Actually it's flatter - or so this article in the Journal of Improbable Research would have us believe. I like this sort of science: it's daft, I can understand it and it makes me laugh. Here's the article almost in its entirety. Perhaps it will amuse you as well. Perhaps it will inspire someone to replicate the study to find out how flat Norfolk is? Perhaps I should take some pills and lie down.
PS: Like the Jumbo saga, this one has a while to run yet. You have been warned.
PPS: For my more insular readers, Kansas is a state in the USA somewhere near the top. It sounds a bit like Holland but with less water, fewer tulips and more crops.
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Kansas Is
Flatter Than a Pancake (Mark Fonstad,
William Pugatch, and Brandon Vogt).
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.
A Technical
Approach to Pancakes and Kansas
Barring the acquisition
of either a Kansas-sized pancake or a pancake-sized Kansas, mathematical
techniques are needed to do a proper comparison. Some readers may find the
comparing of a pancake and Kansas to be analogous to the comparing of apples
and oranges; we refer those readers to a 1995 publication by NASA’s Scott
Sandford 3, who used spectrographic techniques to do a comparison of
apples and oranges.
|
Figure 1. (a) A well-cooked pancake and (b) Kansas. |
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.
Materials
and Methods
|
Figure 2. Pancake cross-sectional surface being digitized. |
We purchased a
well-cooked pancake from a local restaurant, the International House of
Pancakes, and prepared it for analysis by separating a 2-cm wide sample strip
that had not had time to desiccate. We collected macro-pancake topography
through digital image processing of a pancake image and ruler for scale
calibration (see Figure 2). We made another topographic profile from the sample, using a confocal
laser microscope. The importance of this research dictated that we not be
daunted by the “No Food or Drink” sign posted in the microscopy room. The
microscope collects one elevation point every 10 mm and has a maximum surface
diameter of 2 cm (see Figure 3).
|
Figure 3. When viewed at a scale of 50 mm, a pancake appears more rugged than the Grand Canyon |
We measured a west-east profile across Kansas taken
from merged 1:250,000 scale digital elevation model (DEM) data from the United
States Geological Survey. In general, the spacing between adjacent elevation
points on the landscape transects was approximately 90 meters. We extracted
surface transects and flatness estimates from the Kansas and pancake DEM data
using a geographic information system.
Results
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).
|
Figure 4. Surface topography of Kansas and of a pancake. |
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.”
Conclusion
Simply put,
our results show that Kansas is considerably flatter than a pancake.
Notes
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.