A question on circles

geometry packing-problem circles

I doubt that anybody has ever found this precisely: for example this seems to give the best results known for using a given number of gircles, but only goes as far as 12 circles at which point the radius of the bigger disk is 2.769... times the smaller disk.

In your problem there is an obvious lower bound of 100 lampposts, since the radius of the bigger circle is 10 times that of the smaller circles, and so the area 100 times.

This bound can be improved, since the optimal coverage of a plane involves hegaxonal packing, which reduces the effective area of each small circle by a factor of $\frac{3 \sqrt{3}}{2 \pi} \approx 0.82699$ so you would need at least 121 lamposts, and probably a few more.

Related

Math and Cubism Theory books?
Origin of the name 'test functions'
3D picture of the 38-sided Engel space-filling polyhedron
The p-adic numbers as an ordered group
If a subspace of $X^*$ separates points, is it weak-* dense?
Could someone prove they had a halting oracle?
A question about the tensor product of $\mathbb{Q}$
The Math behind rotation puzzles?
Any compact embedded $2$-dimensional hypersurface in $\mathbb R^3$ has a point of positive Gaussian curvature
Solving systems of linear equations when matrix of coefficients is singular
Practical Use of Series Expansion at $x=\infty$
Deriving the Area of a Sector of an Ellipse