If it's desired for the district boundaries to be lines of latitude & longitude, and if it's desired to not use a map, then define the district boundaries as follows:
The state is divided into bands of east-west extent. The 1st band has as its northern border the northern border of the state. Each subsequent band has as its northern border the southern border of band adjacent to it, to the north (and maybe sometimes part of the state border).
"A" is the average area per district, (state's area divided by the number of districts).
Starting with the northernmost band, define each band in turn as follows:
The initial width (north-south) of the band is sqr(A). If the band is the northernmost band, or if part of the band's border includes part of the state's border, then the width measurement is to be made at the middle of the band.
Starting at the west end of the band, mark off rectangles each of which contains the desired population per district. Those are districts. The eastmost district will have less than the desired population.
(of course the westernmost & easternmost districts might not be rectanales, due to irregular state borders).
If the eastmost district has more than half of the desired district population, then move the band's south border southward till the band contains population for an integer number of districts. Repeat the procedure to divide the band into rectangles each containing the desired district population.
If the eastmost district has less than half of the desired district population, then move the band's south border northward till the band contains population for an integer number of districts. Repeat the procedure to divide the band into rectangles each containing the desired districit population.
Mike Ossipoff
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