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Small circles

Is there any article on small circles (or what it its name in the English language) ? // Rogper 21:09, 25 Oct 2003 (UTC)

measures that reference the earths great circle

1 stadia = 1/600 Degree of the Earths Great Circle
1 passus = 1/75,000 Degree of the Earths Great Circle
1 pes = 1/375,000 Degree of the Earths Great Circle

[75 Roman miles equals a degree Nile map legend 1775]

1 Roman degree = 75 milliare = 111 km

7.5 milliare = 1 schoenus = 1 kapsu = 60 stadiums of 185 m
60 stadiums = 60 furlongs = 11.1 km = 1/10 degree

The degree of Aristotle

[The degree of Aristotle]

"In the second half of the eighteenth century A.D. a number of French scholars came to the conclusion that ancient linear units of measure were related to the length of the arc of meridian from the equator to the pole. They concluded that all Greek statements about the size of the earth provide the same datum, except that different stadia were employed. Several ancient authors used different figures and different stadia to say what Aristotle says in De Coelo (298B), namely, that the circumference is 400,000 stadia. The scholars of the French Enlightenment were hampered by the lack of modern exact data about the size of the earth. "

1 Degree = 1/360 of 400,000 stadia = 1111.1 stadia = 111 km
10 stadions = 1 km
1 stadion = 100 m = 300 pous of 333.3 mm
111 km divided into 600 stadions of 600 pous of 308.4 mm = 185 m

The degree of Posidonius

[The Degree of Posidonius]

Eratosthenes and Posidonius considered that several inhabited worlds must exist on the Earth's spherical surface, separated by uncrossable oceans and by a torrid, uninhabitable belt. Marinus took the liberty of extending the inhabited world to 225º longitude and reached latitude 24º S, leaving no room for other inhabited worlds. In the east, his world ended in a country called Thina or ‘Land of the Chinese'. Marinus seemed to believe that the Land of the Chinese might extend another 45º to the east of the capital (supposedly in the centre of the country), which would give us an inhabited world of 270º in longitude, starting from the Canaries Meridian zero. This arrangement leaves only 90º between these islands and the east coast of China, which is about halfway between Martin Behaim's geographical calculations and those of Christopher Columbus.

1 Degree = 1/360 of 216,000 stadia
1 Degree = 600 stadions = 111km
111 km divided into 600 stadions of 600 pous of 308.4 mm = 185 m

The degree of Marinus

"Marinus's only work of which we have direct reference is Diorosis tou geographikon pinokos, to which Ptolemy dedicates fifteen chapters. There were numerous editions, and his basic theories have their roots in Eratosthenes, Hipparchus, and Posidonius in particular. The title of his work literally means ‘Corrections in the map of the world' or ‘Corrections in the map of the inhabited world', which goes to show that Marinus of Tyre wanted to improve and revise one or several works of earlier mapmakers. He appears to wish to amend Posidonius, and that he intended to do so, using Hipparchus's astronomical work and the accounts of several recent voyages.

Marinus made use of the measurement of the Earth made by Posidonius, who lived from 135 to 50 BC. While Strabo, who lived between 58 BC and 24 AD, kept Eratosthenes' measurements of 252 thousand stadia for the circumference of the Earth, that is 700 stadia per degree, Marino uses Posidonius's calculations of 180 thousand stadia, with a degree of 500 stadia (Antonio Ballesteros Beretta: Génesis del descubrimiento, vol 3, Barcelona, Salvat 1947). A stadium is an old Greek measurement of length, the equivalent of 600 old Greek feet (192.27m) or 125 paces, which was the exact distance separating the columns in the great amphitheatre of Olympia. The question is as to why Marinus and Posidonius himself adopted Posidonius's measurements instead of those of Eratosthenes. Posidonius's map, which was drawn around 60 BC, was passed on to us by Dionysius Perigetes in about 125 AD. On Posidonius's map the Earth forms a single continent and there is no trace of the Dragon's Tail.

The work of Marinus of Tyre, which Ptolemy had at his disposal, did not seem to include any actual map. There were only some general instructions on how to make a map of the world and tables of geographical coordinates."

