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#2 2012-01-02 04:15:57
Re: Cool Math Discovery with Squares
And the differences of that set is two.
Now let's consider cubes. I'll type out the first ten...
{1, 8, 27, 64, 125, 216, 343, 512, 729, 1000}
Differences between the numbers:
{7, 19, 37, 61, 91, 127, 169, 217, 271}
Tier 2 differences:
{12, 18, 24, 30, 36, 42, 48, 56}
And the difference between those numbers is 6.
If this pattern keeps on going, then it takes [n-1] difference iterations to see a definate pattern, where n is the exponent in x^n.
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#4 2012-01-02 04:28:46
- scimonster
- Community Moderator
- Registered: 2010-06-13
- Posts: 1000+
Re: Cool Math Discovery with Squares
7 x 7 = 49
- 1
8 x 6 = 48
- 3
9 x 5 = 45
- 5
10x4 = 40
- 7
11x3 = 33
- 9
12x2 = 24
-11
13x1 = 13
- 13
14x0 = 00
12 x 12 = 144
- 1
13 x 11 = 143
- 3
14 x 10 = 140
- 5
15 x 09 = 135
- 7
16 x 08 = 128
- 9
17 x 07 = 119
- 11
18 x 06 = 108
- 13
19 x 05 = 095
- 15
20 x 04 = 080
- 17
21 x 03 = 063
- 19
22 x 02 = 044
- 21
23 x 01 = 023
- 23
24 x 00 = 000
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#5 2012-01-02 04:34:32
Re: Cool Math Discovery with Squares
roijac wrote:
and the difference is always n!, isn't it?
Yep! Good observation! 
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#6 2012-01-02 07:58:55
- RedRocker227
- Scratcher
- Registered: 2011-10-26
- Posts: 1000+
Re: Cool Math Discovery with Squares
Sorry, but I figured that out myself when I was six :p
Vista4563 wrote:
roijac wrote:
and the difference is always n!, isn't it?
Yep! Good observation!
The difference of what?
Why
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#7 2012-01-02 14:15:04
Re: Cool Math Discovery with Squares
RedRocker227 wrote:
Sorry, but I figured that out myself when I was six :p
Vista4563 wrote:
roijac wrote:
and the difference is always n!, isn't it?
Yep! Good observation!
The difference of what?
Of the difference between numbers of cubes or squares.
And Redrocker, Good for you. 
Hai.
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