MathStudent1999
Junior Member
- Joined
- Mar 18, 2012
- Messages
- 76
An infinite plane is completely filled with congruent circles in the pattern shown. What percent of the plane is filled with circles?

I put the circles' radius as one. I found a circle's area would be pi. The area of the shape between the circles is (pi/2) - √3.
I found that for the first three circles there would be a shape between the circles, but after the first three for every new circle there would be another shape. But since the plane is infinite to i just disregard the first part and just do the area of a circle over the area of the circle plus the shape?

I put the circles' radius as one. I found a circle's area would be pi. The area of the shape between the circles is (pi/2) - √3.
I found that for the first three circles there would be a shape between the circles, but after the first three for every new circle there would be another shape. But since the plane is infinite to i just disregard the first part and just do the area of a circle over the area of the circle plus the shape?