
Five is a divisor –> One Hundred Thousand is a root. [One Hundred Thousand^Twenty is Google]
Ten is a divisor –> Ten Billion is a root. [Ten Billion^Ten is Google]
Twenty is a divisor –> One Hundred Million Trillion is a root. [One Hundred Million Trillion^Five is Google]
Twenty Five is a divisor –> Ten Trillion Trillion is a root. [Ten Trillion Trillion^Four is Google]
Fifty is a divisor –> One Hundred Trillion Trillion Trillion Trillion is a root. [One Hundred Trillion Trillion Trillion Trillion^Two is Google]

Oh wait… is One Hundred a divisor of itself? Well if so, Google’s probably a root of itself too. But if not including Google itself, Google has Eight different roots if I’m correct. But how many roots does Googleplex have?

Well of course Googleplex (like any exponent of Ten) actually has only Two prime divisors – Two and Five. Googleplex is actually Google times Two multiplied by Google times Five. So it seems to me he has (Google plus One) times (Google plus One) roots minus One, not including himself. Actually all roots of Google are probably roots of Googleplex too. Since Google is probably a root of Googleplex too. Is he? Let me think. I think he is. One Hundred is a divisor of Google so he is probably a root of Googleplex too. But not all divisors of Google are also Googleplex’s roots. I think only those who have the same number of Two and Five as prime divisors – only those who are exponents of Ten. But not all of them – only those who divide Google – for example One Thousand is not. One Thousand is Three times Ten (Ten^Three), but Three is not a divisor of Google. Only those divisors of Google who are exponents of Ten and their exponent of Ten is a divisor of Google – They are real Googleplex roots.

So lets name them (do they already have names? maybe. but lets name them again):

Ten
One Hundred // Ten^Two
Ten Thousand // Ten^Four
One Hundred Thousand // Ten^Five
Ten Billion // Ten^Ten
One Hundred Million Trillion // Ten^Twenty
Gillion // Ten Trillion Trillion // Ten^{Twenty Five}
<!– all *illion are small numbers; *oo?le are big –>
Goodle // Gillion Gillion // Ten^Fifty
Google // Goodle Goodle // Ten^{One Hundred} // It’s a lovely name – don’t let them give him a bad name…
Doogle // Google Google // Ten^{Two Hundred}
Toogle // Ten^{Two Hundred and Fifty}
Boodle // Ten^{Five Hundred}
Noodle // Ten^{One Thousand}
Noogle // Ten^{Two Thousand}
Nooble // Ten^{Two Thousand Five Hundred}
Nootle // Ten^{Five Thousand}
Tootle // Ten^{Ten Thousand}
Toople // Ten^{Twenty Thousand}
Tooshle // Ten^{Twenty Five Thousand}
Toorle // Ten^{Fifty Thousand}
Toorrle // Ten^{One Hundred Thousand}
Toorrrle // Ten^{Two Hundred Thousand}
Toorrrrle // Ten^{Five Hundred Thousand}
Tooggle // Ten^{One Million}
Toogggle // Ten^{Two Million}
Tooggggle // Ten^{Five Million}
Toottle // Ten^{Ten Million}
Tootttle // Ten^{Twenty Million}
Toozzle // Ten^{Twenty Five Million}

……. // sorry no time to name them all now….

Zoozzle // Ten^Goodle
Poodle // Ten^Google a.k.a. “Googleplex”

Poodle sounds much better. And by the way if you make a mistake with calculations you can always say it’s just a spelling mistake…

Give them names my friends. Pass to your friends and give more names. Create a wiki or something, and send me the best names. I’ll add them here, you can add <!– comments –>too. But remember it’s copyleft, you know the rules, anything can be modified and changed. No name is forever, no comment, no remove. Whatever you change can be undone by others. But since Wikipedia’s boycotting me, I’ll do it elsewhere. Who needs them anyway? For me everything is copyleft GPL. Send me new names my friends, and send to your friends. I will put them here. Or maybe move to another post, I don’t know. But please don’t call it Googleplex, I hate the name. Call it Poodle, or give it your own name. It’s too long a name for such a nice number, don’t you think? And by the way there are bigger numbers than that…

Pooddle // Ten^Doogle
Pootle // Ten^Toogle

<!– to be continued… –>

I love numbers….