Bibliography: p. 269-270.
|Statement||by F.A.P. Barnard.|
|Series||Memoirs of the National Academy of Sciences ;, v. 4, 6th memoir|
|Contributions||National Academy of Sciences (U.S.)|
|LC Classifications||Q11 .N2|
|The Physical Object|
|Pagination||pt. 1, p. 209-270 :|
|Number of Pages||270|
|LC Control Number||05031932|
Get this from a library! Theory of magic squares and of magic cubes. [Frederick A P Barnard; National Academy of Sciences (U.S.)]. 7x7 magic squares of cubes 7x7 magic squares of fourth powers. According to Lee Morgenstern's computation done in May , there is no 7x7 semi-magic square of cubes using any possible set of 49 cubes between 1 3 and 55 3. He extended his computation in August also impossible up to 57 3. Get this from a library! Magic squares and cubes.. [W S Andrews] -- Describes and analyzes various kinds of magic figures, explaining how to use algebraic methods to work out squares and how to apply the theory of reversions. A magic square consists of a series of numbers so arranged in a square that the sum of each row and column and of both the corner diagonals shall be the same amount which may be termed the summation. In "Magic Squares and Cubes" W.S. Andrews writes "The study of magic squares probably dates back to prehistoric s: 5.
Magic Squares and Cubes by W. S. Andrews. Publisher: Open Court Publishing Company ISBN/ASIN: Number of pages: Description: The essays that appear in this book cover topics such as magic squares, magic cubes, the Franklin squares, magics and Pythagorean numbers, the theory of reversions, magic circles, spheres, and stars, and magic . Magic Squares and Cubes Dover books explaining science and mathematics Dover books on mathematical and word recreations Volume of Dover books on science Volume of Dover books: Author: William Symes Andrews: Edition: 2, illustrated, reprint: Publisher: Dover Publications, Original from: the University of Michigan: Digitized: Feb 2. Behforooz, Hossein: On Constructing 4 by 4 Magic Squares with Pre-assigned Magic Sum, J. of Mathematical Spectrum; Vol. 40, No. 3, /, pp Hossein: Permutation Free Magic Squares. Magic squares are arrangements of numbers into squares, cubes, or hyper-cubes where the sum of each row and each column is identical. Additionally, the sum along the "principal diagonals" is also equal to the same number. The magic square below was known in antiquity in China, Greece, and Egypt.
Hence, the probable origin of the term magic, which has survived to the present day." Topics such as magic squares, magic cubes, the Franklin squares, magics and Pythagorean numbers, the theory of reversions, magic circles, spheres, and stars, and magic octahedroids, among other things. Seller Inventory # AAV Some new and not well know references on magic squares. Books. Jacques Bouteloup: Carrés Magiques, Carrés Latins et Eulériens Éditions du Choix, Bréançon, (Includes some material on magic cubes.) kov: Magic squares - number theory, algebra and combinatorial analysis (Russian) St. Petersburg ; Vladimír Karpenko. The magic square of squares problem is an important part of unsolved problem D15 of Richard K. Guy’s Unsolved Problems in Number Theory book , third edition, , summarizing the main published articles on this subject since Hence, the probable origin of the term magic, which has survived to the present day.' This book covers topics such as magic squares, magic cubes, the Franklin squares, magics and Pythagorean numbers, the theory of reversions, magic circles, spheres, and stars, and magic octahedroids, among other s: 5.