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RxGregory
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I'm with Xanatos and the golden ratio (also known as the divine proportion), or PHI (pronounced fee). It came up in Dan Brown's book The DaVinci Code. Awesome book, by the way. Here are the facts:

PHI is derived from the Fibonacci sequence (see above). Not only because the sum of adjacent terms equals the next term, but because the quotients of adjacent terms possess the astonishing property of approaching the number 1.618---PHI!

-divide the number of female bees by the number of male bees in any beehive in the world---1.618

-the ratio of each spiral's diameter to the next in a nautilus shell---1.618

-Measure the distance from your shoulder to your fingertips, and then divide it by the distance from your elbow to your fingertips - PHI

-Hip to floor divided by knee to floor - PHI

Pages 95, 96, and 97 of the book go into greater detail, but it's amazing! Something magical about that number, for sure.

Greg
If it was easy, everybody would do it, and if everybody did it, it wouldn't be magic.
David Roth (Ultimate Coin Magic Vol. 11)
xanatos
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RxGregory:

You may also enjoy the book "The Golden Ratio". It goes into VERY greta depth on the astounding relevance of Phi in almost every process in the universe- the spirals in hurricanes & tornadoes, even the ratios of structures in galaxies- and atoms. The ratio, it seems, is at the heart of nearly everything in one form or another. There has to be a way to really IMPACTFULLY incorporate this principle into a magic performance, it's just too amazing.

I'm still looking for a way to combine this ratio with resonance phenomena and do some real magic! Smile

Dave
GALIER
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Observe the less magical black hole, the nine. Why it is called a black hole?

1) Think a date.
2) Write down it as a number.
3) Order their digits in a increasing way.
4) Order their digits in a decreasing way.
5) Substract these two numbers.
6) Add the digits of the result.
7) Add again the digits of the last result.

The final result is always nine.
owen.daniel
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Interesting sum GALIER!!!

I am about to start Dan Brown's "The Da Vinci Code". The rest of my family have read it and they all say I should. I was reading "The Vanished Man" (by Jeffery Deaver) while they read DV Code, and look forward to starting it.

While talking about "The Vanished Man", every one should read it! It is interesting the amount of magic content described, and how well the magic is described...Really Good.

owen

*** Added June 9, 2004
Ok I have read the Da Vinci Code...

I was not as impressed as I had hoped! To me there was little math in it. The book was great though. I agree that the thing about the Divine Proportion of PHI is quite amazing. I mentioned this to my biology teacher...He said that this was not surprising! I think he was just jealous of my knowledge! According to him, this is to be expected, because every thing is made of atoms, and have similar structures...Don't tell him this, but I don't really think he knows what he is talking about!

owen
Scott Cram
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Quote:
On 2004-05-20 22:26, xanatos wrote:
I realize this also doesn't quite fit the parameter, but it's between 0 & 9...

The golden ratio. 1.618033...

The fibbonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...

I *KNOW* there's gotta be an astounding magic effect that can be presented with these, I just haven't seen it, or figured one out yet...

Anyone got anything on this?

Dave



I'm surprised that no one yet has brought up the most classic of Fibonacci effects. The following is a "lightning calculator" stunt.

You ask your audience member to write down any two small (preferably one-digit) numbers, one below the other. For example, let's say they write down 8 and 3:

8
3

You then ask them to add these two numbers together to get a third number, and write that below the other two. In our example, that would be:

8
3
11

You then ask him to add the lowermost two numbers to get a fourth number, as in our example:

8
3
11
14

The adding together of the two lowermost number is continually repeated, until there are ten terms listed on the page. In our example, the final list would look like this:

8
3
11
14
25
39
64
103
167
270

You now ask your audience member to add up all these terms on a calculator, while you attempt to add up all these numbers in your head faster than he can on the calculator.

In this example, as he starts punching in "8 + 3 + 11 ..." you say, "704"! When your audience member finishes totaling the column, they find out you are correct!

This one is simple. You simply look at the seventh number on the list (the one that's fourth from the bottom), and multiply it by 11. That will be the total for all of the numbers!

To show you why, let's do the same routine, but just with numbers X and Y. The list of 10 numbers would then look like this:

X
Y
X+Y
X+2Y
2X+3Y
3X+5Y
5X+8Y
8X+13Y
13X+21Y
21X+34Y

The total of all these numbers is:

55X+88Y

Notice that the seventh term down (fourth up from the bottom) is 5X+8Y? That's why all you have to do is multiply by 11. 55X+88Y is the same as 11*(5X+8Y).
owen.daniel
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Great Scot!
Brilliant application of the Fib Sequence. It was also nice that you added the maths behind the principle. I suppose this is perfectly suited to the method of multiplying any 2 digit number by 11 that I gave previously...
Owen
landmark
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Scott,

I once did that trick, but did it with multiple participants, who passed an index card to each other, each one writing a subsequent term in the series. I did not even know the first two terms.

After the the seventh number was written, I took back the folded card, (ostensibly to hand it to someone on the other side of the room) got a quick peek of the seventh number, and said, "What the heck let's keep going."

After the eighth person wrote their number, I said "I'd like to make a prediction," and then wrote down a prediction, sealed it in a envelope. The index card was then passed to a 9th and 10th person. Of course the nice thing was that I didn't need to be anywhere near the card when I wrote the prediction, and the prediction was written before the 9th and 10th people wrote their numbers. An eleventh person added up the terms and strange to say, my prediction was miraculously correct! Smile

Jack Shalom

P.S.

