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The great American total solar eclipse of 21 August 2017 offered a fortuitous opportunity to study the response of the atmosphere and ionosphere using a myriad of ground instruments. We have used the network of U.S. Global Positioning System receivers to examine perturbations in maps of ionospheric total electron content (TEC). Coherent large-scale variations in TEC have been interpreted by others as gravity wave-induced traveling ionospheric disturbances. However, the solar disk had two active regions at that time, one near the center of the disk and one at the edge, which resulted in an irregular illumination pattern in the extreme ultraviolet (EUV)/X-ray bands. Using detailed EUV occultation maps calculated from the National Aeronautics and Space Administration Solar Dynamics Observatory Atmospheric Imaging Assembly images, we show excellent agreement between TEC perturbations and computed gradients in EUV illumination. The results strongly suggest that prominent large-scale TEC disturbances were consequences of direct EUV modulation, rather than gravity wave-induced traveling ionospheric disturbances.