Welcome to Studio Infinity! You most likely reached this page via the link on the Gengzhi Goblets given away at G4G13. Here are pointers to more in-depth discussions of the Goblets. I’d love to hear from you, so please leave a comment here, and if you want to reach me, my email is glen (at) the domain of this site.
Oh, and please see my call for problems/puzzles. If I can get four or five problems collected from G4G attendees, I can do one of my columns in MAA Math Horizons dedicated to Martin Gardner!
P.S. You may have noted that this URL seems to refer to something called the Cavalieri Content Cups. Well, that was the working name for this project before I realized, courtesy of Wikipedia, that the Chinese mathematician Zu Gengzhi elucidated the principle on which the the Goblets are based more than a millennium before Bonaventura Cavalieri did. Naturally, once that fact came to light, these items needed to be renamed, as indeed the principle itself should be, to the Gengzhi Principle.
In any case, to the links:
Mathematical Free Association, in which the question of a suitable G4G13 giveaway is pondered
Archimedean Variations, in which the realm of possibilities identified is explored
Portion Prototyping, in which the leading candidate is converted to physical reality
Gengzhi Goblets, in which the final design is produced in quantity
I hope you enjoy your measuring cups; if you happen to reach here and do not have a set and would like to, please contact me via the means listed above to find out how you can obtain a set.