Abstract Helge Tverberg published more than forty years ago his original
proof of the theorem which has been widely acclaimed and today
bears his name. This beautiful result has been one of the most
celebrated results of discrete geometry and, together with its
relatives, still remains a central and one of the most intriguing
results of geometric combinatorics. Here we give a reasonably
non-technical presentation of this result having in mind a larger
mathematical audience, particularly school teachers and their
talented students, hoping that it may raise their interest for
this very attractive area of mathematics. In the remaining part of
the article we briefly visit some of other branches of convex
geometry and outline how ``smashing'' and `slicing'' of convex
bodies offers a deep insight into their structure and behavior. ![Creative Commons License](https://i.creativecommons.org/l/by/4.0/80x15.png)
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