Little explorations with HP calculators (no Prime)

03272017, 07:39 PM
Post: #41




RE: Little explorations with the HP calculators
(03272017 12:14 PM)pier4r Wrote:Quote:Brilliant.org Let's divide one of the righttriangles into four righttriangles (two with sides lengths equal to r and x and two with side lengths r and 1x) and a square with side r. Then it's area is S = r*x + r(1x) + r^2 S = r^2 + r The area of the larger square, witch we know is equal to 1, is the sum of the areas of these four righttriangles plus the area of the smaller square in the center, with side 2*r: S = 4(r^2 + r) + (2*r)^2 = 1 Or 8*r^2 + 4*r  1 = 0 Here I am tempted to just take my wp34s and do 8 ENTER 4 ENTER 1 +/ SLVQ and get a valid numerical answer for the quadratic equation, but I decide to go through a few more steps by hand and get the exact answer: r = (sqrt(3)  1)/4 

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