Magic Squares

“This is certainly a definitive comprehensive treatise on the history of magic squares from their known beginnings to 1600. There is a wealth of material, containing methods of construction as well as individual magic squares, including bordered and pandiagonal magic squares, that is astonishing.” (Victor V. Pambuccian, zbMATH 1422.01002, 2019)

• I. Introduction.- II. Ordinary magic squares.- A. Squares of odd orders.- B. Squares of evenly-even orders.- C. Squares of evenly-odd orders.- III. Composite magic squares.- A. Equal subshares displaying different sums.- B. Equal subshares displaying equal sums.- C. Division into unequal parts.- IV. Bordered magic squares.- A. Squares of odd orders.- B. Squares of evenly-even orders.- C. Squares of evenly-odd orders.- V. Bordered squares with separation by parity.- 1. The main square and its parts.- 2. Filling the inner square.- 3. Filling the remainder of the square by trial and error.- A. Methodical filling of the oblique square.- B. Methodical placing of the even numbers.-  C. Particular case of the order 5.- VI. Magic squares with non-consecutive numbers.- A. Squares of odd orders.- B. Squares of evenly-even orders.- C. Squares of evenly-odd orders.- VII. 1. Literal squares.- 2. Squares with one empty cell.- 3. Squares with divided cells.- 4. Magic triangles.- 5. Magic crosses.- 6. Magic circles.- 7. Magic rectangles.- 8. Magic cubes.- Appendices.- Bibliography.- Index.