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[edit] meaningless reference to pi.
The article states:"The ancient Egyptians had no concept of pi and never made any efforts to calculate it, but they could approximate the area of a circle using a simple formula, which was to subtract 1⁄9 of the diameter and square the result." Isn't that exactly the concept of pi? In modern mathematics we use Constant times Radius squared = area. This statement says the Egyptions used constant times diameter squared = area. Sorry folks but that is both the concept of pi, and a calculation of it, just using diameter(which is directly measurable) rather than radius. As the diameter is of course twice the radius, the egyptian approximation of pi is clearly 2X2X8/9 r squared = 32/9. I am removing this erroneous statement. IdreamofJeanie (talk) 12:02, 23 March 2008 (UTC)
- Why did you remove the formula though, which is clearly cited and appropriate? I added it back. 2X2X8/9 may indeed be 32/9 but the ancient Egyptians made no attempt to calculate this as such. Apparently it did not occur to them that there was this special ratio, and the written sources indicate they simply used the approximation without the realization of its special significance. The real meaning of pi is that the ratio is constant and true for every circle, and there is no source that indicates they understood this profound truth, let alone tried to make calculations of it. Jeff Dahl (Talk • contribs) 13:04, 23 March 2008 (UTC)
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- I don't have the knowledge on this subject, but a few questions come to mind. Did they use the formula more than once? Assuming they did, obviously they understood that the same formula is usable on every circle, just as I'm sure they understood that the same formula is used to discover the area of any square, or any rectangle, etc. Just because they didn't give the fraction a name didn't mean they didn't understand it's importance. On the other hand, if it was only used a few times in one area, and not throughout the empire, then that should be mentioned. IanCheesman (talk) 18:01, 23 March 2008 (UTC)
- It was routinely used, or at least it was a common "textbook" problem. Like the ancient Egyptians, we can think of their formula as a rule of thumb. The ancient Egyptians were interested only in getting the answer to real world problems and were not interested in math for math's sake. I guess I take issue when people say that the ancient Egyptians had "a close approximation of pi", because it implies they were interested in abstract mathematical thought. Allow me to quote from Clarke (page 222, ref on the article)
- "Although the ancient approximation of the ratio of the circumference of a circle to its diameter, or pi, is not given in the mathematical papyri, the determination of the area of a circle occurs in the Rhind Papyrus (No. 50). The method was to subtract 1/9 of the diameter from it and to square the result. This would now be expressed by the formula A = (8/9)D2. This approximation is fairly close, the area thus obtained being (.7902)D2 instead of the true value (.7854)D2, and must have been originally have been obtained by drawing a circle on a finely squared surface and counting the squares."
- Note that the approximation is for the area and not for the ratio. For us, it is an easy conclusion to draw that the ratio would follow naturally from the approximation but not so for the ancient Egyptians--they simply would not have thought of it in those terms. I'll remove the sentence IdreamofJeanie found objectionable since it doesn't actually add anything, but I'm not going to delete the whole paragraph as that user tried to do. Jeff Dahl (Talk • contribs) 18:45, 23 March 2008 (UTC)
- Thanks Jeff, that's ideal, I just found the earlier wording contradictory. cheers IdreamofJeanie (talk) 20:50, 23 March 2008 (UTC)
- Thanks for bringing this up as it lead me to notice other red flags in this section. I am more troubled by the fact that a high school geometry textbook was used as a reference in the article! Furthermore, the quote above by Clarke shows that original research is being introduced into the article in violation of WP:SYNTH, something I've pointed out before on the article FA review page. A closer examination of the sources cited would be a good idea at this point. — Zerida ☥ 21:43, 23 March 2008 (UTC)
- Some of your additions to the math section were good, others not. As they are currently formatted, I think the hieroglyphs at the end are confusing and unhelpful to a casual reader, I would either delete or make it more intelligible. I'm going to partially undo some of your changes and move a few things, see what you think. Jeff Dahl (Talk • contribs) 05:35, 24 March 2008 (UTC)
[edit] Alexandria mob
I removed the clarify tag on the Alexandrian mob quote. Shaw (418, under the section "A Long Decline") says: "These problems were often aggravated by the fury of the Alexandrian mob, which first surfaced at the death of Ptolemy IV..." Shaw goes on to quote from Polybius of their "unbridled and vicious temper". (Zerida) I think this is what you are looking for, right? Otherwise what needs to be clarified? Thanks for your copyedits. Jeff Dahl (Talk • contribs) 05:13, 24 March 2008 (UTC)
- Yes, thanks, I found it and made a small addition for context. — Zerida ☥ 05:21, 24 March 2008 (UTC)
[edit] Math section
Starting a new heading. I removed some parts because:
- Having a litany of 5 or 6 math papyri doesn't add value, just pick the two most important.
