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Science communication is important in today's technologically advanced society. A good part of the adult community is not science savvy and lacks the background to make sense of rapidly changing technology. My blog attempts to help by publishing articles of general interest in an easy to read and understand format without using mathematics. You can contact me at ektalks@yahoo.co.uk

Friday 17 September 2021

p = sqrt(N+k) + sqrt(N-k); An Interesting Mathematical problem: Maths is Fun

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Recently, I came across an interesting mathematical problem on the internet that I thought could be generalised to provide much greater insight into how mathematics works.  The problem requires use of school level maths and I found it great fun to work on. 

(Click on the slide to see its full page image)




Equations 3, 4 and 5 provide the full solution of the problem.  Only even values of p are possible and their range is defined by eqns. 3 and 4.  Eqn.5 may then be used to calculate the corresponding values of k

The next slide shows the allowed values of p.
The range of p is seen to be quite small - in fact for N < 200, the number of allowed p values are less than four.  

For example, for N = 80, p(min) = 12.65 and p(max) = 17.89.  Since p is an even integer, only possible values of p are 14 and 16.  The corresponding values of k are (use eqn.5) 77.95 and 64. 


Final Word:  I find the problem to be very instructive - particularly, it demonstrates that some serious conclusions may be obtained by initial observations of the problem.  For example, by looking at the expression in eqn.1, we could establish the range of p values - later confirmed by the general analysis.  

Plotting a graph of the results is also very useful as this provides a wholesome view of the results obtained.

I hope that you enjoyed our little excursion and agree that 'Maths is Fun'.

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