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Tantek Çelik

Tantek Çelik

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:
https://en.wikipedia.org/wiki/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:
https://indieweb.org/Gemini#four%5Fcircle%5FVenn%5Fdiagrams
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%5Ftemplates/EW%5Fvenndiagram%5F4
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%5Fdiagram
  • https://en.wikipedia.org/wiki/Euler%5Fdiagram
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#Blaugust #Blaugust2026
https://tantek.com/2026/235/t1/venn-diagrams-euler-difference

#venn#diagram#diagrams#venndiagram#venndiagrams#eulerdiagram#math#maths

tantek.comDiscussed 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: https://upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Diagramo_de_Ikigajo_-en.svg/1280px-Diagramo_de_Ikigajo_-en.svg.png (Ikigai diagram showing four overlapping circles of what you LOVE, are GOOD AT, can be PAID FOR, the World NEEDS, and most of their intersection regions labeled as well) https://en.wikipedia.org/wiki/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: https://indieweb.org/images/2/2d/2026-08-23-google-gemini-four-circle-venn-error.png (Google results for “examples of four circle venn diagrams” showing errant answers from Gemini) https://indieweb.org/Gemini#four_circle_Venn_diagrams 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 - Tantek
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