square number classification

all square numbers are either:

a multiple of 4 or

one bigger than a multiple of 4

prove this using algebra

try to prove it using diagrams

why x?

one story:
Rene Descartes (1596 to 1650) popularised the idea of using letters from the back end of the alphabet for variables 
and letters from the front end of the alphabet for known constants (or parameters)
that much is pretty definite

being French and writing in french, a typesetter would normally use many more y's and z's than x's, so they preferred to use the less frequently used letter: x      
or so it is said


another story:

is found as a TED talk by Terry Moore, who maintains that difficulties in translating from the Arabic al-shalan for 'the unknown thing' 




( "Shei" first letter of al-shalan)



led to using the Greek, Kai symbol

which later was adapted to the Latin, x
  











others try to link the use of this particular letter with the Greek word 'Xenos'
an imprecise word, indicating a stranger or alien or unknown

anyway, 
it is time to change this historical quirk to use 'n' as a variable ('n' standing for a'n'y number) if we want two commonly used variables we can use 'm' and 'n' and if we want three we can use k, m and n

this is a firm proposal
time to move on from x