Notices tagged with maths

Why are there two pentagons in the otherwise hex-tiled American continents displayed in TRON: Legacy’s Rectifier Globe computer graphics?

I was watching the TRON: Legacy 4K Ultra HD Blu-ray remaster (only my second time watching the 4K remaster) in the background earlier today when I sensed something “off” in the land mass tiling of the rotating globe graphic.

I paused the video and after less than a minute of scrutinizing the dark globe with orange outlined hexagon tiling, spotted a single pentagon (among the hexagons) inside the 2d projections of the American continents. See if you can spot it.

After writing the first draft of this post, I double-checked the graphic and found one more pentagon!

Credit: Image from https://ilikeinterfaces.com/2015/03/24/map-ui-tron-legacy/, fair use from Walt Disney, Inc.

The first pentagon I spotted is in the northwest quadrant of South America, and clearly visible at time index 1:38:03. The second pentagon is near Alaska. Now I can't unsee either. How did only two pentagons make it in there? Seems unlikely to be an accident or rendering bug. The only thing I can think of is the designer/artist(s) that created the graphic animation placed the two pentagons deliberately. But why?

GMUNK Studio’s post about the Rectifier Globe (https://gmunk.com/TRON-Rectifier-Globe) doesn’t mention the pentagons.

Yes, I know the math/geometry about how you can’t tile a sphere with only hexagons, that several pentagons are necessary at various points on a sphere to stitch together the hexagons. This is just two small pentagons, not several, and the Rectifier Globe only has/uses hex-tiling for the land masses, not the entire sphere. Nor is the hex-tiling “perfect” by any measure. The hexagonal edges of the continents don’t match-up with hex-tiling much (most?) of the way around the coasts of the continents either, so it can’t have been to fix that.

Are those two pentagons merely imperfections (necessary or accidental)? Or an Easter-egg or secret reference of sorts from the graphic artist(s)?

I searched the web and could not find any answers or even mentions of these two pentagons in this graphic. Did anyone notice them previously?

#TRON #TRONLegacy #pentagon #pentagons #hex #hexagon #hexagons #hexTile #hexTiles #hexTiled #Rectifier #RectifierGlobe #globe #computerGraphic #computerGraphics #math #maths #geometry #sphere #tile #tiled #tiling
#Blaugust #Blaugust2026

Discussed Venn diagrams with a couple of friends this morning, especially in the context of illustrating the utility of including all 3 or 4 of a specific set of design principles when creating certain kinds of things, and learned about the difference between Venn diagrams and Euler diagrams.

In short:
* a Venn diagram shows ALL possible relationships between different sets
* an Euler diagram shows only some relationships between different sets, typically focused on conveying relevant or the more important relationships

If you want to dive into their history and why these differences matter, bookmark (or open new tab) this Scientific American article to rabbithole later:
* https://www.scientificamerican.com/article/venn-diagrams-history-and-popularity-outside-of-math-explained/

In pop culture and media, nearly any diagram of overlapping circles with labeled regions is (errantly) referred to as a “Venn diagram”.

This is imprecise at best, outright incorrect in many cases, especially diagrams of four circles.

A classic example is the “Ikigai” diagram:

Many (examples below) call this a Venn diagram. It is not a Venn diagram. It is an Euler diagram.

The Ikigai diagram fails to express two specific relationships between different sets, the two that contain opposing side circles but neither of the other two. The missing Ikigai sets relationships in particular:
1. only “you are good at” AND “the world needs” (with neither of the other two)
2. only “you love” AND “you can be paid for” (again with neither of the other two)

If you Google web search for "examples of four circle venn diagrams", Gemini gets this wrong:

And so do the majority of articles that Google shows in top results (which I’m not helping by linking here, but hey it’s Google’s job to fix its search quality, not mine. I was able to use Internet Archive links for two of them at least.)
* https://web.archive.org/web/20260823204717/https://boardmix.com/knowledge/4-circle-venn-diagrams/
* https://miro.com/templates/4-circle-venn-diagram/ (Miro’s own top template there is wrong, though others have contributed proper 4 set Venn diagrams)
* https://web.archive.org/web/20260823205434/https://www.istockphoto.com/illustrations/venn-4-circles-diagram
* https://www.educationworld.com/tools_templates/EW_venndiagram_4

This has interesting implications for expertise and trust.

Clearly by this one example search result, we cannot trust the expertise of "design tool" websites (boardmix, miro), nor stock photo websites.

Nor can we trust educationworld as a place to be educated.

Nor can we trust Google Search (or Google Gemini) to surface expertise above popular misconceptions.

Perhaps a good example of when to use Wikipedia search instead of Google (or other generic) web search.

Personally I generalize this example to “all proper nouns”, that is:

* Wikipedia search proper nouns instead of Google or other general web searching.

You can make this more convenient by setting up “w” as a search shortcut for Wikipedia: https://tantek.com/2024/287/t2/setup-search-shortcuts-firefox

For reference / more reading on Venn diagrams and Euler diagrams:
* https://en.wikipedia.org/wiki/Venn_diagram
* https://en.wikipedia.org/wiki/Euler_diagram

#Venn #diagram #diagrams #VennDiagram #VennDiagrams #EulerDiagram #math #maths #sets #setTheory #relationships #Ikigai #fourCircles #fourCirclesVenn #fourCirclesVennDiagram #misconception #popMisconception #Google #GoogleSearch #GoogleWebSearch #webSearch #search #Gemini #GoogleGemini #GeminiWrong #expertise #trust #webTrust #Wikipedia
#Blaugust #Blaugust2026

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Notices tagged with maths