Friday, June 28, 2019

Short online games recommendation

Each game should be finishable within an hour.

The Company of Myself
https://www.kongregate.com/games/2DArray/the-company-of-myself
Sad philosophical game about a loner.

Missed Message
https://zephyo.itch.io/missed-message
Interactive fiction. Depression, cyclic day, suicide, lesbianism... also 2018 memes.

Fixation
https://www.kongregate.com/games/2DArray/fixation
Prequel to The Company of Myself. Has comics as transitions. Even sadder.

Viricide
https://www.kongregate.com/games/2DArray/viricide
An AI talks about someone of their lifestory. The AI might be depressed just like their programmer.

Sunday, June 9, 2019

Geometry quickie: volume of a tetrahedron

I saw this formula on Wikipedia for the volume of tetrahedron and was intrigued.
Any two opposite edges of a tetrahedron lie on two skew lines, and the distance between the edges is defined as the distance between the two skew lines. Let $d$ be the distance between the skew lines formed by opposite edges... 
then it gave a volume formula. I want to derive it. This post gives my thought process, where I keep using the trick of reducing a general problem to a good example. This is a general strategy for solving problems, often written as "wlog".
(I write it as "wolog" and pronounce as "volog", as if it's a German adverb. So that I can write "We assume wolog that...", "... and thus wolog we have...")

How would a true geometer approach this problem? She would first do a dimension analysis. The volume has dimension $meter^3$, and the lengths have dimension $meter$, so it ought to look like
$$Volume = k \cdot AB \cdot CD \cdot h$$
where $h$ is the distance between the two skew lines of $AB$ and $CD$, and $k$ is some dimensionless number yet to be determined.

Let's Read: Neuropath (Bakker, 2009)

Neuropath  (Bakker 2009) is a dramatic demonstration of the eliminative materialism worldview of the author R. Scott Bakker. It's very b...