Talk:Chronology of computation of π
|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
- 1 What's in a name, that which we call
- 2 Egyptian value of Pi
- 3 Another Egyptian value of Pi
- 4 possible misrepresentation of one estimate
- 5 "dps"?
- 6 Pi and the pyramids
- 7 Explanation of move from "π" to "pi"
- 8 Move discussion in progress
- 9 Move discussion in progress
- 10 Move discussion in progress
- 11 houkouonchi got first prize
- 12 Decimal places
- 13 External links modified
What's in a name, that which we call
I think there is an orthographic and/or grammar and/or spelling error in the page title "Chronology of computation of pi". I think it should read Chronology of computations of pi (or "Chronology of the computation of pi"). I post this comment here with the current date; if someone runs across this page in some months and there has not been any protest, I think we should move it to the new title (creates a redirect, anyway).
Egyptian value of Pi
You have included the value of Problem 50 and ignored the value of problem 48 in your stated value of Pi. The 3x3 grid square of 9 units convereted to an octagon goes hand in hand with the 9 unit diameter circle. This is to give a maximum (3.16) and minimum (3.111') value for Pi. The egyptian are not stating Pi - 3.16 !
--Michael saunders 22:27, 18 March 2006 (UTC)
Another Egyptian value of Pi
It might be that the Egyptians had an better approximation of pi than it says now in the article, also at an earlier date. E.g. in the wikipedia article about the "Great Pyramid of Giza" it says the pyramid is thought to be 280cubits high with 440cubits long basesides (cubits stands for Royal Cubit, a standard egyptian length used in those days).
It makes the ratio between height and sum of the 4 baseside-lengths of this pyramid as 2 pi (1760 diveded by 280). This all might mean that the egyptians had an about two times more accurate number for pi with 22/7 in about 2500 BC (the generally accepted estimated date of completion of the Great Pyramid as stated in the same article about the pyramid). 220.127.116.11 (talk) 08:42, 28 January 2008 (UTC)sonty567
NB: Yes, your statement above it quite correct. Flinders Petrie, the top Egyptologist and surveyor Giza published on this at least 5 times through his career, including in Nature Journal in 1925. Other top Egyptologists have concurred on this point including IES Edwards and Miroslav Verner in 2000. I have studied this intensively for nearly ten years now, and Petrie and the others were quite correct on this point. Dave Lightbody. The 2x 22/7 would have been expressed as 2 x 3+1/7th in the Egyptian unit fraction system. —Preceding unsigned comment added by 18.104.22.168 (talk) 22:03, 14 March 2011 (UTC)
possible misrepresentation of one estimate
I'm not an expert in this field but while doing research I discovered that the 339/108 ratio attributed to the Indian mathematician might need to be 62,832/20,000 which actually yields a more accurate result. I can't find anything quoted in a scholarly work to support either number however and hence will not edit the page. —Preceding unsigned comment added by 22.214.171.124 (talk) 10:29, 11 February 2009 (UTC)
- I've changed it. Feel free to change it to something better/shorter. Does "decimal places" include the 3? (e.g. is "3.1415" four decimal places or five? Do all the records report using the same convention?) Shreevatsa (talk) 04:19, 17 March 2009 (UTC)
Pi and the pyramids
Most Egyptologists do not think the pyramid builders knew and used Pi in constructing the pyramids.
