# The Mathematica Story: A Scrapbook

Over Three Decades of Contributions to Invention, Discovery and Education

# Thomas H. Meyer, Ph.D., Associate Professor of Geodesy

A Mathematica memoir. It does sound fun, in a very geeky sort of way.

I think my best Mathematica presentation was with Craig Rollins when we introduced the geodesy group at the National Geospatial-Intelligence Agency to Mathematica at their GeoInt conference in St. Louis maybe six years ago. Peter Overmann and Joshua Martel also attended, as I recollect, as did some other Wolfram people.

Craig and I began the talk by adding 1/3 + 1/3 + 1/3 in a C program that, of course, did not return exactly one for the answer. The audience laughed, and we were off. We demonstrated how the exact arithmetic works and how it makes life quite nice for us geospatial people because latitudes and longitudes that are simple fractions or multiples of +/-pi are extremely common in our algorithms. We need to test for special cases that occur at the poles and being able to do that test easily might sound like it’s not a big deal, but it is.

We then moved on to replicate some famous geodesy results that were originally created using FORTRAN in programs that probably required hundreds of lines of code but with us doing the same thing with a line or two of Mathematica. These included creating nationwide graphics that show the geometric relationships between datums, how they shift their reference ellipsoids, and how that shift causes places to have different coordinates and thus, it would seem, to have moved. David Doyle (NGS, ret.) was on television in the last year or two to address how someone got a hold of the old NAD27 coordinates for the Four Corners marker in the Southwest and noted that his GPS gave him the “wrong answer” because it produces WGS84 coordinates. Our graphic showed this kind of shift for the entire US. We then moved on to doing some series expansions that are common in geodesy, expansions that arise, for example, from special functions like elliptic integrals. Manipulating these series is usually quite tedious but Mathematica‘s algebra made it all work out like magic.

While on sabbatical at NGA, I was once asked whether I could find the expansions of some Legendre polynomials using trig functions for their arguments plus their derivatives. I had the results about as fast as the question was asked, much to their amazement. I sometimes forget how astonishing all this is to people who don’t use Mathematica.