Are All Triangles Actually Isosceles? Discover My Greek-Euclidean Proof!

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SUMMARY

This discussion centers on the assertion that all triangles are isosceles, supported by a Greek-Euclidean proof. The conversation references Lewis Carroll's similar yet fallacious proofs, highlighting the subtlety of the errors involved. Participants explore the linguistic connection between the Greek phrase ὅπερ ἔδει δεῖξαι (hoper edei deixai) and the Latin "quod erat demonstrandum" (QED), confirming their equivalence in meaning.

PREREQUISITES
  • Understanding of basic geometric principles, particularly triangle properties.
  • Familiarity with Greek and Latin mathematical terminology.
  • Knowledge of logical proof structures in mathematics.
  • Awareness of historical mathematical figures, specifically Lewis Carroll.
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  • Research the implications of the Greek-Euclidean proof in modern geometry.
  • Explore Lewis Carroll's mathematical works and his approach to proofs.
  • Study the significance of "quod erat demonstrandum" in mathematical literature.
  • Investigate other fallacious proofs in mathematics and their educational value.
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Mathematicians, educators, and students interested in geometric proofs, historical mathematics, and the interplay between language and mathematical concepts.

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That is my Greek-Euclidean proof that all triangles are isosceles. Any doubts?
 

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Is this different from Lewis Carroll's proof of the same "theorem"?

He had a couple of these fallacious proofs, which are a lot of fun to try to analyze. The error is subtle. I won't spoil the fun yet.

Is your last line in Greek the same meaning as the traditional Latin closing "quod erat demonstrandum" (QED)?
 
RPinPA said:
Is your last line in Greek the same meaning as the traditional Latin closing "quod erat demonstrandum" (QED)?

Yes, exactly this: The phrase, quod erat demonstrandum, is a translation into Latin from the Greek ὅπερ ἔδει δεῖξαι (hoper edei deixai; abbreviated as ΟΕΔ).
https://en.wikipedia.org/wiki/Q.E.D.
 
A nice way to draw the sketch to hide the flaw.
 

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