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

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In summary, the conversation discusses a Greek-Euclidean proof that all triangles are isosceles and compares it to Lewis Carroll's proof of the same "theorem". The speaker also mentions a subtle error in Carroll's proof and discusses the use of the phrase "quod erat demonstrandum" in both Greek and Latin. They also mention a sketch that can hide the flaw in a proof.
  • #1
Konstantinos88
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That is my Greek-Euclidean proof that all triangles are isosceles. Any doubts?
 

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  • #2
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)?
 
  • #3
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.
 
  • #4
A nice way to draw the sketch to hide the flaw.
 

1. What is an isosceles triangle?

An isosceles triangle is a triangle with two sides of equal length.

2. Are all triangles isosceles?

No, not all triangles are isosceles. Only triangles with two equal sides are considered isosceles.

3. How can you prove that all triangles are isosceles?

You cannot prove that all triangles are isosceles because it is a false statement. All triangles cannot be isosceles because there are different types of triangles, such as equilateral and scalene, that do not have two equal sides.

4. What is the difference between an isosceles triangle and an equilateral triangle?

An isosceles triangle has two equal sides, while an equilateral triangle has three equal sides.

5. Can an isosceles triangle have angles of different measures?

Yes, an isosceles triangle can have angles of different measures. However, the two equal sides will always be opposite the two equal angles.

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