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A circle of radius 5 with its center at the origin is drawn on a Cartesian coordinate system. How many lattice points (points with integer coordinates) lie within or on this circle?

 Apr 2, 2020
 #1
avatar+626 
+1

Hint: Use the pythagorean theorem. In other words, how many pythagorean triples can you find?

 Apr 2, 2020
 #2
avatar+111321 
+1

Number  of  latttice  points  =

 

5 * 4  + 1  =   21   points  on the  axis

 

Plus

 

4 *   [  greatest  integer  [ sqrt ( 25 - 1^2)]  +  greatest integer  [ sqrt (25 - 2^2) ]  +  greatest integer [ sqrt (25 - 3^2) ]  +  greatest  integer  [ sqrt (25 - 4^2 ]  ]   =

 

4  [ 4   +  4  +  4   +  3 ]   =  4 [ 15]  =   60

 

So....total lattice points =  21  + 60   =    81

 

 

cool cool cool

 Apr 2, 2020

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