Whats with this? #9

[arkain101]

I request masterz of the numberz to shed some light for my curiousity or possibly confusion :doh:

 

I do not have the mathamatical knowledge to know where to begin piecing this puzzle together with patterns with 9's in our base 10 system of, umm, ?numerology?

 

I was reading over this post of another persons:

 

 

If your birth year adds up to a NINE, there's a funny little trick you can do in certain years with the year you're in and the age you turn in that year.

 

For instance, I was born in 1962 (I know, I know, I'M OLD!)

 

1+9+6+2=10+8=18=9

 

There are periods of your life when you can add the digits of the year and it will give you the age you turn in that year.

 

For instance, in 1983, I was 21. 1+9+8+3=21

 

If you add the 2 and the 1, you get the age the person born in 1980 would have turned that year: 3.

 

I may be one of the oldest ones here but all of this would apply to any of you born in any of the following years: 1908, 1917, 1926, 1935, 1944, 1953, 1962, 1971, 1980, 1989, and 1998.

 

For instance, someone born in 1998 turns 7 this year (2005 - 2+0+0+5 =7)

 

For the folks born in 1980, this is an interesting time in that as you look at the year you see the age you will turn in that year. For instance, it's 2005. You will be 25. This will continue until 2009, when you turn 29.

 

Then I noticed the following when looking it over.

 

Each of those dates, are also seperated by 9 year incriments. 1908 to 1917 is 9 years, so on and so forth.

 

The last digit of the year, ie; 190'8' decreases by 1 for each increase of the 9 year 'sets'.

 

ie: 1899, 1908, 1917, 1926, 1935, 1944, 1953, 1962, 1971, 1980

 

Of those 10 digits, is a span of 81 years, which is infact the square of nine. [math]9^2[/math]

 

If you have numbers layed out such as;

 

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

 

And you want to multiply a number by 9, cross out that digit, and you have your answer, by how many numbers are on either side of that digit.

IE:

9x5=?

 

[1, 2, 3, 4] / [6, 7, 8, 9, 10]

 

4 numbers and 5 numbers. 9x5= 4 5

 

Then 4+5=9

 

Infact, the amount of numbers on either side of the 'crossed out' number always adds up to 9.

 

It would be interesting to hear an educated description to these patterns.

 

Thanks.

 

I have a feeling there is something right under my nose that is clouded by all these details that explains this very straightforward and simply. :D Alas I cant see under my nose!

[Buffy]

My daughter had big trouble with her nines multiplication tables until I showed her that last trick. Her reaction? "Coooool!"

 

Try looking up number theory and abstract algebra if you're interested in this stuff. Its less magical once you understand what's going on.

 

To wit, an exercise for the reader:

 

Try working through the examples arkain poses above with the digit 7 in Base 8.... ;)

 

Where is Turtle when you need him? This is right up his alley. "Help Mr. Wizard!"

 

Modulus,

Buffy

[arkain101]

My daughter had big trouble with her nines multiplication tables until I showed her that last trick. Her reaction? "Coooool!"

 

Yes, I shouldnt of added that part to the post, it wasnt much related, as I copy and pasted this from another post of mine.

[Turtle]

I request masterz of the numberz to shed some light for my curiousity or possibly confusion

 

I do not have the mathamatical knowledge to know where to begin piecing this puzzle together with patterns with 9's in our base 10 system of, umm, ?numerology?

 

Where is Turtle when you need him? This is right up his alley. "Help Mr. Wizard!"

 

Modulus,

Buffy

 

Drizzle drazzle drozzle drone, time for this one call we home. :phones: The first several posts of the Katabatak thread describe an experiment with stones that explains 'casting out nines' in a hands on way.

http://hypography.com/forums/physics-mathematics/1343-katabatak-math-exploration-pure-number-theory.html

[Bec]

I request masterz of the numberz to shed some light for my curiousity or possibly confusion :doh:

 

I do not have the mathamatical knowledge to know where to begin piecing this puzzle together with patterns with 9's in our base 10 system of, umm, ?numerology?

 

I was reading over this post of another persons:

 

 

 

 

Then I noticed the following when looking it over.

 

Each of those dates, are also seperated by 9 year incriments. 1908 to 1917 is 9 years, so on and so forth.

 

The last digit of the year, ie; 190'8' decreases by 1 for each increase of the 9 year 'sets'.

 

ie: 1899, 1908, 1917, 1926, 1935, 1944, 1953, 1962, 1971, 1980

 

Of those 10 digits, is a span of 81 years, which is infact the square of nine. [math]9^2[/math]

 

If you have numbers layed out such as;

 

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

 

And you want to multiply a number by 9, cross out that digit, and you have your answer, by how many numbers are on either side of that digit.

IE:

9x5=?

 

[1, 2, 3, 4] / [6, 7, 8, 9, 10]

 

4 numbers and 5 numbers. 9x5= 4 5

 

Then 4+5=9

 

Infact, the amount of numbers on either side of the 'crossed out' number always adds up to 9.

 

It would be interesting to hear an educated description to these patterns.

 

Thanks.

 

I have a feeling there is something right under my nose that is clouded by all these details that explains this very straightforward and simply. :D Alas I cant see under my nose!

That way of finding answers for the 9 times tables is something I've never seen, but is really quite interesting!

 

(I'm sure it would help those battling fourth graders if they were ever taught it which I don't believe it is. :D)

 

Your first two queries I don't believe have any indepth maths link; as if you were to add 10 to the first number, lets say, the last digit would remain constant. As 9 is one less than 10 the last digit will decrease by one each time, of course. I think the reason that it will work for the selected years which all differ by 9 is that by adding 9 you are reducing the last digit by one and increasing the second last digit by one the total value the year adds up to is actually remaining constant, which is 9 (1 and 9 in 19_ _ will stay, and by adding one and subtracting one the total value for the last two digits is actually remaining constant).

 

The pattern doesn't appear to work for people born in years which do not begin with 19, which would make sense. And by the span being the square of 9 does not appear to hold any special value as each year has 9 years added on, and it just happens to be that within the 19 _ _ time frame it may only fit 9 times. 9 by 9 = 81. Your answer :D

 

EDIT: I see you other guys have pointed out some proper theories in relation to 9s (which I didn't read to do lack of time, so hopefully they don't overlap too much with what I was saying!) but I believe this straight forward one is consistent with the question and any 'quirks' you think you're seeing.

 

As for that thing with the 9 times tables, I guess that also works with what I was saying about adding 9, one down, one up. Not necessarily tricky maths but more that I was saying. :D