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<p>proved in 1773 that the highest-density lattice packing of circles is the <a href="page.php?w=hexagon">hexagon</a>al packing arrangement, in which the centres of the circles are arranged in a <a href="page.php?w=hexagonal_lattice">hexagonal lattice</a> (staggered rows, like a <a href="page.php?w=honeycomb">honeycomb</a>), and each circle is surrounded by six other circles. For circles of diameter  and hexagons of side length , the hexagon area and the circle area are, respectively:<br/>
:The area covered within each hexagon by circles is:<br/>
:Finally,</p><p>
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