The article you linked says the number 588 is based off of the 1990 census, when it says the population was about 203 million (This census document says the 1990 population was 249 million, so who knows). According to the linked document, the 2000 census counted 281 million Americans, which by the method in question would produce a 655 member house.
Glad you caught that. The 1990 census indicated that there were 203,578,000 citizens of voting-age (18 years or older) in that time-frame, which according to the cube-root formula would be ~588.27, which rounded down to a whole number of 588 potential Representatives as indicated in the linked article. The 2000 census indicates that there were 209,128,094 citizens of voting-age 18 years or older, of which the cube-root is ~593.56, rounded up to the whole number of 594 Representatives. Not too unwieldy a number...
Source: U.S. Census Bureau: DP-1. Profile of General Demographic Characteristics: 2000
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And I'm glad you reminded me that it's based on voting age population. My neglecting that was the reason for the inconsistent numbers.