Synergy User Manual and Tutorial. - THE CORE MEMORY

Synergy User Manual and Tutorial
200 BC the 14 th century, the
Chinese invented a more advanced
abacus device. The typical
Chinese swanpan (abacus) is
approximately eight inches tall and
of various widths and typically has
more than seven rods, which hold
beads usually made from
hardwood. This device works as a
5-2-5-2 based number system,
which is similar to the decimal
system. Advanced swanpan techniques are not limited to simple addition and
subtraction. Multiplication, division, square roots and cube roots can be calculated very
efficiently. A variation of this devise is still in use by shopkeepers in various Asian
countries. ii There is direct evidence that the Chinese were using a positional number
system by 1300 BC and were using a zero valued digit by 800 AD.
Sometime after 200 BC, Eratosthenes of Cyrene (276-194 BC) developed the Sieve of
Eratosthenes, which was a procedure for determining prime numbers. It is called a sieve
because it strains or filters out all non-primes. The process is as follows:
1. Make a list of all integers greater than one and less than or equal to n
2. Strike out the multiples of all primes less than or equal to the square root of n.
3. The numbers that are left are the primes.
The table below show the result for n = 50 with primes in the white squares.
2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
Eratosthenes is also credited with being the first person to accurately estimate the
diameter of the Earth and also served as the director of the famed Library of Alexandria. iii
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