PS: Like the Jumbo saga, this one has a while to run yet. You have been warned.
In this report, we apply basic scientific techniques to answer the question “Is Kansas as flat as a pancake?” While driving across the American Midwest, it is common to hear travellers remark, “This state is as flat as a pancake.” To the authors, this adage seems to qualitatively capture some characteristic of a topographic geodetic survey 2. This obvious question “how flat is a pancake” spurned our analytical interest, and we set out to find the ‘flatness’ of both a pancake and one particular state: Kansas.
|Figure 1. (a) A well-cooked pancake|
and (b) Kansas.
|Figure 2. Pancake cross-sectional surface being digitized.|
|Figure 3. When viewed at a scale of 50 mm, |
a pancake appears more rugged than the Grand Canyon
The topographic transects of both Kansas and a pancake at millimeter scale are both quite flat, but this first analysis showed that Kansas is clearly flatter (see Figure 4).
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.”
Simply put, our results show that Kansas is considerably flatter than a pancake.
1. The photograph of Kansas is of an area near Wichita, Kansas. It may be of significance that the town of Liberal, Kansas hosts the annual ‘International Pancake Day’ festival.
2. To pump up our cross-disciplinary name-dropping, we should also mention that recently some quick-thinking cosmologists also described the universe as being “flatter than a pancake” after making detailed measurements of the cosmic background radiation.
3. “Comparing Apples and Oranges,” S.A. Sandford, Annals of Improbable Research, vol. 1, no. 3, May/June 1995.