## Wednesday, August 4, 2010

### 25

25 = 52, a perfect square.

25 has a representation as a sum of two squares: 25 = 32 + 42. It is the smallest square that can be written as a sum of two squares.

25 is the hypotenuse of a primitive Pythagorean triple: 252 = 72 + 242.

25 is the sum of the first five odd numbers: 25 = 1 + 3 + 5 + 7 + 9.

25 = 3 + 4 + 5 + 6 + 7.

Every square number is the sum of two triangular numbers: 25 = 10 + 15.

Pachisi, the Hindu word for 25, is one of the national games of India.

Source: Phillips, R. 1994. Numbers: Facts, Figures and Fiction. Cambridge University Press.

#### 1 comment:

Anonymous said...

Other properties of the number 25
25 is an octahedral number since (2n-1)(2n^2-2n+3)/3 =25 with n=3,
See A001845 and http://mathworld.wolfram.com/OctahedralNumber
25 is a octagonal number since (2n-1)=25 with n=3
25 is an automorphic number since 5^2=25 is termination of one's own number, see
A003226
25 is a Friedman number since 25=5^2 uses the same digits, see
A036057
25 is a Cullen number since n*2^2=25 with n=3, see A002064 and
http://math.world.wolfram.com/CullernNumber
25 is a number trimorphic since n^3= 5,625 where the last two digits correspond to n, with n=25, see A033819 and http:mathworld.wolfram.com/Trimorphic/Number
25 is a Hilbert number since 25=4*6+1, see A016813 and http://mathworld.wolfram.com/HilbertNumber
25 is a number of Brown since 25=4!+1
As 5^2=25, if all digits (except the exponent) is added the unit is
6^2=36
If 25 is subtracted from or added the number 6, we get two prime numbers:
25-6=19 and 25+6=31
If 25 is subtracted or added the number 12, get two prime numbers:
25-12=13 and 25+12=37
The number 25 can be represented as Pythagorean triples
25^2=15^2+20^2
25^2+312^2=313^2
Also
25=13^2-12^2
If 25^2=625 and 16^2=256, repeat 25to the end and beginning of the output.
Rafael Parra Machio