"Marinus made use of the measurement of the Earth made by Posidonius, who lived from 135 to 50 BC. While Strabo, who lived between 58 BC and 24 AD, kept Eratosthenes' measurements of 252 thousand stadia for the circumference of the Earth, that is 700 stadia per degree, Marino uses Posidonius's calculations of 180 thousand stadia, with a degree of 500 stadia (Antonio Ballesteros Beretta:"

1 degree = 1/360 of 180,000 stadia
1 Ptolomaic Degree = 500 stadions = 111km
111 km divided into 500 stadions of 600 remen of 14.7" = 222m

The degree of Ptolemy

[The degree of Ptolemy]

"Ptolemy's other main work is his Geography. This too is a compilation, of what was known about the world's (Study of the earth's surface; includes people's responses to topography and climate and soil and vegetation) geography in the Roman empire at his time. He relied mainly on the work of an earlier geographer, Marinos of Tyre, and on gazetteers of the Roman and ancient Persian empire, but most of his sources beyond the perimeter of the Empire were unreliable."

"The first part of the Geography is a discussion of the data and of the methods he used. Like with the model of the solar system in the Almagest, Ptolemy put all this information into a grand scheme. He assigned coordinates to all the places and geographic features he knew, in a grid that spanned the globe. Latitude was measured from the equator, as it is today, but Ptolemy preferred to express it in the length of the longest day rather than degrees of arc (the length of the midsummer day increases from 12h to 24h as you go from the equator to the polar circle). He put the meridian of 0 longitude at the most western land he knew, the Canary Islands."

"Ptolemy also devised and provided instructions on how to create maps both of the whole inhabited world (oikoumenè) and of the Roman provinces. In the second part of the Geography he provided the necessary topographic lists, and captions for the maps. His oikoumenè spanned 180 degrees of longitude from the Canary islands in the Atlantic Ocean to China, and about 80 degrees of latitude from the Arctic to the East-indies and deep into Africa; Ptolemy was well aware that he knew about only a quarter of the globe."

"The maps in surviving manuscripts of Ptolemy's Geography however, date only from about 1300, after the text was rediscovered by Maximus Planudes."

"Maps based on scientific principles had been made since the time of Eratosthenes in the 3rd century BC, but Ptolemy invented improved projections. It is known that a world map based on the Geography was on display in Autun, France in late Roman times. In the 15th century Ptolemy's Geographia began to be printed with engraved maps; an edition printed at Ulm in 1482 was the first one printed north of the Alps. The maps look distorted as compared to modern maps, because Ptolemy's data were inaccurate."

"Eratosthenes found 276-194 BC used 700 stadia for a degree on the globe, in the Geographia Ptolemy uses 500 stadia."

"It is not certain if these geographers used the same stadion, but if we assume that they both stuck to the traditional Attic stadion of about 185 meters, then the older estimate is 1/6 too large, and Ptolemy's value is 1/6 too small."

"Because Ptolemy derived most of his topographic coordinates by converting measured distances to angles, his maps get distorted. So his values for the latitude were in error by up to 2 degrees. For longitude this was even worse, because there was no reliable method to determine geographic longitude; Ptolemy was well aware of this. It remained a problem in geography until the invention of chronometers at the end of the 18th century AD. It must be added that his original topographic list cannot be reconstructed: the long tables with numbers were transmitted to posterity through copies containing many scribal errors, and people have always been adding or improving the topographic data: this is a testimony of the persistent popularity of this influential work."

1 degree = 1/360 of 180,000 stadia
1 Ptolomaic Degree = 500 stadions = 111km
111 km divided into 500 stadions of 600 remen of 14.7" = 222m

The Ptolomaic stadia is divided into remen instead of pous because in Egypt Remen had always been used for land surveys.

The degree of Erathosthenes

[The degree of Eratosthenes"

" If he has used a stadion definition of 1 stadion = 158,7m = 300 Egyptian royal cubits = 600 Gudea units (length of the yardstick at the statue of Gudea (2300 b c) in the Louvre/Paris), he has already observed the meridian arc length to 252000 ⋅ 0,1587 = 40000km. How could Eratosthenes obtain in ancient times already such an accurate result?"

