Image: 3 utilities problem proof
Size of this PNG preview of this SVG file: 512 × 341 pixels. Other resolution: 320 × 213 pixels.
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Description: Proof without words that the three utilities problem has no solution by CMG Lee. The leftmost house is first deleted. The lines connecting the remaining houses and the utilities divide the plane into three regions, shaded purple, green and off-white. Whichever region the deleted house is placed into, one of the utilities is outside the region. The Jordan curve theorem states that a line connecting them must intersect one of the existing lines.
Title: 3 utilities problem proof
Credit: Own work
Author: Cmglee
Usage Terms: Creative Commons Attribution-Share Alike 4.0
License: CC BY-SA 4.0
License Link: https://creativecommons.org/licenses/by-sa/4.0
Attribution Required?: Yes
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