The Beauty of Mathematics

[aleish]

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321


1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111



9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888


Brilliant, isn't it?
And finally, take a look at this symmetry:

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=123456789 87654321

[Broken Arrow]

Re: The Beauty of Mathematics

I remember an informercial about a guy who professed to have some kind of mathematical insights. My parents were so impressed that they decided to buy it for us when we were kids. It turns out that they were more like shortcuts that you have described. It's still impressive in its own way, and not without merit. Then again, its practical use are somewhat limited, I think, and nowadays, I'd be more worried about the mathematics involved with the cost. The package was nearly $100!

But please don't take this as a criticism or anything. It is indeed aesthetically impressive, and I'm just thinking out loud.

[PrincessPerky]

Re: The Beauty of Mathematics

Math magic, the kind where you pick a number then do what the dude says to it and it always ends up the same..weird...cool...I always tell people math is the easiest subject in the world if I say 2 plus 2 is 4 today I promise to say the same tomorrow, no matter what, no extra E making it 5, no special from france rule making it 10, really 2 plus two is always 4, my favorite subject.

[PRICEPLUS]

Re: The Beauty of Mathematics

Aleish, that is quite interesting!

[cptacek]

Re: The Beauty of Mathematics

Math magic, the kind where you pick a number then do what the dude says to it and it always ends up the same..weird...

PrincessPerky, these things are just a more complicated version of:

pick a number.
add one
subtract one
THERE! IT IS YOUR NUMBER!!!

All of these tricks can be figured out if you use some Algebra...just pick the number "x" and do what they tell you to do. The reason we find it so interesting is we are concentrating on the values instead of the process of getting there.

[froggie]

Re: The Beauty of Mathematics

I love math!!! These cool types of things are what teachers need to use to get students psyched up for math! Forget that whole theory of only one way to get the answer!

[Joan.of.the.Arch]

Re: The Beauty of Mathematics

When my son was in high school he used to participate in math competitions. Also at his school was an otherwise so-so student who could do calulations in his head very quickly. Kids called him, "the human calculator." It was really quite impressive! However, he did not clean up at every competition because, quick as he was at the calculations, he was not always so quick at the concept. It sometimes took him a bit of extra time to figure out just what calculation he needed to do in order to solve a problem. My kid is also a math-in-his-head person, just not to the extent that "the human calcualtor was." But my kid is very good with the concepts, too. So sometimes he managed to bring home the top ribbon. Mine clobbered the other in the math SAT, too.

[s.saver]

Re: The Beauty of Mathematics

Pretty Impressive. I like it