Stray Thought about the Number 9


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1x9=9

2x9=18; 1+8=9

3x9=27; 2+7=9

4x9=36; 3+6=9

5x9=45; 4+5=9

6x9=54; 5+4=9

7x9=63; 6+3=9

8x9=72; 7+2=9

9x9=81; 8+1=9

10x9=90; 9+0=9

11x9=99; 9+9=18; 1+8=9

12x9=108; 10+8=18; 1+8=9; 1+0+8=9

13x9=117; 11+7=18; 1+8=9; 1+1+7=9

14x9=126; 12+6=18; 1+8=9; 1+2+6=9

Etc.

Ellen

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Determined little number, is it not?

I notice too, that however you mess with the first order of addition, that pesky 9 is still there.

i.e.

14X9 = 126; 12+6 = 18...etc

-or- ...............1+26 = 27; 2+7 = 9.

15X 9 = 135; 1+35=36; 3+6=9

-or- .............;13+5=18; 1+8 =9

(Damn, there goes my sleep tonight.)

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Determined little number, is it not?

I notice too, that however you to mess with the first order of addition, that pesky 9 is still there.

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Your result can be generalized to the number b-1 where b is the base of the positional system. One less then the base, whatever the base is is a magic number.

9 was also the favorite number of Nikola Tesla so you are in good company.

Ba'al Chatzaf

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Your result can be generalized to the number b-1 where b is the base of the positional system. One less then the base, whatever the base is is a magic number.

I suspected that when I made the post, but hadn't yet checked to see if it's true. I've subsequently checked.

9 was also the favorite number of Nikola Tesla so you are in good company.

Ba'al Chatzaf

9 isn't my "favorite number." I don't have a favorite number, but you've gotten me curious re Tesla and 9.

Ellen

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Your result can be generalized to the number b-1 where b is the base of the positional system. One less then the base, whatever the base is is a magic number.

This implies for b=2, 1 is the magic number. That makes 1 both magic and the loneliest number. :smile:

Another stray thought.

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It just occurred to me that if you substitute 6 for 9 you get all of the value of 9 plus the 6. How? Simple: take your 6 and turn it upside down. Ergo, you've got a 9! What's really good about this is if someone wants to steal your 9 they'll walk right by your 6 not realizing it's your 9 hiding in plain sight!

--Brant

money in the bank

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It just occurred to me that if you substitute 6 for 9 you get all of the value of 9 plus the 6. How? Simple: take your 6 and turn it upside down. Ergo, you've got a 9! What's really good about this is if someone wants to steal your 9 they'll walk right by your 6 not realizing it's your 9 hiding in plain sight!

--Brant

money in the bank

Turning the symbol for a digit upside down, backward, inside out or mirror reversed has no necessary mathematical connection to the quantities represented by such symbols.

Ba'al Chatzaf

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It just occurred to me that if you substitute 6 for 9 you get all of the value of 9 plus the 6. How? Simple: take your 6 and turn it upside down. Ergo, you've got a 9! What's really good about this is if someone wants to steal your 9 they'll walk right by your 6 not realizing it's your 9 hiding in plain sight!

--Brant

money in the bank

Turning the symbol for a digit upside down, backward, inside out or mirror reversed has no necessary mathematical connection to the quantities represented by such symbols.

Ba'al Chatzaf

I'm gong to side with Brant on this one.

Besides, I saw this done once at a carnival.

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It just occurred to me that if you substitute 6 for 9 you get all of the value of 9 plus the 6. How? Simple: take your 6 and turn it upside down. Ergo, you've got a 9! What's really good about this is if someone wants to steal your 9 they'll walk right by your 6 not realizing it's your 9 hiding in plain sight!

--Brant

money in the bank

Turning the symbol for a digit upside down, backward, inside out or mirror reversed has no necessary mathematical connection to the quantities represented by such symbols.

Please, stop, you're hurting my brain.

--Brant

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Tesla and 3 - link.

9 only seems to get in there thus:

Post by Dotini - link

Quote by Evo

Please post a link to an article that claims this [that Tesla was obsessed by the number 3].

Quote by ampakine

I read somewhere that he said "he who knows the magnificence of the number 3 will understand the mechanisms of the universe" or something to that effect. [....]

We are getting warmer. Here is the exact quote found on hundreds of websites:

"If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe." [....]

I've scoured dozens of them, but as to when and where Tesla said this, no one seems to know. So it may be apocryphal.

Ellen

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Lay your hands palms down on a table, then number the fingers (and thumbs) 1-10 left to right. To calculate 9x4, turn under the finger numbered 4 (the left index finger). Then count by tens on the fingers to the left of the turned under finger (10,20,30) then count by ones on the fingers to the right of the turned under finger (1,2,3,4,5,6). 30+6=36. 9x4=36. It works for the entire multiplication table for 9 up to 9x10!

Who freaking knew?!?!?

My third-grader has also been studying the concepts of supply and demand, scarcity, international trade, and (gasp!) free markets. Between that and this multiplication of 9s trick, it's been a good couple of weeks for us during homework time.

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  • 1 month later...

Nine ain't got nothin' on 142,857.

1 × 142,857 = 142,857

2 × 142,857 = 285,714

3 × 142,857 = 428,571

4 × 142,857 = 571,428

5 × 142,857 = 714,285

6 × 142,857 = 857,142

7 × 142,857 = 999,999 (oh look who it is)

If you multiply by an integer greater than 7, there is a simple process to get to a cyclic permutation of 142857. By adding the rightmost six digits (ones through hundred thousands) to the remaining digits and repeating this process until you have only the six digits left, it will result in a cyclic permutation of 142857

142857 × 8 = 1142856

1 + 142856 = 142857

142857 × 815 = 116428455

116 + 428455 = 428571

1428572 = 142857 × 142857 = 20408122449

20408 + 122449 = 142857

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