i 'red' in a maths popularization book of steven strogatz that 1+3=4, 1+3+5=9, 1+3+5+7=16, and so on; wich would be the hypothesis when trying to demonstrate this striking 'fact'?
Hello Mircea,
Which fact?
1. The sum of successive odd integers (starting with 1) yields a perfect square?
2. The root of the perfect square equals the median value of the set of integers used?
3. Something else?
Either (1) or (2) could be evaluated as a proposition, and a proof attempted.
Or, did you have something else in mind?
Good luck with your work.
the first one seems to me the most interesting, dear david; regards, mircea
dear david, i;m not a mathematician, but i believe that we must find firstly a property of the perfect squares, to be 'linked' with odd numbers, or something like that; best wishes, mircea
in his famous 'principia', newton uses mathematical considerations to demonstrate the angular momentum conservation; in the 'first' triangle one of the side is the velocity--its value, so a number--, and the other two sides are the 'distances' at t and t+1, respectively; now, if the ares are the same, could we say that theese two sides express the flow of the time
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