On Thu, Jun 4, 2009 at 7:28 AM, kimjo...@ozemail.com.au
<kimjo...@ozemail.com.au> wrote:
> On Thu Jun  4  1:15 , Bruno Marchal  sent:
>>Very good answer, Kim,
>>Just a few comments. and then the sequel.
>>Exercice 4: does the real number square-root(2) belongs to {0, 1, 2,
>>3, ...}?
>>No idea what square-root(2) means. When I said I was innumerate I wasn't 
>>kidding! I
> could of course look
>>it up or ask my mathematics teacher friends but I just know your explanation 
>>will make
> theirs seem trite.
>>Well thanks. The square root of 2 is a number x, such that x*x (x times x, x 
>>multiplied by
> itself) gives 2.For example, the square root of 4 is 2, because 2*2 is 4. The 
> square root of
> 9 is 3, because 3*3 is 9. Her by "square root" I mean the positive square 
> root, because we
> will see (more later that soon) that numbers can have negative square root, 
> but please
> forget this. At this stage, with this definition, you can guess that the 
> square root of 2
> cannot be a natural number. 1*1 = 1, and 2*2 = 4, and it would be astonishing 
> that x
> could be bigger than 2. So if there is number x such that x*x is 2, we can 
> guess that such
> a x cannot be a natural number, that is an element of {0, 1, 2, 3 ...}, and 
> the answer of
> exercise 4 is "no". The square root of two will reappear recurrently, but 
> more in examples,
> than in the sequence of notions which are strictly needed for UDA-7.
> OK - I find this quite mind-blowing; probably because I now understand it for 
> the first
> time in my life. So how did it get this rather ridiculous name of "square 
> root"? What's it
> called in French?

I don't know what it is called in French, but I can answer the first
part.  I remember the day I first figured out where the term came

When you have a number multiplied by itself, the result is called a
square.  3*3 = 9, so 9 is a square.  Imagine arranging a set of peas,
if you can arrange them in a square (the four cornered kind) with the
same number of rows as columns, then that number is a square.  Some
examples of squares are: 4, 9, 16, 25, 36, 49, 64, 81, see the
pattern?  And the "roots" of those squares are 2, 3, 4, 5, 6, 7, 8,
and 9.  The square root is equal to the number of items in a row, or
column when you arrange them in a square.

This is a completely extraneous fact, but one I consider to be very
interesting: Multiply any 4 consecutive positive whole numbers and the
result will always be 1 less than a square number.  For example,
5*6*7*8 = 1680, which is 1 less than 1681, which is 41*41.  Isn't that


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