mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
the Padovan cuboid spiral is the
spiral
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
Helices
Two major definitions of "spiral" in the American Heritage Dictionary are:cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a cub ...
s added to a unit cube. The cuboids are added sequentially so that the resulting cuboid has dimensions that are successive Padovan numbers... See in particular pp. 96–97..
The first cuboid is 1x1x1. The second is formed by adding to this a 1x1x1 cuboid to form a 1x1x2 cuboid. To this is added a 1x1x2 cuboid to form a 1x2x2 cuboid.
This pattern continues, forming in succession a 2x2x3 cuboid, a 2x3x4 cuboid etc. Joining the diagonals of the exposed end of each new added cuboid creates a
spiral
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
Helices
Two major definitions of "spiral" in the American Heritage Dictionary are:spiral
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
Helices
Two major definitions of "spiral" in the American Heritage Dictionary are:
The cuboids are added in a sequence that adds to the face in the positive y direction, then the positive x direction, then the positive z direction. This is followed by cuboids added in the negative y, negative x and negative z directions. Each new cuboid added has a length and width that matches the length and width of the face being added to. The height of the ''n''th added cuboid is the ''n''th Padovan number.
Connecting alternate points where the spiral bends creates a series of triangles, where each triangle has two sides that are successive Padovan numbers and that has an obtuse angle of 120 degrees between these two sides.