I cite the following blocks from Agustinus Kristiadi's webpage about an interesting problem:
Suppose we are standing at the origin of bounded regular forest in R^2 , with diameter of 26 m, and all the trees inside have diameter of 0.16 m. Can we see outside this forest? This problem can be solved using Minkowski’s Theorem. We will see the theorem itself first, and we shall see how can we answer that question.
Theorem (Minkowski’s Theorem) Let C ⊆ R^d be symmetric around the origin, convex, and bounded set. If vol(C)>2^d then C contains at least one lattice point different from the origin.
Given Minkowski’s Theorem, now we can answer our original question. We assume the trees are just lattice points, and our visibility line is now a visibility strip, which has wide of 0.16 m and length of 26 m. We note that the preconditions of Minkowski’s Theorem are satisfied by this visibility strip, which has the volume of ≈4.16>4=2^d. Therefore, there exists a lattice point other than the origin inside our visibility strip. Thus our vision outside is blocked by the tree.
Once I found this problem I didn’t hesitate in visualize it using wolfram language:

You can’t see outside the forest

In[]:=
Manipulate[​​Graphics[​​{{Black,PointSize[.02],Point[{0,0}]},{Green,Circle[#,.08]&/@TreePositions},​​Circle[{0,0},13],​​{Dotted,Translate[InfiniteLine[{0,0},{Cos[t],Sin[t]}],.08{-Sin[t],Cos[t]}]},​​{Dotted,Translate[InfiniteLine[{0,0},{Cos[t],Sin[t]}],-.08{-Sin[t],Cos[t]}]},​​{Red,​​Disk[#,If[highlight,.16,0.08]]&/@​​(Which[​​0<=t<π/2||3π/2<t<=2π,Select[TreePositions,Tan[t]#[[1]]+.08/Cos[t]>#[[2]]>Tan[t]#[[1]]-.08/Cos[t]&],​​t==π/2||t==3π/2,Select[TreePositions,#[[1]]==0&],​​π/2<t<π||π<=t<3π/2,Select[TreePositions,Tan[t]#[[1]]+.08/Cos[t]<#[[2]]<Tan[t]#[[1]]-.08/Cos[t]&]​​])​​}​​},​​PlotRange->15,​​AspectRatio->Automatic,ImageSize->Large​​],​​{{t,0,Style["angle of sight",15]},0,2π},​​{{highlight,False,Style["highlight strip lattice points",15]},{True,False}},​​Initialization:>(TreePositions=DeleteCases[​​Select[Flatten[Outer[List,Range[-13,13],Range[-13,13]],1],Norm[#]<=13&],{0,0}])​​]
Out[]=
​
angle of sight
highlight strip lattice points

CITE THIS NOTEBOOK

Visualizing Minkowski's theorem​
by Diego Ramos​
Wolfram Community, STAFF PICKS, December 13, 2023
​https://community.wolfram.com/groups/-/m/t/3082489