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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 ...
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Asimov's Guide to the Bible is a work by Isaac Asimov that was first published in two volumes in 1968 and 1969, [1] covering the Old Testament and the New Testament (including the Catholic Old Testament, or deuterocanonical, books (see Catholic Bible) and the Eastern Orthodox Old Testament books, or anagignoskomena, along with the Fourth Book of Ezra), respectively.
[6] [7] In April 2016, The Bible App became available on the Apple Watch [8] allowing users to read the Verse of the Day, view trending verses, and access their own Verse Images, Bookmarks, and Highlights. [9]
The NIV Study Bible is a study Bible originally published by Zondervan in 1985 that uses the New International Version (NIV). Revisions include one in 1995, a full revision in 2002, an update in October 2008 for the 30th anniversary of the NIV, another update in 2011 (with the text updated to the 2011 edition of the NIV), and a fully revised update in 2020 named "Fully Revised Edition". [1]
Given a bivector r = r 1 + hr 2, the ellipse for which r 1 and r 2 are a pair of conjugate semi-diameters is called the directional ellipse of the bivector r. [4]: 436 In the standard linear representation of biquaternions as 2 × 2 complex matrices acting on the complex plane with basis {1, h},
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.