Tag: iteration

Using Maxima To Do Some Math Described in the Movie “Hidden Figures”

I looked in the NASA archives for the work of Katherine Johnson described so dramatically in the film “Hidden Figures”.  I found this 1960 paper:

nasa_title

In particular, I was struck by the film’s use of “Euler’s Method” as the critical plot point, and sadly couldn’t find anything about the use of that method in the archive, nor mention of it in the text of  Margot Lee Shetterly’s book on which the film “Hidden Figures” is based.

I did however read in the paper about an “iterative procedure” needed to solve for one variable.

Turns out the sequence of equations described in the report, when assembled into an expression in the single variable of interest, defines  a contraction mapping and so converges by functional iteration, as is numerically demonstrated in the paper.

At the bottom I’ve linked a fuller treatment in a .wxmx file.  Briefly, the authors describe the problem:

nasaeq19

nasaeq20

nasaeq89

nasa_iteration

Here’s everything from the paper needed to do that in Maxima:

nasaconstants1

nasaconstants2

nasaconstants3

I put together equations 19,20,8, and 9, together with all those constants defined by the paper and customized trig function that act on angles measured in degrees, into an expression of the form

  \theta_{2e}=F(\theta_{2e})

and applied the built-in Maxima numerical solver find_root().  The result agrees reasonably well with the result  \theta_{2e}=50.806 quoted in the paper.

nasaiteration_findroots

In the above, I computed the derivative of the mapping F evaluated at the solution and found that the value is much less than one, showing it is a contraction.

Here’s my full wxMaxima session.

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