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? >

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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 from. 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 neat? Jason --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---