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 ----- 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] ----- 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, 7«11=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) ----- 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