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Whether this proof is complete depends on what was known before. Was the lemma introduced by a teacher? was it not actually proven, and the student missed the h
by akho 2y ago
Whether this proof is complete depends on what was known before. Was the lemma introduced by a teacher? was it not actually proven, and the student missed the hole in their proof? these are different teachable moments.
I think the two facts, by themselves, are roughly equivalent in difficulty. Moving from Thales to equal diagonals parallelogram requires drawing an extra circle; moving from parallelogram facts to Thales requires either the construction in the article, or continuing the missing radius to get the same rectangle.
- jacobolus 2y agoI don't understand why you are invested in nitpicking the work of an anonymous 7th grader from decades ago. Clearly, filling in all of the details of any formal proof in Greek style is going to require a careful knowledge of the axioms in use and some list of previously proven theorems which are allowed to be used without re-proof. Depending on which theorems are at hand already, one or another proof might be shorter or longer or more or less obvious. When trying to construct a whole mathematical treatise, the best order for the theorems so that each proof depends only on previously proven theorems is a tricky choice involving some trade-offs between pedagogical goals and concision of individual proofs. But all of that is missing the point.