"Ptolemaios describes in his "Geographike hyphegesis" a method used by the "elder" to

determine the size of the Earth; this ancient method to measure the meridian arc length between the latitude circles of two cities (e.g. Alexandria/Syene, Syene/Meroe) is based on a traversing technique, as will be shown."

"Geographical latitudes could be measured using a "Skiotheron" (shadow seizer). An

according to ancient information reconstructed instrument will be shown and explained; the accuracy of sun observations with such a kind of instrument is comparable with those of a modern sextant."

"A recovery of the two systems of ancient geographical stadia (Alexandrian and Greek) is

presented. It is presently used for a rectification of the digitalised maps given in Ptolemy's "Geographike hyphegesis". The stadion definition Eratosthenes has used (1 meridian degree = 700 stadia) was applied also in northern and western Europe and in Asia east of the Tigris river; using it as a scale factor we got very good results for the rectification."

1 Degree = 1/360 of 252,000 stadia
1 Persian degree = 700 stadia = 111 km
10 Egyptian schoeni = 20 Persian parasangs = 600 furlongs
1 Persian stadia = 157 m = 3 Egyptian st3t

The Egyptian degree

[The Egyptian degree]

"Since Egypt lies north of the equator, shadow lengths are greatest there during the time of winter solstice, when the noon sun is at its most southern yearly position in the sky. The winter solstice therefore affords the most advantageous opportunity to make comparative shadow measurements. It was likely known by the time of the building of the Great Pyramid that on the day of the summer solstice, (i.e., when the sun was highest in the sky), the noon sun was directly overhead (casting no shadow) at a point along the Nile near what is now Aswan (called Syene by the Greeks). This concurrence was used by Eratosthenes (ca. 250 B.C.) in the first recorded attempt to measure the size of the Earth. From Syene, it would have been fairly straightforward to have determined that the sun's noon winter solstice position was very nearly 48 (2/15ths of a full rotation) lower in the sky than its noon summer solstice position. It could then have been logically inferred that Syene must lie 24 (1/15th of a full rotation) north of the mid-point of the sun's yearly north/south travel, and hence 24 north of the Earth's north/south mid-point (equator).30 By accurately measuring shadow lengths cast by tall objects of known height, one could then determine, through the use of trigonometry, one's angular separation from the Earth's mid-point. "

1 Degree = 1/360 of 2,520,000 itrw
1 Egyptian degree = 10 itrw = 700 stadia = 210,000 royal cubits
1 itrw = 21,000 royal cubits = 70 stadia of 3 st3t
3 st3t of 100 royal cubits = 157 m

700 × 157 = 10.99 km
1 itrw is 1 hours river journey
1 atur is 1 hour of March
1 Egyptian Minute of March is 350 royal cubits of 525 mm = 183 m

The degree of Herodotus

1 Greek degree = 75 milions = 111 km
7.5 milions = 1 schoenus = 1 kapsu = 60 stadions of 185 m
60 stadions = 60 furlongs = 11.1 km = 1/10 degree

The stadium mille passus

A stadia is a division of a degree into a fraction of a mile.

The ordinary Mesopotamian sos or side at 6 iku and 180 meters was the basis for the Egyptian minute of march
the Egyptian minute of march at 183 m and 350 royal cubits was the basis for the stadion of the Greek Milos or milion
The stadion of the Greek Milos at 6 plethrons or 100 orguia and 600 Atic pous of 308.4 mm at 185 m was the basis for the stadium of the Roman milliare
The stadium of the Roman Milliare at 625 pes of 296 mm was also 185 m and at 1000 passus of 5 pes was the basis for the furlong of 625 fote of the English Myle

The league of the mille passus

A league is a division of a degree into a multiple of a mile.

