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[2] [3] In layman terms, any surface defines the same bivector if it is parallel to the same plane (same attitude), has the same area, and same orientation (see figure). Bivectors are generated by the exterior product on vectors: given two vectors a and b , their exterior product a ∧ b is a bivector, as is any sum of bivectors.
Author: Orr, James, 1844-1913, ed: Short title: The International standard Bible encyclopedia; Date and time of digitizing: 03:09, 24 November 2009: Software used
The term "Bible" can refer to the Hebrew Bible or the Christian Bible, which contains both the Old and New Testaments. [2]The English word Bible is derived from Koinē Greek: τὰ βιβλία, romanized: ta biblia, meaning "the books" (singular βιβλίον, biblion). [3]
The torque or curl is then a normal vector field in this 3rd dimension. By contrast, geometric algebra in 2 dimensions defines these as a pseudoscalar field (a bivector), without requiring a 3rd dimension. Similarly, the scalar triple product is ad hoc, and can instead be expressed uniformly using the exterior product and the geometric product.
A bivector is an element of the antisymmetric tensor product of a tangent space with itself. In geometric algebra, also, a bivector is a grade 2 element (a 2-vector) resulting from the wedge product of two vectors, and so it is geometrically an oriented area, in the same way a vector is an oriented line segment.
Robert Estienne (Robert Stephanus) was the first to number the verses within each chapter, his verse numbers entering printed editions in 1551 (New Testament) and 1553 (Hebrew Bible). [24] Several modern publications of the Bible have eliminated numbering of chapters and verses. Biblica published such a version of the NIV in 2007 and 2011.
Now (hr 2) 2 = (−1)(−1) = +1, and the biquaternion curve {exp θ(hr 2) : θ ∈ R} is a unit hyperbola in the plane {x + yr 2 : x, y ∈ R}. The spacetime transformations in the Lorentz group that lead to FitzGerald contractions and time dilation depend on a hyperbolic angle parameter. In the words of Ronald Shaw, "Bivectors are logarithms ...
A Dictionary of the Bible (1863), edited by William Smith, title page for the third volume. A Bible dictionary is a reference work containing encyclopedic entries related to the Bible, typically concerning people, places, customs, doctrine and Biblical criticism. Bible dictionaries can be scholarly or popular in tone.