#pseudoscalar

[peeterjoot]

Equation of a hyperplane, and shortest distance between two hyperplanes.

[Click here for a PDF version of this post] Scalar equation for a hyperplane. In our last post, we found, in a round about way, that Theorem 1.1: The equation of a \(\mathbb{R}^N\) hyperplane, with distance \( d \) from the origin, and normal \( \mathbf{\hat{n}} \) is \begin{equation*} \Bx \cdot \mathbf{\hat{n}} = d. \end{equation*} Start proof: Let \( \beta = \setlr{ \mathbf{\hat{f}}_1, \cdots…

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[peeterjoot]

Triangle area problem: REVISITED.

[Click here for a PDF version of this post] On LinkedIn, James asked for ideas about how to solve What is the total area of ABC? You should be able to solve this! using geometric algebra. I found a couple ways, and this last variation is pretty cool. fig. 1. Triangle with given areas. To start with I’ve re-sketched the triangle with the areas slightly more to scale in fig. 1, where areas \( A_1 =…

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[peeterjoot]

Bivector transformation, and reciprocal frame for column vectors of a transformation

[Click here for a PDF version of this and previous two posts] The author of a book draft I am reading pointed out if a vector transforms as \begin{equation}\label{eqn:adjoint:760} \Bv \rightarrow M \Bv, \end{equation} then cross products must transform as \begin{equation}\label{eqn:adjoint:780} \Ba \cross \Bb \rightarrow \lr{ \textrm{adj}\, M }^\T \lr{ \Ba \cross \Bb }. \end{equation} Bivectors…

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[peeterjoot]

second experiment in screen recording

second experiment in screen recording

Here’s a second attempt at recording a blackboard style screen recording:

  To handle the screen transitions, equivalent to clearing my small blackboard, I switched to using a black background and just moved the text as I filled things up.  This worked much better.  I still drew with mischief, and recorded with OBS, but then did a…

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