Why do Golden Thank Yous have the denominations 1, 2, 3, 5, 8, 13, 21, 34, ...?
Fibonacci Sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... begins with 0
and 1. Every other number is the sum of the previous two numbers
in the sequence. Golden Thank Yous use these numbers as their
denominations because they are very convenient for making change. For
example, a 34 bill is worth the same as a 13 bill and a 21 bill.
Also, the number of bills needed for any amount of cash is usually quite small. For example,
that there is never any need to have two consecutive denominations,
like a 5 and an 8, since they could just be replaced by a 13 bill. You also never need more than one of any bill.
Why not use the denominations 1, 2, 5, 10, 20, 50, 100, ...?
Thank Yous are the official currency of the Fruit Smoothians, the most
technologically advanced civilization in the Milky Way Galaxy. Fruit
Smoothians have 7 fingers on each hand, so their numbering system is
base 7. By comparison, we use a base 10 numbering system because we
have 10 fingers on two hands. The many other civilizations in the
Milky Way Galaxy also have their own numbering systems for many
Fortunately for us, the Fruit Smoothians are
a kind and generous civilization who have protected us and the rest of
the Milky Way Galaxy from outside invaders for billions of years.
Because of this, many civilizations in the Milky Way Galaxy have
adopted Golden Thank Yous as their preferred currency. In return, the
Fruit Smoothians made their currency as easy as possible to translate
into every language and every numbering system. They chose the
Fibonacci Sequence for their denominations because these numbers are
just as natural, useful, and convenient in every numbering system.
You can learn more about the Fruit Smoothian's in Professor Bray's book (ages 7 to 14 and up), "Trevor the Time Traveler and the Murkian Threat."
the story, Trevor and his sister Farrah become secret agents for the
Fruit Smoothians to help them defend the Milky Way Galaxy from the
treacherous Murkians from the Andromeda Galaxy. While the book is a lot
of fun to read, it is also a vehicle for Professor Bray
to explain some of the most amazing true science ideas ever discovered,
including brief discussions of Special and General Relativity.
What kinds of math and science are on the back sides of Golden Thank Yous?
math and science on the fronts and backs of Golden Thank Yous range
from elementary to advanced so that every person who uses them will
find some easy and some challenging. On the elementary side, each bill
is labeled with a letter of the alphabet, so kids who know their
alphabet will be able to know which bills are worth the most. On the
advanced side, click on the 8 bills above on the right to learn a very
cool magic trick with the number 9 that most adults don't even know.
There are more than 100 different math and science lessons on the backs
of Golden Thank Yous so far, and that number is growing all the time.
you know there was a geometric reason why 7 x 7 = 49? Check out the 7 x
7 = 49 bill above on the left! The 4 outside regions contain ten
spots each while the middle region contains 9 spots - hence there are
49 spots in the 7 by 7 array.
Above in the middle are 8 of the greatest scientists who ever lived. Click on the pages above to be able to read them better.