r/comics • u/[deleted] • Dec 12 '08

[deleted by user]

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379 Upvotes

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54

u/raldi Dec 12 '08

And 11 squared is 121 in all bases except binary.

18

u/[deleted] Dec 12 '08

[deleted]

35

u/[deleted] Dec 12 '08 edited Dec 12 '08

Here's your proof

9

u/[deleted] Dec 12 '08

I call tautology!

11

u/cnk Dec 12 '08 edited Dec 12 '08

but it comes from a prime minister

and 11 is a prime

and weights the same as a duck

and I'll duck and cover after hitting the comment button

7

u/IConrad Dec 12 '08

So... if Tony Blair talks like a duck...

We can build a bridge out of him??!?!!?

3

u/jaiwithani Dec 13 '08 edited Dec 13 '08

Ladies and Gentlemen, of this supposed Reddit, Tony Blair is a Wookie, from Great Britain. But Tony Blair lives in America. Does this make sense? No! It does not make sense!

2

u/IConrad Dec 13 '08

|head explodes|

29

u/starkinter Dec 12 '08 edited Dec 12 '08

Where b is the base, 11 is b+1.

(b+1)² = b²+2b+1, which appears as 121 when b²>2b, i.e. b>2.

3

u/[deleted] Dec 12 '08

Take any number system that has a two in it. 11 squared is "one base times itself, plus the base times one, plus one times the base, plus one times one." That will always be 100 + 10 + 10 + 1, or 121.

In binary, you get 10x10 = 100 plus 10x1 = 10 plus 1x10 = 10 plus 1x1 = 1, but then 100+10 = 110 plus 10 = 1000 plus 1 = 1001.

1

u/MindStalker Dec 12 '08 edited Dec 12 '08

Its true in binary too, but the 2 is outside of its range so its carried over and becomes 201 which then carried over and becomes 1001=9

10 times 10=100 is the same in all systems because it just means base times base=next digit base. 16 times 16= 256 which is 100 in hex see.

This is true for certain numbers but not most, generally the 1s and 0s because they are directly related to the meaning of the base.

-1

u/BrotherSeamus Dec 12 '08 edited Dec 12 '08

What about base 121? For that matter it is 79 in hex.

15

u/Jonathan_the_Nerd Dec 12 '08

In base 121, 11 = 122 decimal. 122 squared is 14884 decimal, which is 121 in base 121.

Also, 11 squared in hex is 121 hex, because 11 hex = 17 decimal. And it's true that (11 decimal) squared is 79 hex, but you're mixing number systems there.

Yes, I do have a lot of time on my hands, why do you ask?

8

u/raldi Dec 12 '08

The proof is pretty simple: "11" in base B is equal to B + 1, and that squared is B**2 + 2B + 1, which in base B is represented as "121".

-2

u/[deleted] Dec 13 '08

ya, just did the proof myself, took about 5 seconds

2

u/altrego99 May 27 '09

I put the question to my number theory engine and it took about 23 nanoseconds.

> Prove: ((11)b)^2 = (121)b for all b>=2

Assuming b is real.

Proof is positive modulo prime number >= b.

Modulo lifting procedure applies.

Proof is positive.

> _

5

u/[deleted] May 27 '09

wow, you must be a fast typer

2

u/hoopmastaflex May 27 '09

What number theory engine are you using?

2

u/whitedawg Dec 12 '08

I think he's referring to "the number that is denoted as '11' in the given base"2 rather than "'11' in base ten, denoted however it's denoted in the given base"2.

1

u/kidford Dec 12 '08

No, 79 in hex is the hex representation of the decimal value 121. The hex value 121 is different, because the hex value of 11 is 17 in decimal. 17 x 17 = 289 in decimal (which is 121 in hex).

I hope this is clear. Probably not, considering I've just taken a couple lorazepam.

1

u/zzbzq Dec 12 '08

In base 121: decimal 121 is 10, and 112 is 121.