Choi Seok-Jeong studied Latin squares at least 60 years earlier than Euler.
He introduced a pair of orthogonal Latin squares of order 9 in his book.
Interestingly, his two orthogonal non-diagonal Latin squares produce a magic
square of order 9, whose theoretical reason was not studied. There have been a
few studies on Choi's Latin squares of order 9. The most recent one is Ko-Wei
Lih's construction of Choi's Latin squares of order 9 based on two 3×3
orthogonal Latin squares. In this paper, we give a new generalization of Choi's
orthogonal Latin squares of order 9 to orthogonal Latin squares of size n2
using the Kronecker product including Lih's construction. We find a geometric
description of Chois' orthogonal Latin squares of order 9 using the dihedral
group D8​. We also give a new way to construct magic squares from two
orthogonal non-diagonal Latin square, which explains why Choi's Latin squares
produce a magic square of order 9.Comment: 18 pages revised slightly from Dec. 5, 2018 versio