Broken diagonal
Encyclopedia
A broken diagonal is a sequence of n
diametrically-positioned cells in a panmagic square
which spans the vertical boundary. Examples of broken diagonals from the below square
are as follows: 3,12,14,5; 10,1,7,16; 10,13,7,4; 15,8,2,9; 15,12,2,5; and 6,13,11,4.
Notice that because one of the properties of a panmagic square is that the broken diagonals add up to the same constant, the following pattern is evident:
;
;
One way to visualize a broken diagonal is to imagine a "ghost image" of the panmagic square adjacent to the original:
It is easy to see now how the set of numbers {3, 12, 14, 5} result to form a broken diagonal: once wrapped around the original square, it can now be seen starting with the first square of the ghost image and moving down to the left.
Although this specific article relates to broken diagonals in panmagic square
s, the "broken diagonal" also has uses in matrices
and other areas of geometry
such as determining the area of a polygon
solely from its Cartesian coordinates
.
N
N is the fourteenth letter in the basic modern Latin alphabet.- History of the forms :One of the most common hieroglyphs, snake, was used in Egyptian writing to stand for a sound like English ⟨J⟩, because the Egyptian word for "snake" was djet...
diametrically-positioned cells in a panmagic square
Panmagic square
A pandiagonal magic square or panmagic square is a magic square with the additional property that the broken diagonals, i.e...
which spans the vertical boundary. Examples of broken diagonals from the below square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
are as follows: 3,12,14,5; 10,1,7,16; 10,13,7,4; 15,8,2,9; 15,12,2,5; and 6,13,11,4.
Notice that because one of the properties of a panmagic square is that the broken diagonals add up to the same constant, the following pattern is evident:
;;One way to visualize a broken diagonal is to imagine a "ghost image" of the panmagic square adjacent to the original:
It is easy to see now how the set of numbers {3, 12, 14, 5} result to form a broken diagonal: once wrapped around the original square, it can now be seen starting with the first square of the ghost image and moving down to the left.
Although this specific article relates to broken diagonals in panmagic square
Panmagic square
A pandiagonal magic square or panmagic square is a magic square with the additional property that the broken diagonals, i.e...
s, the "broken diagonal" also has uses in matrices
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
and other areas of geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
such as determining the area of a polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
solely from its Cartesian coordinates
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
.