hcschuetz

Deriving Conformal Geometric Algebra from the Norm Condition

Given a "base space" V$=\mathbb{R}^n$ with a Euclidean dot product ., we want to find

• a "superspace" V' ⊃ V,
• a mapping _' : V => V', and
• a (commutative) dot product .' in the superspace V'

such that a' .' b' = (a - b)^2.

hcschuetz

This code systematically explores the solution space for the puzzle "Das Haus vom Nikolaus". It finds various things:

• Solutions: Paths that use each (undirected) connection exactly once.
• Failures: Paths ending in a vertex where you cannot continue (because all connections of the vertex have been used already), but there are still unused connections elsewhere.
• "Early Failures": Paths where the last step was a mistake. That is, the path cannot be completed to a solution but without the last step it could have been (by continuing another way).

Usually one is only allowed to cross the middle of the house (the X in the sketch near the beginning of the code) in a straight line from b to e or from c to d or in the opposite direction. But some people consider the crossing as an actual vertex where you may start or end the path or change the direction. The program handles both variants.

Here are the numbers of paths of each kind found by the program for each variant of the puzzle:

|| solutions

hcschuetz

This gist contains some experiments/ideas for typing geometric-algebra code in TypeScript.

These ideas might be applied to PEGEAL at some point.

hcschuetz

Phanpy Bookmarklet

I like to read mastodon content with phanpy.social (primarily because it displays threads nicely). But of course links to accounts and toots usually point to the original mastodon UI. The bookmarklet here jumps from there to the corresponding phanpy UI.

hcschuetz

(Zur deutschen Version 🇩🇪)

On Hashtags, Groups and Toot Propagation on Mastodon

$\Huge\textbf{\color{#f44}Note:}$

$\Huge\textbf{\color{#f44}While the considerations about hashtags}$

hcschuetz

Two Equations with Two Variables

a^2 - b = 133                   (1)
b^2 - a = 133                   (2)

The original problem, about which there are several Youtube videos, has the additional condition a ≠ b. But I did not see this in the banner pictures. So I found more solutions.

hcschuetz

Using a Free Certificate on DomainFactory

Introduction and Preliminaries

I hope that these instructions help you to get started, but notice that
I AM TAKING NO RESPONSIBILITY FOR ANY DAMAGE THAT MIGHT BE CAUSED.