Published on: 2025-06-23 15:56:12
The Transwedge Product Introductory texts on geometric algebra often begin by showing how the geometric product is a combination of the wedge product and the dot product, giving us the formula[1] \(\mathbf a \mathbin{\unicode{x27D1}} \mathbf b = \mathbf a \wedge \mathbf b + \mathbf a \cdot \mathbf b\).(1) However, the above formula holds only for vectors \(\mathbf a\) and \(\mathbf b\). When \(\mathbf a\) and \(\mathbf b\) are allowed to assume values of higher grade, the geometric product ge
Keywords: geometric mathbf mathbin product unicode
Find related items on AmazonPublished on: 2025-08-07 09:06:31
Computer architects can’t agree on a way to find the average. For years, academic practitioners in this field have been arguing about the appropriate way to summarize the average performance of their designs. That is: given \(n\) workloads, if system \(A\) outperforms system \(B\) by \(S_1, S_2, \ldots, S_n\) on each, how much faster should you say system \(A\) is, on average? I think this argument is kind of pointless through. For the most part, people tend to use the arithmetic mean \(\left(
Keywords: geometric mean meaning physical use
Find related items on AmazonPublished on: 2025-08-15 14:20:13
This article has been reviewed according to Science X's editorial process and policies . Editors have highlighted the following attributes while ensuring the content's credibility: Intruder detection task. Two carrion crows were trained to detect an intruder stimulus in an array of six simultaneously presented stimuli. The crows initiated the trial by moving their head in front of the screen whenever a go-stimulus appeared. After a prestimulus period of 200 ms, an array of six stimuli was displ
Keywords: crows geometric intruder regularity science
Find related items on AmazonPublished on: 2025-08-20 23:30:21
As longtime readers of this blog have probably noticed, I like to poke around in Unicode occasionally. It’s an endless system of rabbit holes to explore. This morning I was looking at the Miscellaneous Mathematical Symbols block. These are mostly obscure symbols, though I’m sure for each symbol that I think is obscure, there is someone out there who uses it routinely. Perpendicular The only common symbol in this block is ⟂ (U+27C2) for perpendicular. Even so, this symbol is a variation on ⊥ (
Keywords: block geometric symbol symbols used
Find related items on AmazonPublished on: 2025-10-14 01:32:53
Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake. Vanderbei’s analysis is an elegant and subtle exercise in classical trigonometry. In this post, I would like to present an alternative analysis in a different language: Geometric Algebra. I believe that geometric algebra is a more powerful system for formulating and solving trigonometry problems than the classi
Keywords: algebra geometric left product vectors
Find related items on AmazonPublished on: 2025-11-13 15:54:17
Projective Geometric Algebra Using one extra dimension, we obtain the plane-based Projective Geometric Algebra for 2 and 3 dimensions. Its elements are points, lines and planes. It includes elements at infinity and has exception free join and meet operations. Its even subalgebra provides in rotations & translations and is isomorphic to the dual quaternions
Keywords: algebra dimensions elements geometric projective
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