Kansas Is Flatter than a Pancake

pancake-stack

Tomorrow, of course, is International Pancake Day, and the occasion for the annual pancake race held simultaneously in Liberal, Kansas, and Olney, England.

It’s also a perfect opportunity to revisit the old saw that Kansas is flatter than a pancake — an issue addressed scientifically, if serendipitously, half a dozen years ago in the ever-entertaining and illuminating Annals of Improbable Research. Writing for the May/June issue of 2003, scientists from the Departments of Geography at Texas State University and Arizona State University reported conclusively that “Kansas is Flatter than a Pancake”

As they explain, “barring the acquisition of either a Kansas-sized pancake or a pancake-sized Kansas, mathematical techniques are needed to do a proper comparison . . . . One common method of quantifying ‘flatness’ in geodesy is the ‘flattening’ ratio. The length of an ellipse’s (or arc’s) semi-major axis a is compared with its measured semi-minor axis b using the formula for flattening, f = (a – b) / a. A perfectly flat surface will have a flattening f of one, whereas an ellipsoid with equal axis lengths will have no flattening, and f will equal zero.

“For example, the earth is slightly flattened at the poles due to the earth’s rotation, making its semi-major axis slightly longer than its semi-minor axis, giving a global f of 0.00335. For both Kansas and the pancake, we approximated the local ellipsoid with a second-order polynomial line fit to the cross-sections. These polynomial equations allowed us to estimate the local ellipsoid’s semi-major and semi-minor axes and thus we can calculate the flattening measure f.” See the article for a further — and hilarious – description of their methodology.

Their conclusion? “Mathematically, a value of 1.000 would indicate perfect, platonic flatness. The calculated flatness of the pancake transect from the digital image is approximately 0.957, which is pretty flat, but far from perfectly flat. The confocal laser scan showed the pancake surface to be slightly rougher, still.

“Measuring the flatness of Kansas presented us with a greater challenge than measuring the flatness of the pancake. The state is so flat that the off-the-shelf software produced a flatness value for it of 1. This value was, as they say, too good to be true, so we did a more complex analysis, and after many hours of programming work, we were able to estimate that Kansas’s flatness is approximately 0.9997. That degree of flatness might be described, mathematically, as ‘damn flat.’”

For further coverage of the study and its conclusions, see “Zero Gravity: The Lighter Side of Science” from the American Physical Society, and the article “Holy Hotcakes! Study Finds Kansas Flatter than a Pancake” in the Lawrence Journal-World for July 27, 2003.

It is worth pointing out, of course, that by the very measure the geographers used, Florida (with a variation of only 345 feet from sea level to its highest point at Britton Hill), Delaware (with a variation from sea level to its highest point of 448 feet), Louisiana (with a variation from sea level to the top of Driskill Mountain at 535 feet), and 18 other states are in fact flatter than both pancakes and Kansas. And, as the Journal-World avers, by measuring in terms of the elevation changes in one-kilometer sections, Kansas ranks all the way down at 32nd in flatness. But perhaps that all is just a matter of comparing apples to oranges.

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Published in: on February 23, 2009 at 6:16 pm  Comments (1)  

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One CommentLeave a comment

  1. Thanks for sharing those precious information, indeed i do need those infor. to accomplish my translation homework.


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