Talk:Menelaus's theorem

Article title

This title was chosen after doing a google count of variations:

Theorem of Menelaus: 185 hits
Menelaus theorem: 2180 hits
Menelaus' theorem: 2180 hits
Menelaus's theorem: 552 hits

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 named.--Tokek 06:44, 8 Feb 2005 (UTC)

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 titles.

About the equation

According to the Chinese Wikipedia 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 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. Thomas Yen 14:18, 11 September 2007 (UTC)[reply]

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 grateful if you could add it as a reference. -- Jitse Niesen (talk) 14:40, 14 September 2007 (UTC)[reply]

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. Qoou.Anonimu (talk) 01:53, 31 December 2008 (UTC)[reply]

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.

If no one convinces me on the contrary in the next few days, I will change again the 1 to -1.

Jose Brox (talk) 14:55, 6 November 2013 (UTC)[reply]

Dual?

Does someone have a source for the claim that this is dual to Ceva? In my opinion this is an erroneous claim. Tkuvho (talk) 15:58, 6 October 2010 (UTC)[reply]

I found corroboration on From Funk to Hilbert geometry Athanase Papadopoulos and Marc Troyanov on page 63

Jackass

What jackass has an absolute value evaluating to minus one?

Thank you for pointing that out, it is now corrected. --Bill Cherowitzo (talk) 20:06, 27 November 2019 (UTC)[reply]