2891: Log Cabin

2024-02-08T01:32:18Z

Hydratedsphere3: Alternate interpretation of title text.

{{comic
| number = 2891
| date = February 7, 2024
| title = Log Cabin
| image = log_cabin_2x.png
| imagesize = 353x265px
| noexpand = true
| titletext = I'm sure the building inspectors will approve my design once they finally manage to escape.
}}

==Explanation==
{{incomplete|Created by a TRAPPED BUILDING INSPECTOR APPROXIMATELY 1.6180 METERS TALL- Please change this comment when editing this page. Do NOT delete this tag too soon.}}

[[File:log_cabin_golden_spiral.png|thumb|301px|Golden spiral (approximately) overlaid on the floor plan]]

This is a comic featuring a {{w|floor plan}}, presumably of a {{w|log cabin}}, and a pun on the word "log". The odd part about it is the right half, which appears to be infinitely recursive copies of the building, like a {{w|fractal}}. The house as a whole represents a "golden rectangle" with a ratio of approximately 1.618, with sucessively smaller living areas (further subdivided into rooms, to a common but shrunken and rotated plan) being square adjoined by a golden-rectangle of all smaller living areas in the manner of the areas defined by the classic {{w|Golden spiral}} diagram. The joke is that Randall is intentionally conflating the word "log" in the common phrase "log cabin," where "log" refers to the wood the cabin is made of, as opposed to the mathematical function of the "log" ({{w|logarithm function}}), of which the ratios here are a special case (base phi).

Every square subunit of the premises consists of a main combined kitchen/lounge area, off which leads a shower-equipped bathroom, two bedrooms (a double-bed one with ensuite bath-equipped bathroom, and another with a single bed; both having suitable walk-in closet space) and the door that serves as the entry into the next inwards level of the floorplan.

In the title text, Randall says that he is confident that building inspectors will approve his log cabin, assuming that they can escape. As one moves deeper into the infinite spiral of architecture, the entire log cabin ''seems'' to be a denser labyrinth of rooms and hallways.

It is unknown how the inspectors lost in the inner rooms would shrink in the same ratio, and would actually only have to head out through the last door they walked in through (or two, if they're currently in the en-suite) and then exit each 'main' area in turn until they exited the building itself. If they have any trouble at all (other than rescaling themselves), it would be that there is ''always'' a further inward area which they might consider needs exploring in order to fulfil their inspection routine.

Alternatively, this may imply that the repetition continues outside of what is drawn here, continuing to grow larger as it moves further out.

The most famous bad math joke on the title is
$\int 1/cabin d(cabin) = houseboat $
as a houseboat is (log cabin + C). This does not seem to be related to the topic of this comic.

[https://www.generations-quilt-patterns.com/log-cabin-quilt-block.html Log Cabin] is also a classic quilting block, which starts with a tiny square and spirals outwards.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[A drawing of the top view of a log cabin, which includes two beds, a kitchen, a bathroom and furniture. A smaller version of the log cabin is connected to the main building. An even smaller version is connected to the smaller version, and so on, forming a golden rectangle.]

:[Caption below the panel]:
:Log cabin

{{comic discussion}}

[[Category:Engineering]]
[[Category:Math]]
[[Category:Puns]]

explain xkcd - User contributions [en]

2891: Log Cabin