Cities of the Leviim

The Torah gives instructions on how to construct the cities of the Levites. We need to give 1,000 amahs outside the city for open space (Bamidbar 35: 4).Then it states that we need to give 2,000 amahs outside the city for open space (Bamidbar 35: 5). The commentators give different resolutions to this apparent contradiction.  

The Ramban explains that city itself is a square with the length of 1,000 amahs (See A). We need to make circle around the city with the city in the center. The circle has a diameter 2,000 amahs. (See B) The area of the circle around the city is meant to be left as empty space. Around the circle is a square. The square is 2,000 amahs in length. (See C) The area of the square outside the circle is designated for fields and vineyards. (Based on the commentary on the Ramban by Rabbi Chiam Chavel)

Question: What is the area of the city?

Answer: 1,000 amahs x 1,000 amahs = 1,000,000 square amahs

Question: What is the area of the circle outside the city? (Use 3.14 for π)

Answer: {area of the circle} – {area of the square} 

{ π r2}– {length of square2}

{3.14 – 1,0002} – {1,0002}

3,140,000 – 1,000,000  = 2,140,000 square amahs

Question: What is the area of the land designated for fields and vineyards?

Answer: {Area of outer square} – {area of whole circle}

{2,0002}- {3.14 – 1,0002}

4,000,000 – 3,140,000 = 860,000 square amahs