Because I feel that Magic Squares is a suitable subject
for math enrichment, this page is dedicated to providing material
suitable for use in the mathematics department of secondary schools.
All material presented here is copyright free and is presented
with no conditions or guarantees.
Because of size restrictions, I have chosen not to display
most posters on this page. They may be reviewed by clicking on the .PDF link and
should then
open in your browser. hdh
This page will consist of two sections.
Posters will contain short documents (one or
two pages) suitable for downloading and printing for the purpose of
displaying on a Bulletin Board. Some will also be displayed on this page.
Simply double click on a link to download
that document.
Documents will be MS Word of MS Excel files
meant for downloading and then read locally or printed out.
Do you wish to
download this poster?
Order Four-ad.doc
Download Some
Numbers.doc or Some
Numbers.pdf One page 8 1/2 x
11 inches.
Shows the number of
ways that the numbers 1, 2, 3, …. mn can be placed
into a partitioned hypercube of
order m and dimension n is shown below. It shows how little is known on the
numbers of magic ones and
how rare they are.
Download The
Ellipse.doc or The Ellipse.pdf
One page 8 1/2 x 11 inches.
You may see this poster
online.
Download Perfection.doc or
Perfection.pdf
Two pages 8 1/2 x 11 inches.
This document shows the number of magic lines and magic hypercubes of lower
dimensions, for each perfect hypercube from dimension 2 to dimension 5. Also the
lowest order possible for each of these perfect hypercubes.
Download Count.doc or
Count.pdf
1 page 8 1/2 x 11
This poster illustrates the count and number of aspects for orders 3 to 5 and
dimensions 2 to 6.
Download Inlaid
Poster 1.doc or
Inlaid Poster 1.pdf One page 8 1/2 x 11 inches
This poster shows two order 5 inlaid magic squares and an order 24 with 4
sets of 4 inlaid magic squares.
Download
Inlaid 24 Pan 9.doc or
Inlaid 24 Pan 9.pdf One page 8 1/2 x 11
inches.
This poster shows an order 24 magic
square
with four order 9 magic squares inlaid in the quadrants.
Download Inlaid
24 Overlap.doc or Inlaid
24 Overlap.pdf One page 8 1/2 x 11 inches
This order 24 magic square contains 4
order 9 magic squares that each contain 2 order 4 and 2 order 5 magic squares.
Download Inlaid
24 composite.doc or
Inlaid
24 composite.pdf One page 8 1/2 x 11 inches
This order 24 magic square contains 4
order 9 magic squares that each contain 9 order 3 magic squares
Download
Inlaid 24 Pan 5.doc or
Inlaid 24 Pan 5.pdf One page 8 1/2 x 11
inches.
This poster shows an order 24 magic
square with four order 5 magic squares inlaid in the quadrants.
Download
Inlaid 24 Pan 7.doc or
Inlaid 24 Pan 7.pdf One page 8 1/2 x 11
inches.
This poster shows an order 24 magic
square with four order 7 magic squares inlaid in the quadrants.
Download
Inlaid 24 mixed.doc or
Inlaid 24 mixed.pdf One page 8 1/2 x 11
inches.
This poster shows an order 24 magic
square with four order 9 magic squares inlaid in the quadrants.
Download Inlaid
24 - hh.doc or Inlaid
24 - hh.pdf One page 8 1/2 x 11 inches
This poster shows an order 24 magic
square with four order 9 magic squares inlaid in the quadrants. It is a
demonstration of how the student can construct his own version of a magic square
with his choice of inlaid squares.
Download
Hypercube Constants.doc or
Hypercube Constants.pdf One page 8 1/2 x 11
inches.
This poster shows a short Basic program and the output generated, Sums for
squares, cubes, and tesseracts.
Download
Tetrahedron.doc or
Tetrahedron.pdf One page 8 1/2 x 11
inches.
This poster shows a 4 x 4 magic square and a transformation to a magic
tetrahedron.
Download
Inlaid Poster dia.doc or
Inlaid Poster dia.pdf One page 8 1/2 x 11
inches.
This poster shows a 24 x 24 magic square with nested magic square inlays
with magic diamonds in the centers.
Download New
diamond.doc or
New diamond.pdf One page 8 1/2 x 11
inches.
This poster shows a 5 x 5 magic square containing an order 3 magic
diamond in the center.
Download
Poster on 5x5 Inlaid.doc or
Poster on 5x5 Inlaid.pdf One page 8 1/2 x 11
inches.
This poster discusses the number of unique order 5 magic squares with an
inlaid diamond.
Download
Poster magic tesseract.doc or
Poster magic tesseract.pdf
One page 8 1/2 x 11 inches.
This poster shows and order 3 magic tesseract and has some descriptive
text.
Download 4 related posters, discussing magic
squares, magic cubes, and magic tesseracts. Each is 2 pages 8 1/2 x 11.
Inlaid Semi
Bi-magic.doc or
Inlaid Semi
Bi-magic.pdf
What is MS.doc or
What is MS.pdf
What is MC.doc or
What is MC.pdf
What is MT.doc or
What is MT.pdf
Order Four.doc
This document is an introduction to order 4 magic squares. It is
formatted as
8 pages 8 1/2 x 11 inches.
S & P.doc
Simplicity and Perfection is an 8 page document that discuses the smallest
order 3 hypercube
from each
dimension from two to six.
Math Teachers.xls is an
Excel program for generating odd order magic squares.
Sheet two contains an explanation of Modular Equations.
2D Aspects.xls is an Excel
program for generating the ONE basic order 3 magic square and it’s 7 variations.
3D Aspects.xls is an Excel
program for generating the FOUR basic order 3 magic cubes and the 47 variations
of each.
4D Aspects.xls is an Excel
program for generating the FIFTY-EIGHT basic order 3 magic TESSERACTS
and the 383 variations of each.
Perfect
Tesseract by Cross-sections.xls An Excel program that displays
cross-sections of the first perfect magic tesseract.
It was constructed by John Hendricks in 1998 and confirmed by Dr. Clifford
Pickover using mainframe IBM computers in 1999.
It uses the numbers 1 to 65536 and there are 163,840 lines that sum to 524,296.
It also includes 65 perfect magic cubes and
1536 perfect magic squares.
Hypercube_Statistics.xls
is an Excel program that displays 13 values for Hypercubes of dimension n
and order m.
Catalogue.xls is an Excel program
that list all 62 order 5 associated magic squares with inlaid magic diamonds. It
also generates a square for each catalogue signature.
Magic Square Borders.doc
and Magic Square Borders.pdf
discuss bordered magic squares and catalog the 10 order 5 borders. Each document is 16 pages 8 1/2 x 11.
Magic Squares by
Equation.xls is a spreadsheet for generating odd order magic squares of any
size by the use of Equations.
More material for downloading will be posted later.
Last updated
Tuesday September 01, 2009
