Contents.Order of variables how does making abc change the formula? I can't see how it influences it.It changes the stability of the numerical compuation on a floating-point processor. In the limit case of needle triangles, where one side is very small, you want that side to be 'c' in the formula. In perfect real-number computation it doesn't make any difference, of course, but if you're not worried about numerical stability, you wouldn't use this version of the formula anyway; you'd just use the millenia-old original one. 05:51, 9 November 2005 (UTC)It would seem to be the unique parenthesization minimizing the intermediate results while keeping them all nonnegative, subject of course to the triangle inequality.

As such it never uses addition when subtraction is possible. However I'd be interested to see an example where (a+b)+c is less accurate than a+(b+c). 20:42, 22 February 2008 (UTC)When did Heron, otherwise known as Hero discover the fomula?The article says in the 1st century A.D. Do you need a date? - 14:22, 25 July 2006 (UTC)It would be nice but my homework is due in tomorow so you prob. Won't tell me in time. I'm sure 1st Century AD is enough (hopefully).:D JessI don't have a date, probably sometime near 50 A.D.

It was published. 19:13, 28 July 2006 (UTC)The section 'Ch'in Chiu-shao's fomula' really belongs to the history section. Most of it doesn't add to Heron's formula and can be found on. The sentence 'This fomula was proved recently by Wu Wenjun' is very strange!

Anyone can say were did it came from?Anyway I am deleting this section and making the appropriate changes. 05:19, 9 July 2007 (UTC)Spelling is another name for this formula Hero's Formula? —Preceding comment added by 00:57, 27 November 2007 (UTC) Yes, Hero's Formula and Heron's Formula are the same. The spellings 'Hero of Alexandria' and 'Heron of Alexandria' are both used, and neither is correct, although the Greek language purists would probably prefer the version with the n. 08:11, 27 November 2007 (UTC) Properly he is Hero in English, not Heron.

Just as it is Plato and Meno. I have no idea of the history of this in math circles, but the name is very definitely Hero. If this were in Greek, we could worry about those purists, but even classicists say Hero. 02:27, 24 March 2014 (UTC) For anyone who is interested, the situation is as follows. In Greek, the name is Ἡρων, which transliterates into the Latin alphabet as Hērōn. Latin, being reasonably closely related to Greek, had a noun recognisably related to the Greek declension that included the name Hērōn. However, at an early stage of development of the Latin language, the n at the end of the was lost.

Romans tended to use a Latinised form of Greek names of this type, in which the n was omitted, by analogy with Latin words in the corresponding declension. Cases other than the nominative retained the n, so that for example the was Heronis. The name 'Hero' was in this respect treated in exactly the same way as many other Greek names, such as Plato. In English, it has long been common practice to use ancient Greek names in their Latinised form, thus we refer to Plato, and not Platon, but this is not universal, and some ancient Greek names are used in a form which is a direct transcription of the Greek, even when that differs from the Latin spelling. In the case of the name Ἡρων, both the Greek form Heron and the Latin form Hero have been widely used in English. What about which form is 'correct', or, as Eponymous-Archon puts it 'proper'?

It is possible to take the view that the Greek form is the 'correct' one, since it is a Greek name. It is also possible to take the view that what is 'correct' in language is defined by what is used and accepted, and since both forms are widely accepted, both are equally correct. I find it difficult to see, however, any justification for the view that 'Hero' is in some sense more proper in English.

The editor who uses the pseudonym ' 12:48, 24 March 2014 (UTC) Errors There is an error in the expression that follows 'Expressing Heron's formula with a determinant in terms of the squares of the distances between the three given vertices,'. It is missing a necessary minus sign in front of the determinant and under the square root radical. See —Preceding comment added by (. ) 09:20, 6 March 2008 (UTC)There is an error in the formula that discusses the equivalency of Heron's formula to that of the Chinese Qin Jiushao, published in A.D. As stated, the Chinese version does not give the correct value for the area of a general triangle in 3-space with edge lengths a,b,c.' A' Is it sensible to use A both for the area of the triangle and for the name of a vertex in the diagram.

How about chnaging the diagram and all related text from ABCabc to PQRpqr? - 09:40, 22 June 2008 (UTC)The reason that this question has remained unanswered for ten years is that it is a non-issue. Why not change the symbol most commonly used for area to a K as many authors have done?

The possibility of confusing a vertex label with a quantity associated with a triangle is very, very small. We report on what is in the literature and do not try to 'fix' it or make it better, as this suggestion would have it. Labeling the vertices of a triangle ABC is almost universal and that is what we should do here. 20:09, 5 December 2018 (UTC)Fixed this -Jam 20:06, 5 December 2018 (UTC)First formula has an oddity and so does the 2nd one. Ok whoever wrote this didnt really know what they were doing in math, the formula sqrt(s(s-a)(s-b)(s-c)) does not seem equal to (sqrt((a+b+c)(a+b-c)(a-b+c)(-a+b+c))/4pulled out of the sqrt sign for ease on the eyes), but seems to work regardless. Can anyone explain this?

— Preceding comment added by (. ) 19:29, 25 September 2009 (UTC) It's fine. A+b+c = s/2, a+b-c = (s-c)/2, etc. Multiplying them all together puts 16 in the denominator, and then moving it outside the square root reduces it to 4. 20:10, 25 April 2010 (UTC) You were a bit too eager to simplify, above.

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