3 Milion or Milos of 4800 pous = 24 stadions = 14,400 pous
1 league of a Milion = 4440 m
3 Milliare of 5000 pes = 24 stadiums = 15,000 pes
1 leauge of a Milliare = 4440 m
3 Myles of 5000 fote = 24 furlongs = 15,000 fote = 9375 English cubits
1 League of a Myle = 4440 m
3 Miles of 5280 feet = 24 furlongs = 15,840 feet = 9900 English cubits
1 Leauge of a Mile = 4828 m

Rktect 02:56, September 1, 2005 (UTC)

A Great Circle

A great circle is a line that cuts the globe or earth into two seperate and eqaul pieces. These lines may look like an elipse when drawn on a map because of the curve of the real earth. These Great Circles are the shortest distance to travel from point to point.

A Great Circle Route

A Great Circle Route is a route that you take that is actually a Great Circle.

What is that, a joke?

Disambiguation needed.

There is a shipping route between the west coast and asia known as "the Great Circle Route". — Preceding unsigned comment added by 106.170.116.236 (talk) 07:04, 6 April 2012 (UTC)[reply]

Meridians as great circles?

Can an oblate have more than a single great circle? 89.0.221.28 13:19, 26 March 2007 (UTC)[reply]

Only the equator is a great circle——all of the meridians are "great ellipses"! P=) ~Kaimbridge~13:47, 26 March 2007 (UTC)[reply]

This depends on the definition. If a "great circle" corresponds to any plane which passes through the origin(center) but does not need actually to be a circle, then any convex bounded shape has exactly as many great circles as the sphere has. Incnis Mrsi (talk) 12:16, 3 September 2011 (UTC)[reply]

Theorem of Great Circles

The Theorem of Great Circles ("great circle lines") has been proven by the well-known Russian mathematician and physicist, A. I. Fet. I don't see any link here to his proof, and I don't see any biography of A. I. Fet in English-language Wikipedia (though there is a stub mentioning his Theoreme of Great Circles in Russian-language Wikipedia). I am not proficient in creating Wikipedia articles, and it pains me to follow Wikipedia's many meticulous and dubious rules -- so, if anybody has time and desire to fill this gap, I can provide this magnanimous person with an accurate translation of the Russian Wiki article into English, for the purpose of using it in the English article. I am a professional English-Russian translator, my e-mail is afeht@aol.com. Thank you. --69.19.14.15 01:38, 26 October 2007 (UTC)[reply]

Rossia rodina slonov. Katzmik (talk) 11:14, 29 October 2008 (UTC)[reply]

These are two closed geodesic curves, not "great circles". Incnis Mrsi (talk) 12:16, 3 September 2011 (UTC)[reply]

ábaco trigonométrico para calculo do grande círculo

trigonometrical, simulator Abacus of the great circle —Preceding unsigned comment added by 201.53.100.102 (talk) 20:01, 16 September 2008 (UTC)[reply]

Estão associando o meu nome com o IP (?) porque???

Encaminhei um assunto a página de discussão, porque senti-me enganado e por isso nem assinei. Porem fiz isso logado (vejam no histórico), sendo assim não há razão de associar o meu nome com o IP em questão. Já que esse número também não cometeu nenhum crime.

They are associating my name with the IP () because? I directed the censured topic the quarrel page, because I felt deceived me and therefore nor I signed. To put I made this logado (they see in the description), thus being does not have reason to associate the name to the IP. Since this number also did not commit vandalism some. They only verify if the information proceeds and is in its (already it was time to finish with this panelinha). —Preceding unsigned comment added by 3signmain (talk • contribs) 20:23, 16 September 2008 (UTC)[reply]

Já disse isso é uma página de discussão sobre a edição , nesse sentido não tem que trazer o histórico , e se eu quiser assinar sei como fazer.3signmain (talk) 20:27, 16 September 2008 (UTC)[reply]

"actually divides into four separate areas"?

