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Update2: it seems like one query can also count other results, e.g. searching for "menelaus theorem" results in also counting "menelaus's theorem" so the google way isn't a very good way of finding out what is the most popular. I will create redirects for now of the four that I think are reasonable
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According to the
Chinese Knowledge and my math textbook, the right-hand side of the equation should be 1, instead of -1. The common assumption in school(the high school I attend, at least)is that length measurements are restricted to being a positive value, which in turn restricts the value of the
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Well, you cannot simply change the formula without changing the rest of the text, including the explanation of what negative lengths mean in this context. I changed the article so that it allows both formulations. I hope that the current version agrees with your textbook, in which case I would be
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Update: actually, it seems like Google does not distinguish between "Menelaus' theorem" and "Menelaus theorem", so item 2 above probably includes counts of
Menelaus' as well. Now I think "Menelaus' theorem" is a better title since it has consistency with how theorems are generally
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I think that the equation along with the subsequent explanation, as they are now, are just wrong: either you take unsigned segments and assert that the product equals 1, or take signed segments and equal the product to -1.
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Menelaus's theorem is in fact supposed to have a -1 in it. The reason why is because the orientation of segments matter: AB=-BA. Otherwise the trigonometric version of
Menelaus's theorem would yield a different result.
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right-hand side to 1. The idea that a length value can be negative is a bit confusing. Please correct me if I am mistaken.
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Does someone have a source for the claim that this is dual to Ceva? In my opinion this is an erroneous claim.
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I found corroboration on From Funk to
Hilbert geometry Athanase Papadopoulos and Marc Troyanov on page 63
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If no one convinces me on the contrary in the next few days, I will change again the 1 to -1.
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This title was chosen after doing a google count of variations:
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Thank you for pointing that out, it is now corrected. --
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