When the railroad first came to what is now Random Lake, the officials gave the place the name of Greenleaf, the financial agent of the company; but the name was soon changed so as to conform to that of the lake on the edge of which it was laid out... The lake was named by the government surveyors who made the original government survey of that section of the country in 1835. "Running a random line" is the surveying expression, and it is probably while the surveyors were running such a line through the thick woods (that) they accidentally came upon the lake.

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Random Lake, Wisconsin

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[Source: Buchen's Historic Sheboygan County, p. 270.]