- This statement above is wrong. Professors IES Edwards, Petrie and Verner all stated that the proportions of the circle were deliberately incorporated into the designs of some of the Great Pyramids. The article by Greenberg is also wrong, and he is clearly unaware of the archaeological data that has been uncovered and published in numerous publications since as far back as 1883.** Dave Light 14/2/2011
See this by Professor of Mathematics Ralph Greenberg (and associated links), , and  The article should be reworded to clarify this, not put forward a minority view. Dougweller (talk) 13:27, 9 September 2010 (UTC)
- I removed the citation of Edwards, The Pyramids of Egypt p.269. This book says "The normal angle of incline was about 52° - a slope which in the Pyramid of Meidum and in the Great Pyramid would have resulted if the height had been made to correspond with the radius of a circle the circumfere
nce of which was equal to the perimeter of the pyramid at ground level." This does not support the assertion that these pyramids were involved in an early computation of pi. Kenilworth Terrace (talk) 17:14, 10 September 2010 (UTC)
- Above. You should have left that quote because it shows that the premier authority of pyramid design from the 20th centuiry supported professor Petrie's conclusions. These conclusions were not just about proportion but about the numerical values of approximations for a circle's proportions.
This may not be analagous to a modern value of pi, but it is as valid a piece of information about pi as the PRhind and Babylonian examples are.** Dave Light 14/2/2011
Explanation of move from "π" to "pi"
It is unconventional to use a math symbol in a title even when that symbol is common usage. It's Three Blind Mice, not "3 Blind Mice", a Dirac delta function, not a δ function, and so forth. In this case, "pi" is a far more common usage than "π". On Google books, the "computation of pi" -wikipedia gets twice as many hits as "computation of π" -wikipedia. CNN uses "pi", the BBC uses "pi", and the New York Times uses "pi". This entry in Merriam-Webster is entitled "pi". The "pi" entry in Britannica is a good model. They clearly have no policy or technical issue that prevents them from publishing a "π", yet they use it only for equations. Van Nostrand's Scientific Encyclopedia does the same, and that is an even better authority (p. 4105 -- sorry no link). Math journals can go either way. Check here and here for journal articles with "pi" in their titles. Kauffner(talk) 02:31, 19 April 2011 (UTC)
Move discussion in progress
There is a move discussion in progress on Talk:Liu Hui's pi algorithm which affects this page. Please participate on that page and not in this talk page section. Thank you. —RM bot 07:16, 27 April 2011 (UTC)
Move discussion in progress
There is a move discussion in progress on Talk:Liu Hui's π algorithm which affects this page. Please participate on that page and not in this talk page section. Thank you. —RM bot 16:31, 27 April 2011 (UTC)
Move discussion in progress
houkouonchi got first prize
What's the meaning of numbers in "decimal places" column? As I understand, "decimal places" precision usually refers to digits after decimal separator, not total number of digits. This is in line with first two rows: ancient Egyptians value of 3.16045... and ancient Babylonians value of 3.125 both calculate two digits, or one decimal place, correctly and the value in the column is stated as "1". However, this is succeeded by China and Bible value of 3, so one digit/zero decimal places correct, but "decimal places" value is still stated as "1". After that we have a mix of values that don't seem to be in line with any coherent definition.
|Date||Whom||Formulation||Value of pi||Current value in the table||Digits correct||Decimal places correct|
|2000? BCЕ||Ancient Egyptians||4*(8/9)^2||3.16045...||1||2||1|
|2000? BCЕ||Ancient Babylonians||3+1/8||3.125||1||2||1|
|550? BCЕ||Bible (1 Kings 7:23)||"...a molten sea, ten cubits from the one brim to the other: it was round all about,... a line of thirty cubits did compass it round about"||3||1||1||0|
|434 BCE||Anaxagoras attempted to square the circle||compass and straightedge||Anaxagoras didn't offer any solution||0||0||0|
|350? BCЕ||Sulbasutras||(6/(2+√))^2||3.088311 …||1||1||0|
|c. 250 BCE||Archimedes||223/71 < π < 22/7||3.140845... < π < 3.142857...
|5||Liu Xin||the exact method is unknown||3.1457||2||3||2|
|130||Zhang Heng (Book of the Later Han)||√ = 3.162277...
|263||Liu Hui||3.141024 < π < 3.142074
|480||Zu Chongzhi||3.1415926 < π < 3.1415927
Zu's ratio 355/113
|1150||Bhāskara II||3927/1250 and 754/240||3,1416||3||4||3|
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