Little explorations with HP calculators (no Prime)
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04-08-2017, 09:17 PM
(This post was last modified: 04-08-2017 09:20 PM by Gerson W. Barbosa.)
Post: #161
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RE: Little explorations with the HP calculators
(04-08-2017 05:19 PM)Han Wrote: For anyone who is curious about the tedious algebra using Heron's formula as shown by Gerson, here is a text output from Maple 17: Good idea leaving the square roots aside until the last step! I did this on the two Heron's formula results only and got a better simplified expression for the ratio between the areas: Sabc a b c ------ = ----------------------------------- Sdef a(b - r)(c - s) + t(c r + b(s - c)) Making r = b/2, s = c/3 and t = a/4 per the original problem, the expression easily evaluates to 24/7. Perhaps r should be associated with side a, s to side b, t to side c and the expression rewritten accordingly for mnemonic purposes. This is exactly the approach I thought of since the beginning. I decided to use a triangle with sides proportional to 2, 3 and 4 as I realized the shape didn't matter (so did SlideRule as well). This simplified the solution, but required Heron's formula twice, the one for the inner triangle being a bit more laborious to solve by hand. Since the shape was irrelevant, why not to choose an even more convenient one? Indeed this allowed for an even more immediate solution. I still don't understand all the fuss about the use of these particular shapes, since they would have spared lots of tedious calculations as we've seen :-) |
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