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The most external matrix rotates the other two, leaving the second rotation matrix over the line of nodes, and the third one in a frame comoving with the body. There are 3 × 3 × 3 = 27 possible combinations of three basic rotations but only 3 × 2 × 2 = 12 of them can be used for representing arbitrary 3D rotations as Euler angles.
Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the n × n rotation matrices form a group, which for n > 2 is non-abelian, called a special orthogonal group, and denoted by SO(n), SO(n,R), SO n, or SO n (R), the group of n × n rotation ...
The spiral is a frequent symbol for spiritual purification, both within Christianity and beyond (one thinks of the spiral as the neo-Platonist symbol for prayer and contemplation, circling around a subject and ascending at the same time, and as a Buddhist symbol for the gradual process on the Path to Enlightenment).
Luck. Fate. Blessing. A glitch in the matrix. Or, if you’re more skeptical, just a coincidence.. It’s a phenomenon that, from a statistical perspective, is random and meaningless.
The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. The term Archimedean spiral is sometimes used to refer to the more general class of spirals of this type (see below), in contrast to Archimedes' spiral (the specific arithmetic spiral of ...
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‘Black Swan’ author Nassim Taleb, who correctly called the 2008 financial crisis, says the U.S. is in a ‘death spiral’ over government debt. Eleanor Pringle. January 31, 2024 at 6:29 AM.
Due to the non-commutativity of the matrix product, the rotation system must be ordered. Sometimes the order is imposed by the geometry of the underlying problem. For example, when used for vehicles, which have a special axis pointing to the "forward" direction, only one of the six possible combinations of rotations is useful.