[VA] SRC #012d - Then and Now: Area

[Valentin Albillo]

  
Hi, all,

Welcome to the 4^th part of my ongoing SRC #012 - Then and Now, where I'm showing that advanced vintage HP calcs which were great problem-solvers back THEN in the 80's are NOW still perfectly capable of solving recent, non-trivial problems intended to be tackled using modern PCs, never mind ancient calcs.

In the next weeks I'm proposing six increasingly harder such problems for you to try and solve using your vintage HP calcs while abiding by the mandatory rules summarized here:

You must use VINTAGE HP CALCS (physical/virtual,) coding in either RPN (inc. mcode), RPL (variants existing at the time, inc. SysRPL) or HP-71B languages (inc. BASIC, FORTH, Assembler), so NO XCAS, MATHEMATICA, MAPLE, EXCEL, C/C++/C#, PYTHON, LUA, etc., NO LENGTHY MATH SESSIONS and NO CODE PANELS.

On the plus side, you may use any official/popular modules, pacs or libraries available at the time such as the Math Pac, HP-IL and JPC ROMs for the HP-71B, the Advantage Module, PPC ROM and EM for the HP-41, and libraries for the RPL models, etc..

Once P1 (Probability), P2 (Root) and P3 (Sum) are over, now's the turn for Problem 4, which deals with area and it's ever-so-slightly harder than the previous ones. Also, lest you'd think it looks like a textbook exercise, rest assured there's some nice surprises to deal with (if you've got what it takes, that is ...)

Problem 4:  Area

The thermodynamic efficiency of the combined cycle for a hypothetical gas turbine using ethane as fuel is related to the area of the region R of the X-Y plane defined by the expression
    
where radians are used, M is 30.070 (ethane's Molar mass in g/mol, see Properties,) and d is 1.598 (Molar density in mol/dm³). Write a program to compute this area.

Here the focus is on computing the area of R, so you might begin by locating R via estimating (2 decimal digits at most, ±d.dd) the coordinates of some rectangle that fully encloses it, either by writing code to sweep the X-Y plane or simply by using a graphing calculator or online function plotter, your choice.

Once obtained, your program (which should take no inputs,) can refine and use them to compute and output R's area accurate to 10-12 correct digits (give or take a few ulp,) and the faster the running time the better.

If I see interest, in a week or so I'll post my own original solution for the HP-71B, which is a very short program that does the job. In the meantime, let's see your very own clever solutions AND remember the above rules. this is strictly for vintage HP calcs, Ok ?

Also, please be kind and avoid spoiling it for other interested people by immediately posting your solution and/or results. Wait instead until next Wednesday 9:00 pm GMT+1 so that other people will have a chance. In the meantime you can mull it over so that you eventually post the one (1) message featuring your fully refined solution instead of a myriad posts refining it little by little. Got it ?

V.