There's no trick to figure out... it's a mathematical anomaly.
The width of the triangle is 13 - the height is 5. Both of these
numbers are part of a sequence known as the Fibonnacci Sequence. It's
a very simple sequence, of the form
x0 = 0, x1 = 1, x2 = x0 + x1, x3 = x1 + x2, ..., x(n) = x(n-1) +
x(n-2). the first 10 numbers in the sequence are
0,1,1,2,3,5,8,13,21,34. If you take the limit of each pair of numbers
as a ratio x(n) / x(n+1) (such as 5/8 or 8/13) then as n approaches
infinity the limit is a number denoted as the greek letter phi,
approximating 1.61. There are many interesting things about this
number.
This number is what you get when you take a line segment and break it
into two pieces, such that the ratio of the larger piece to the length
of the whole is the same as the ratio of the smaller piece to the
larger piece:
Whole stick is 1 foot long
Broken into two pieces: X and 1-X where X < 1
Ratio = X/1 = (1-X)/X
Solving for X you first get X^2 - X +1 then you use the quadratic
equation which results in (1+- sqr(5))/2 which approximates 1.61
Phi is also known as the golden ratio, used frequently in greek
architecture. It's also found in nature as a growth scale of many
living organisms.
As each pair of Fibonnacci numbers is taken as a ratio, the ratio
hovers closer and closer to Phi, although it never reaches Phi. The
ratio alternates in magnitude: one pair is higher than Phi, the next is
lower.
The puzzle has something to do with the fact that Phi is the only
number that grows both geometrically and exponentially simultaneously.
Google "Fibonnacci" or look at http://indigo.ie/~peter/F19.htm for more
information on this sequence.
- Matt Small
On Friday, December 19, 2003, at 07:40 PM, Ian Skinner wrote:
> Here's a simpler version of the same trick that has been around for
> years.
> http://www.caveofmagic.com/pickcrd2.htm
>
> Now this puzzle from the same site has my mind boggled.��I have not
> figured
> out how this one works.
> http://www.simeonmagic.com/triangle/triangle1.htm
>
> ----- Original Message -----
> From: <[EMAIL PROTECTED]>
> To: "CF-Community" <[EMAIL PROTECTED]>
> Sent: Friday, December 19, 2003 2:54 PM
> Subject: It's MAGIC...
>
> > http://www.zorstec.net/copperfield.htm
> >
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>
>
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