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A circle of radius 5 with its center at (0,0) is drawn on a Cartesian coordiante system.  How many lattice points lie within or on this circle?

 Nov 18, 2019
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We will have   4(5) + 1  =  21  lattice points on the x, y axis

 

To find the number of the rest of the points we have

 

4  [ floor (sqrt [ 5^2 - 1^2])  + floor (sqrt [ 5^2 - 2^2 ]) + floor (sqrt [ 5^2 - 3^2 ])  + floor( sqrt [ 5^2 - 4^2] )  ]  =

 

4 [ floor [sqrt (24) ]  + floor [ sqrt ( 21) ] + floor [sqrt ( 16 ) ] + floor [sqrt (9) ]  ]   =

 

4 [ 4  + 4   +  4  +  3 ]  =

 

4 [ 15 ] =

 

60

 

So...the total number of lattice points =  21 + 60  =   81

 

 

cool cool cool

 Nov 18, 2019
edited by CPhill  Nov 18, 2019

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