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The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be S = 13×5 / 2 = 32.5 units. However, the blue triangle has a ratio of 5:2 (=2.5), while the red triangle has the ratio 8:3 (≈2.667), so the apparent combined hypotenuse in each figure is actually bent.
Dame Kathleen Ollerenshaw, To Talk of Many Things: an autobiography, Manchester Univ Press, 2004, ISBN 0-7190-6987-4 Kathleen Ollerenshaw, David S. Brée: Most-perfect Pandiagonal Magic Squares: their construction and enumeration, Southend-on-Sea: Institute of Mathematics and its Applications, 1998, 186 pages, ISBN 0-905091-06-X
A most-perfect magic square of order n is a magic square containing the numbers 1 to n 2 with two additional properties: Each 2 × 2 subsquare sums to 2 s , where s = n 2 + 1. All pairs of integers distant n /2 along a (major) diagonal sum to s .
Mathematics, Magic and Mystery, Dover, 1956. ISBN 0-486-20335-2; Graham, Ron. Juggling Mathematics and Magic University of California, San Diego; Teixeira, Ricardo & Park, Jang Woo. Mathemagics: A Magical Journey Through Advanced Mathematics, Connecting More Than 60 Magic Tricks to High-Level Math World Scientific, 2020. ISBN 978-9811215308.
In the example in the figure, the following 4 × 4 most-perfect magic square was copied into the upper part of the magic circle. Each number, with 16 added, was placed at the intersection symmetric about the centre of the circles. This results in a magic circle containing numbers 1 to 32, with each circle and diameter totalling 132. [1]
So, in an n × n magic square using the numbers from 1 to n 2, a magic series is a set of n distinct numbers adding up to n(n 2 + 1)/2. For n = 2, there are just two magic series, 1+4 and 2+3. The eight magic series when n = 3 all appear in the rows, columns and diagonals of a 3 × 3 magic square. Maurice Kraitchik gave the number of magic ...
Emmerdale has unveiled a first look at Rhona and Marlon's Christmas shock as they're forced into a change in circumstances with Gus and Ivy.
Perfect magic cubes of order one are trivial; cubes of orders two to four can be proven not to exist, [4] and cubes of orders five and six were first discovered by Walter Trump and Christian Boyer on November 13 and September 1, 2003, respectively. [5] A perfect magic cube of order seven was given by A. H. Frost in 1866, and on March 11, 1875 ...