Owen,

To multiply by 11 in your head quickly, follow these instructions.

It is always easiest to multiply mentally by 11 by multiplying by 10 first, and then adding on the original number. So for example, 86 x 11:

Think to yourself this way:

86 x 10 = 860 (easy, just add a zero to the number)

Now add 860 + 80 =940,

Then add 940 + 6 = 946.

Yes I know this is exactly the OPPOSITE of what you were taught in school--they told you to multiply starting from the units place first. But trust me on this (I'm a math teacher!) mental math is easier if you do it backwards, and do the units digits last.
owen.daniel
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Landmark,
I am unsure of whether or not this is easier or harder to do than the version that I printed previously. Of course it is quite hard to do a fair test at this sort of thing becuase different numbers maybe harder for some people etc.
Of course I have practiced the method I posted more, so therefore at the moment I find that I can do this considerably quicker...However I shall try practicing your method and then try and devise some sort of test...
owen
landmark
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Owen,

Of course what works best is an individual thing. I'm sure you'll find the method that works best for you.

As you discovered, you have to be careful with the method you posted above. If the two digits add up to more than 9, then you have to "carry" the extra digit. So, in your example of 37 x 11, using your method you might think to yourself :

3+7=10

So the answer is 3, 10, 7. Since the middle term is 10, I'll carry the 1 from the 10 to add to the 3. So now I have 4, 0, 7.

Again: 86 x 11. Think 8+6=14. 8, 14, 6. Therefore, 9, 4, 6.

Jack

P.S. In another thread Scott mentioned The Trachtenberg Speed System of Math book. It's sometimes hard to find, but I think you would really enjoy it.
owen.daniel
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Thanks for the title of the book, I will start searching for it!
As you said it is a personal thing, and I also see the point in your arguement that it is just possible for such a mistake to occur. As I said I am sure after some practice I will change to your method.

Thanks again,
Owen
Brother Kotah
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From a bizarrist point of view, the number 666 is very interesting, Thw number of the beast when inverted is 999, the number for Apollo. Looking at the symbol for infinity which resembles an 8 lying on its side. The symbol may also be seen as a composite of the numbers 6 and 9 over lapping one another.
He who sees strangely
mattmann101
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Going back to the calculator and 9 fugure numbers, if you put in 9to 1 in descending order, then subtract 1 to 9 in ascending order (i.e. 987654321 - 123456789) the answer obtained is a nine digit number containing each of the nine digits! (864197532)

Just thought I'd add this
mattmann101
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Sorry, Forgot to add this:

I might be wrong (but don't think I am) when I say this is the only subtraction using 9 digits where the answer is the digits 1-9 only (though not in any order)
lboudreau
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With a generalized version of the principle Galier noted in an earlier posting, you can create a neat little trick:

(1) Think of a number. (327)
(2) Reverse the digits. (723)
(3) Subtract the smaller number from the larger. (723-327=396)
(4) Discard any one of the digits in your new number and tell me the result. (Suppose you discard the 6 and tell me 39)
(5) I can immediately reveal the discarded digit. (I do it by casting out nines. I add the digits of the number you told me 3+9=12. I add again 1+2=3. Finally, I subtract this total from nine, 9-3=6. If my addition had resulted in a 9 instead of a 3, then a 9 was discarded.)
(6) It works for any number.
LEO
Loz
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9 must rank highly as the most magical number. The whole agebraic sum idea, the mindreading web sites people have posted over the years etc.

take any number, multiply it by 9 or a multiple of 9. Then keep multiplying it by random (thought of) numbers and the result will always have an algebraic sum of 9. Lots of potential here.
k
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MMM I would have to say the most magical numbers would HAVE to be
Pi (3,14...) as it's a perfect number!
and the golden ratio (Phi) : (1+SR(5))/2 = 1.68.. as it is FRIGGIN EVERYWHERE YOU LOOK!!!!!

Fibonnaci is a nice suit though, but not a number...
it interacts nicely with Phi though...
I'm just a blind Con that lost his I...
remember, Magic's everywhere... ("Your are the magic !" - Albert Goshman)

"Voici mon secret. Il est très simple. On ne voit bien qu'avec le coeur. L'essentiel est invisible pour les yeux" St-Exupéry
Parson Smith
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I am awfully partial to the number 9.
Using the root of 9 can create miracles.
Here kitty, kitty,kitty. Smile
+++a posse ad esse+++
bnadworn
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I am partial to the number 9 as well. I was born on the 9th day of the month at 9:09 PM. My brother was born on September 9th. Lots of 9s in the family. If you are playing around on a calculator I have the most fun with the 9 key for changing numbers around. Magic for self amusement. It is just cool to see what the numbers will change into. Plus I don't need any special apparatus to make them disappear!

- Brian Nadworny
"They say the hand is quicker than the eye but I won't believe it until I see it."
Parson Smith
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Bnadworn,
Don't remember where I got it and it is really more of a puzzle thn effect.
First enter the #s 12345679 into the calculator.
Ask someone their favorite #.
Make one entry and the display fills with ther #.
Ah, the root of 9.
Here kitty, kitty,kitty. Smile
+++a posse ad esse+++
bnadworn
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Parson,
I love doing that trick on the calculator. Almost as much fun as spelling the words on the calculator. Thanks for the reminder about it.

- Brian
"They say the hand is quicker than the eye but I won't believe it until I see it."
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