How much of the big square is filled by the five small squares?
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Øystein
@oysteini@mathstodon.xyz
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Joined October 18, 2025
After @loopspace@mathstodon.xyz wrote about his webpage with geometry puzzles in November (@loopspace@mathstodon.xyz), I have from time to time gone to that page to solve a few puzzles. After a while, I started trying to create some puzzles on my own too. Then I thought I could post them here, in case anyone in the Fediverse might be interested in solving them.
Here is my first puzzle:
Two regular pentagons of the same size, each containing a quadrilateral (every point that looks like it could be the midpoint of a line segment is the exact midpoint of that line segment). How large is the pink quadrilateral relative to the blue one?
Replying to
@skewray@mathstodon.xyz @MartinEscardo@mathstodon.xyz I think the lecturer in XKCD 1856 (https://xkcd.com/1856/) might be a destructivist.
Replying to
@aadmaa2 @robinhouston I was able to prove all of them right now, but some with more difficulty than others. The first and last equation on the top row fell out immediately from the figure I drew, while the remaining three equations required a bit of algebraic manipulation (and a bit of trial and error to find those algebraic manipulations).
How much of the big pentagon is filled by the small yellow pentagon in the middle?
@kly@snabelen.no Det er fullt mulig å operere med "typisk tid mellom to busser" (eller tog, trikker, etc) istedenfor konkrete rutetider, og det finnes kollektivtrafikksystemer som gjør det på den måten.
Jeg trodde jeg skulle klare å finne en lang liste med eksempler på Wikipedia, men det beste jeg fant var denne vage påstanden uten kildehenvisning:
"In some cases public transport operators do not publish public timetables for busy times of day, or they may simply state "services run every 3–5 minutes" (or words to that effect), which is the norm for buses in some cities such as Hong Kong even during off-peak hours."
https://en.wikipedia.org/wiki/Public_transport_timetable#Headway_services
Og så er jeg ganske sikker på at jeg har lest om flere steder der de gjør ting på den måten, men det er vanskelig å komme på akkurat hvilke steder det er. Det eneste jeg klarer å komme på nå er Glasgow Subway. Jeg sjekket nettsiden deres, og det ser ut til at jeg husket riktig:
https://www.spt.co.uk/subway/subway-timetables/
How large is the central circle compared to the total area of the three corner circles?