# [EM] 120 Seats

Doreen Dotan dordot2001 at yahoo.com
Sun Apr 16 14:41:19 PDT 2006

```I am asking the following question in the framework of an attempt to write a proposal for a revision of the electoral system in Israel.

There seems to be a large number of parliaments and legislatures that are composed of 120 seats in countries that are very dissimilar demographically, politically, economically, geographically and so on.

Is the number 120 significant because of the particular mathematical properties of the number 120, to wit:

120 is the factorial of 5. It is the sum of a twin prime pair (59 + 61) as well as the sum of four consecutive primes (23 + 29 + 31 + 37). It is highly composite, superabundant, and colossally abundant number, with its 16 divisors being more than any number lower than it has, and it is also the smallest number to have exactly that many divisors. It is also a sparsely totient number. 120 is the smallest number to appear six times in Pascal's triangle, and it is also a Harshad number.
It is the eighth hexagonal number and the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number.
120 is the first multiply perfect number of order three (a 3-perfect number). The sum of its factors (including one and itself) sum to 360; exactly three times 120. Note that perfect numbers are order two (2-perfect) by the same definition.
120 is divisible by the number of primes below it, 30 in this case. However there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number.
120 figures in Fermat's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that multiplied with any of the other numbers in the sequence yields a number that is one less than a square. Euler also searched for this number, but failed to find it, but did find a fractional number that meets the other conditions, 777480 / 287922.
The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120 degrees.

Source: http://en.wikipedia.org/wiki/120_(number)

or is there some other reason? Are there additional reasons?

Doreen Ellen Bell-Dotan, Tzfat, Israel

http://www.geocities.com/dordot2001/ImperativeOfMoralMaths.html

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