Math Is Fun Forum

krollo

Member

Registered: 2007-05-04

Posts: 24

9,8,0,1

I have discovered something amazing.
99*99=9801
999*999=998001
9999*9999=99980001
weird.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: 9,8,0,1

Cool pattern!

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: 9,8,0,1

so basicly.

for a number:

its square is a number with [n-1] 9's, followed by an 8, followed by [n-1] 0's, followed by 1

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The Beginning Of All Things To End.
The End Of All Things To Come.

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: 9,8,0,1

Nice one.

Reminds me of 37.

37*3 = 111
37*6 = 222
37*9 = 333
37*12 = 444
37*15 = 555
37*18 = 666 (ACK!)
37*21 = 777
37*24 = 888
37*27 = 999
37*30 = 1110
37*33 = 1221
37*36 = 1332
37*39 = 1443
37*42 = 1554
37*45 = 1665
37*48 = 1776
37*51 = 1887
37*54 = 1998
37*57 = 2109
37*60 = 2220

...

And so on.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: 9,8,0,1

Last edited by JaneFairfax (2007-05-06 23:54:03)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: 9,8,0,1

I think I came up with a theorem to generalize all of these:

For any two numbers a and b, there exists a third number c such that a * b = c.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: 9,8,0,1

wahahaha!

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A logarithm is just a misspelled algorithm.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 9,8,0,1

You missed the first one!
9x9 = 81.

There's also a very similar pattern that happens with repeated 3s.

3x3 = (0)9
33x33 = 1089
333x333 = 110889
3333x3333 = 11108889
...

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Why did the vector cross the road?
It wanted to be normal.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: 9,8,0,1

An interesting finding! Here is the proof:

(10[sup]n[/sup]-1)²=10[sup]2n[/sup]-2*10[sup]n[/sup]+1

the first two elements add up to

9..980...0

the n zeros and the 8 are derived from substracting 2*10[sup]n[/sup], also the digits of this number are only 2n digits instead of 2n+1 digits. So there are  totally 2n-n-1=n-1   9's in it.

To write the final result, just write n-1 9's and one 8 as the former n digits, then write n-1 0's and the last 1 for the latter n digits.

Last edited by George,Y (2007-05-11 19:16:25)

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X'(y-Xβ)=0

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: 9,8,0,1

I like 37 ~lol

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Numbers are the essence of the Universe

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: 9,8,0,1

I wonder if you might be interested in this index of arithmetical tricks:

http://mathforum.org/k12/mathtips/beatcalc.html

You might find your own in there

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: 9,8,0,1

errh...so many arithmetical tricks........

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X'(y-Xβ)=0

Zhylliolom

Real Member

Registered: 2005-09-05

Posts: 412

Re: 9,8,0,1

Man, that's too much work. I'm not too big on calculations like that. I hate when people are like "you're a mathematician? What is 47236 times 2923.424?" as if all math is just arithmetic. You don't need special mathematical insight to do such things. Dividing 13-digit numbers in your head isn't the same as being able to prove a theorem or understand a mathematical concept. Anyway I just wanted to say that. Have a nice day.

Devantè

Real Member

Registered: 2006-07-14

Posts: 6,400

Re: 9,8,0,1

I wonder if you might be interested in this index of arithmetical tricks:

http://mathforum.org/k12/mathtips/beatcalc.html

You might find your own in there

My God.

I shall now commence memorising.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: 9,8,0,1

Anyway, learning those tricks is only volentary, isn't it??

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X'(y-Xβ)=0

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 9,8,0,1

Heh, the discovery is in there. Number 16. They've also got the one with 3s, and also patterns with repeating 1s and 6s.

1x1 = 1
11x11 = 121
111x111 = 12321
1111x1111 = 1234321
...
(This breaks down at 10 ones, because things start carrying)

Also,
6x6 = 36
66x66 = 4356
666x666 = 443556
6666x6666 = 44435556
...

Perhaps not very useful, but certainly interesting.

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Why did the vector cross the road?
It wanted to be normal.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: 9,8,0,1

I haven't checked to see if this one is in there, but check this out

11^0 =         1
11^1 =        11
11^2 =       121
11^3 =      1331
11^4 =     14641

Pascal's triangle! Or... at least that's what my math teacher told me... After 11^4 its gets a bit weird.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 9,8,0,1

That works because Pascal's Triangle tells you the coefficients of the expansion of (x+1)^n.
11^n is just the case when x=10.

It stops working at the 6th row because in the triangle it would be 1 5 10 10 5 1, but you can't have a 10 digit so things carry over instead.

1 5 10 10 5 1 becomes 1 5 11 0 5 1, which becomes 1 6 1 0 5 1.

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Why did the vector cross the road?
It wanted to be normal.