It is a common observation among travelers crossing the American Midwest that the landscape appears impossibly flat, leading to the popular saying that the state of Kansas is “flatter than a pancake.” This comparison suggests a near-perfect uniformity across a vast geographic area, capturing the sense of endless, unbroken horizon. The question, however, invites a rigorous scientific investigation to move beyond mere perception and determine if this hyperbolic statement holds any measurable truth.
The Origin of the Question
The specific comparison between the state’s topography and a griddle cake was formally addressed in a 2003 paper published in the Annals of Improbable Research. This tongue-in-cheek but technically rigorous study was conducted by geographers Mark Fonstad, William Pugatch, and Brandon Vogt. The researchers, primarily from Southwest Texas State University and Arizona State University, were prompted by the common traveler’s remark. Their goal was to use serious geographic and mathematical methodology to settle the long-standing debate about the state’s levelness. The work emphasized the value of applying scientific principles to unexpected questions.
Quantifying Flatness
To compare two objects of vastly different sizes—a state and a breakfast food—a standard mathematical metric for flatness was required. Geographers use a concept called the “flatness ratio,” or “flattening,” which is a method originally used to describe the shape of the Earth. This ratio measures the degree to which an arc or ellipsoid deviates from being perfectly flat. A value of 1.000 represents perfect, theoretical flatness, while a value closer to zero indicates a more rugged shape. The calculation involves comparing the semi-major axis (the horizontal distance) to the semi-minor axis (the vertical difference) of the measured cross-section.
This metric differentiates between the common perception of flatness and smoothness. A surface can be perfectly flat on a large scale but still have significant small-scale roughness, like an ant walking on a seemingly flat pancake. Conversely, a surface can be smooth but not flat, such as a large, gentle curve. The flatness ratio accounts for the overall topographic variation over an entire transect. The geographers used a second-order polynomial line fit to approximate the local ellipsoid for the cross-sections of both Kansas and the pancake.
The Pancake Comparison Methodology and Verdict
The researchers obtained a well-cooked pancake from a restaurant, the International House of Pancakes (IHOP), for their comparison. To create a topographic profile of the pancake, they cut out a sample strip and used a confocal laser microscope to map its surface terrain. This process allowed them to measure the minute changes in elevation across the pancake’s diameter. For the state, the team used elevation data from the U.S. Geological Survey to create a west-to-east topographic profile across Kansas.
Applying the quantifiable flatness ratio to both subjects yielded a surprising result. The pancake’s flatness was calculated to be approximately 0.957. The same mathematical model, when applied to the state of Kansas, resulted in a flatness value of approximately 0.9997. This number is remarkably close to the theoretical maximum of 1.000 for perfect flatness.
The conclusion was definitive: Kansas is mathematically and considerably flatter than a pancake. The state’s topography is so flat that initial software attempts to calculate the ratio simply returned a perfect value of 1.0, requiring more complex analysis to determine the final, extremely high measurement. This outcome is often counterintuitive because people confuse the visual smoothness of a pancake with the low curvature of the Kansas landscape. The study proved that the common saying is scientifically accurate when applying a geodetic definition of flatness.