- I hid the hieroglyphs at the bottom; should either find a better way to format or remove.
- Removed transliterations: rwy 'r-2' and so on, these are basically gibberish to the average reader. This greatly hinders reading and understanding. Better to use symbols and words people will understand, such as 2⁄3.
- "In geometry, the ancient Egyptians had a grasp of the principles underlying the Pythagorean theorem..." I thought this was a little vague, better to say specifically what principles they did understand (such as certain rise/run produces simple whole numbers for the lengths of the sides of the triangle formed). They certainly did not understand the Pythagorean theorem, which is the impression that a casual reader might get by reading that sentence.
- "The angle of the face of a pyramid was calculated from the ratio of its height to half of its base; for the Great Pyramid of Giza it was 14-11." Not well integrated, not sure why this specific 14-11 ratio is important to mention.
I don't mean to just erase your effort, I want to find a way to integrate this stuff together in a way that doesn't distort or confuse. [[User:Jeff Dahl|e at a given number. My wording says that units are repeated as many times as necessary to add up to the number, the example 80 is chosen arbitrarily and for this example the tens unit is the one necessary.
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- "...compared to the modern approximation 3.1416" We don't need to tell people that pi = 3.141..." We can just say pi, people will know what that means. Writing out 3.1416 complicates the prose and is arbitrarily imprecise, because the number has to be rounded off (why not 3.14159 or 3.14?). Why not avoid the issue by just using the symbol pi?
- Why not "The Egyptians
had a grasp of the principles underlying the Pythagorean theorem such that they knew that a triangle had a right angle opposite the hypotenuse when its sides were of a 3-4-5 ratio." Saying they had a "grasp of the principles" is very vague and the relationship to the theorem is unspecified. The fact that a 3-4-5 triangle has a right angle opposite the hypotenuse is certainly not a "principle" of the pythagorean theorem any more than an apple falling is a principle of the theory of gravity.
- Area ≈ [(8⁄9)D]2 = 256⁄81 is mathematically inaccurate because there are no variables on the right hand side of the equation. Again, what is wrong with the way I had it? Jeff Dahl (Talk • contribs) 07:13, 24 March 2008 (UTC)
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- What's wrong with my wording? The same problem with the "The ancient Egyptians had no concept of pi and never made any efforts to calculate it" bit. It's hyperbolic and glosses over the details of their ability to approximate the area of a circle.
- My sources say that 2/3 is a special case, and that other fractions having numerator greater than 1 were not used Both you and "your sources" are wrong. The equivalent of 3⁄4, i.e. 3-r was also expressed by another glyph; I just happen not to have mentioned it. My wording also sticks to the source I quoted. I am not interested in *your* take on it; it's OR.
- It's not just the tens that can be repeated, any of the units, 1, 10, 100, may be repeated to arrive at a given number. While that part could further be reworded, your previous wording ("The symbol was written as many times as necessary to add up to the desired number,") suggested that in order to express 100 or 1000 or 10000, glyphs representing the number ten had to be continually repeated, which is yet again false.
- We don't need to tell people that pi = 3.141 I disagree because 1. it is based on the source cited, and 2. it lets readers of all levels appreciate the extent of the ancient Egyptians' understanding of the area of a circle.
- Why not "The Egyptians knew that a triangle had a right angle opposite the hypotenuse when its sides were of a 3-4-5 ratio" Because as I said again and again that's what the source, an actual Egyptologist, indicates. And that's what matters.
- Area ≈ [(8⁄9)D]2 = 256⁄81 is mathematically inaccurate because there are no variables on the right It is obvious from the context that what is meant is 256⁄81 ≈ 3.16, but it can be made clearer. — Zerida ☥ 08:19, 24 March 2008 (UTC)
[edit] i passed ss because of this page
i passed yes IPASSED ,and stop complaing this page rocks —Preceding unsigned comment added by Mentleman (talk • contribs) 00:34, 11 April 2008 (UTC)
[edit] Auto peer review
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