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Parallel plane segments with the same orientation and area corresponding to the same bivector a ∧ b. [1] In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar as a degree-zero quantity and a vector as a degree-one quantity, a bivector is ...
A 2-blade is a simple bivector. Sums of 2-blades are also bivectors, but not always simple. A 2-blade may be expressed as the wedge product of two vectors a and b: . A 3-blade is a simple trivector, that is, it may be expressed as the wedge product of three vectors a, b, and c:
If you want to take a closer look at nature's wonders, you've come to the right place!Ian Granström, a photographer from Southern Finland, captures intimate wildlife images of foxes, birds, elk ...
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically . Natural patterns include symmetries , trees , spirals , meanders , waves , foams , tessellations , cracks and stripes. [ 1 ]
A wheeled buffalo figurine—probably a children's toy—from Magna Graecia in archaic Greece [1]. Several organisms are capable of rolling locomotion. However, true wheels and propellers—despite their utility in human vehicles—do not play a significant role in the movement of living things (with the exception of the corkscrew-like flagella of many prokaryotes).
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
The simple rotation in the zw-plane by an angle θ has bivector e 34 θ, a simple bivector. The double rotation by α and β in the xy-plane and zw-planes has bivector e 12 α + e 34 β, the sum of two simple bivectors e 12 α and e 34 β which are parallel to the two planes of rotation and have magnitudes equal to the angles of rotation.