Many more names of $(7, 3, 1)$. (English)

Math. Mag. 88, No. 2, 103-120 (2015).

Summary: The $(7, 3, 1)$ block design is an object that shows up in many areas of mathematics. In fact, $(7, 3, 1)$ seems to appear again and again in unexpected places. [{\it E. Brown}, Math. Mag. 75, No. 2, 83‒94 (2002; Zbl 1064.05031)] described $(7, 3, 1)$’s connection with such areas as graph theory, number theory, topology, round-robin tournaments, and algebraic number fields. In this paper, we show how $(7, 3, 1)$ makes appearances in the areas of error-correcting codes, $n$-dimensional finite projective geometries, difference sets, normed algebras, and the three-circle Venn diagram.