The mathematicians of Pythagoras's school (500 BC to
300 BC) were interested in numbers for their mystical
and numerological properties. They understood the idea
of primality and were interested in perfect and
amicable numbers.

A perfect number is one whose proper divisors sum to
the number itself. e.g. The number 6 has proper
divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors
1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28. A pair
of amicable numbers is a pair like 220 and 284 such
that the proper divisors of one number sum to the other
and vice versa. 

and from "Perfect numbers" at
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Perfect_numbers.html:

It is not known when perfect numbers were first studied
and indeed the first studies may go back to the
earliest times when numbers first aroused curiosity. It
is quite likely, although not certain, that the
Egyptians would have come across such numbers naturally
given the way their methods of calculation worked, see
for example [17] where detailed justification for this
idea is given. Perfect numbers were studied by
Pythagoras and his followers, more for their mystical
properties than for their number theoretic properties.
Before we begin to look at the history of the study of
perfect numbers, we define the concepts which are
involved.

Today the usual definition of a perfect number is in
terms of its divisors, but early definitions were in
terms of the 'aliquot parts' of a number.

An aliquot part of a number is a proper quotient of the
number. So for example the aliquot parts of 10 are 1, 2
and 5. These occur since 1 = 10/10, 2 = 10/5, and 5 =
10/2. Note that 10 is not an aliquot part of 10 since
it is not a proper quotient, i.e. a quotient different
from the number itself. A perfect number is defined to
be one which is equal to the sum of its aliquot parts.


The four perfect numbers 6, 28, 496 and 8128 seem to
have been known from ancient times and there is no
record of these discoveries.

    6 = 1 + 2 + 3,
    28 = 1 + 2 + 4 + 7 + 14,
    496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
    8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064 
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from
http://www-history.mcs.st-and.ac.uk/history/HistTopics/Prime_numbers.html
(accessed 1/7/08)
=================

The number 12 is called abundant because the sum of the proper divisors 1 2 3 4 6 = 16
is greater than 12. [The next abundant number is 18 is less than 21 which = 1 2 3 6 9]
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from
http://209.85.173.104/search?q=cache:-4CjTBuDfvAJ:www.math.colostate.edu/mathday/Past%2520TEAM%2520Questions/mathday96.pdf+math+number+divisors+engine+website+automatic&hl=en&ct=clnk&cd=13&gl=us
(accessed 1/7/08)
=================

...the 11 Rule. When multiplying a single digit number
by 11, the product is the number written twice. For
example, 711=77. To multiply a two digit number by 11
add the two digits and place the sum in between!

25x11=275
32x11=352
47x11=517 (you need to carry the 1) 
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from
http://tutoring.sylvanlearning.com/newsletter/0203/problems.cfm
(accessed 1/7/08)
=================


"Leonardo Pisano lived from 1170 to 1250 Fibonacci played an important role in reviving ancient mathematics and made significant contributions of his own. Liber abaci introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. --------------------- http://www-history.mcs.st-and.ac.uk/history/HistTopics/Arabic_numerals.html (accessed 1/7/08) ================= (taking the street number as a value) ----- tyagi nagasiva 871 ironwood drive = 1145 {229x5} 871 yronwode drive = 1048 {131x8} 871 ironwood drive = 1042 {521x2} 871 ironwood dr = 0906 {151x6} tyagi nagasiva bryan w yronwood = 348 tyagi nagasiva bryan w yronwode = 338 tyagi nagasiva bryan w yronwod = 333 tyagi nagasiva ironwood drive = 307 nagasiva bryan w yronwode = 276 tyagi nagasiva ironwood = 249 catherine anna yronwode = 232 bryan william selfridge = 224 catherine yronwode = 202 nagasiva yronwode = 193 catherine anna manfredi 183 [871] yronwode drive = 177 [871] ironwood drive = 171 bryan selfridge = 145 {29x5} tyagi nagasiva = 136 {17x8} ironwood dr = 135 cathy manfredi = 127 yronwode = 119 selfridge = 85 !!!!!!!!!!!!!! bryan w = 83 catherine = 83 !!!!!!!!!!!!!! william = 79 nagasiva = 74 manfredi = 70 tyagi = 62 bryan = 60 cathy = 57 siva = 51 anna = 30 cat = 24 !!!!!!!!!!!!!! naga = 23 w = 23 !!!!!!!!!!!!!! future research: References for: The Arabic numeral system Version for printing 1. G Ifrah, A universal history of numbers : From prehistory to the invention of the computer (London, 1998). 2. G G Joseph, The crest of the peacock (London, 1991). 3. R Kaplan, The nothing that is : a natural history of zero (London, 1999). 4. L C Karpinski, The history of arithmetic (New York, 1965). 5. K W Menninger, Number words and number symbols : A cultural history of numbers (Boston, 1969). 6. D E Smith and L C Karpinski, The Hindu-Arabic numerals (Boston, 1911). JOC/EFR January 2001 from http://www-history.mcs.st-andrews.ac.uk/HistTopics/References/Arabic_numerals.html accessed 1/7/08 ================ c - 2008 nagasiva yronwode yippie initidivination