I removed the sentence from the 1st paragraph: "A great circle is the intersection of a grander and more large sphere which actually divides into four separate areas with a plane going through its center." The English is very poor, but even beyond that the statement makes no sense. --EEPiccolo (talk) 20:14, 29 September 2008 (UTC)[reply]

Equator is generally considered a spherical great circle

As it is written in a geographical context, what about geoid? The true equator does even not lie in one plane. Incnis Mrsi (talk) 12:16, 3 September 2011 (UTC)[reply]

July 2013 suggestions for moving sections of this article elsewhere

This section is for discussing Fgnievinski's tags suggesting moving articles. cffk (talk) 10:37, 30 July 2013 (UTC)[reply]

I recommend moving (removing) "Earth Geodesics" section (leaving a note on which article to find the information). I recommend leaving "Derivation of shortest paths section". The proof is short enough and the notation is not what is familiar to the geodetic crowd. cffk (talk) 21:41, 29 July 2013 (UTC)[reply]

I cleaned up the Earth Geodesics section a little and removed the merge suggestions. cffk (talk) 11:31, 20 August 2013 (UTC)[reply]

Calculating Great Circle Distance

Is there, or could there be, a function to calculate the great circle distance between two point?

This would be similar to the convert 1,000 feet (300 m) function.

The GC function would want to be flexible enough to read latitudes and longitudes in formats already used by Wiki.

For example, given:

Chipata,Za = 13°39′S 32°38′E
Serenje,Za = 13°15′35″S 30°14′15″E

create: {{GreatCircle|13°39′S 32°38′E|13°15′35″S 30°14′15″E|km}} Tabletop (talk) 03:21, 20 July 2015 (UTC)[reply]

Far too mathematical

An editor recently flagged a link to Great circle in an article on the Aleutians campaign with the comment that the relevance was unclear. The Aleutian Islands happen to lie on the great circle between Japan and Washington State, which is the only reason for their military importance. I was puzzled why the relevance of this was not obvious.

So I clicked through to this article, and lo and behold! You have to read deeply into the article to realize great circles have anything to do with navigating the Earth.

I think this is a serious flaw with this article. I would wager good money that the vast majority of people who enter "great circle" in the Wikipedia search box are interested in terrestial navigation and not in a deep discussion of the mathematics of geodesics on the sphere.

I don't know the best way to address this problem, but I think the discussion needs to take place. --Yaush (talk) 17:10, 3 December 2015 (UTC)[reply]

Riemannian circle and other edits

I recently made some edits that came about as a result of a revert that I should more fully explain. First of all, the term Riemannian circle was being used in the first sentence as a synonym for great circle. This is not technically correct as a Riemannian circle has an intrinsic metric and the term can be applied to objects that are not spheres. As a synonym the term should be bolded, but as a non-synonym it should be linked to. In an earlier revert I reinstated the link that had been removed, but I now realize that the term needed to be put in context, so I moved it down a little and put it where Riemannian geometry is discussed. The other disagreement I had concerned including a statement that all great circles have the same center. The IP felt that this was redundant and removed it; I disagreed. Given the elementary nature of this article, I think that you should err on the side of redundancy in the lead. The fact that the centers of the great circles are the same point follows easily from the definition, but then again, so does the fact that they all have equal diameters and hence all have the same circumferences, etc. Where do you stop relying on the audience's ability to make simple deductions and start talking about properties? I have reworded the statement to de-emphasize this fact, but I still think that it belongs in the lead.--Bill Cherowitzo (talk) 18:21, 17 July 2017 (UTC)[reply]

With regards to the statement about centres, I found it perhaps not technically redundant but unnecessarily repetitive, "same center as the sphere" appearing soon after "center point of the sphere". I think it reads better now. 2.25.45.251 (talk) 05:35, 18 July 2017 (UTC)[reply]

The definition provided at Riemannian circle is pretty confusing. From skimming a few academic papers it seems to me like Riemannian circle is more or less just a synonym for circle, with the "Riemannian" part added just to emphasize out that it has some intrinsic definition of distance attached. I don't really think this needs to be discussed in the lead section here. If someone wants to discuss it in this article at all, maybe it can be moved to a section nearer the end? Also maybe clarify the definition at Riemannian circle to be legible to, say, an average undergraduate science student. –jacobolus (t) 19:54, 9 October 2022 (UTC)[reply]