If you were drawing a map and were using the ratio 1cm:20km how many cm would 22km be? 1.1? —The preceding unsigned comment was added by 81.178.228.183 ( talk • contribs) .
someone added the word 'chicken' to the start of the page. it wasn't in context and i assume it was a mistake so i removed it. if you're terribly fond of chickens and find this edit to be offensive, i apologize.
gba 05:11, 12 February 2007 (UTC)
I'm sorry. I don't edit and don't know what the standards are involved. I just wanted to point out something I think needs correction:
Under: Ratios and fractions
"a) If you have three apples for every four oranges then you have a 3:4 ratio b) If you want to determine what fraction of the total fruit will be apples or oranges then you add the parts of the ratio to determine the total fruit, in this case: 3+4=7 c) The total fruit becomes the common denominator and the parts of the ratio become the numerators, in this case: 3/7 of the fruit are apples and 1/7 are oranges d) The fractions implied in a ratio will always total one whole (or 100% of the fruit), in this case: 3/7 + 4/7 = 7/7 = 1"
Specifically "c) The total fruit becomes the common denominator and the parts of the ratio become the numerators, in this case: 3/7 of the fruit are apples and 1/7 are oranges" I believe the "1/7 are oranges" should read "4/7 are oranges"
24.61.93.51 15:30, 17 March 2007 (UTC)peter
RATIO
A ratio is an ordered finite set of quantities provided two sets are equivalent when their correspondent elements are proportional. For example, <a, b c, d,…> = <A, B, C, D,…> if A=ka, B=kb, C=kc, … for some k≠0. The equality sign is usually used in this case to designate equivalence of the two sets.
The quantities may or may not have units of measurement. Colon is usually used as separator, for example, a:b:c:d:… or A:B:C:D…
Main property of ratios: For any two pairs of corresponding elements, say b, d and B, D, the following equality is held: bD=dB.
Example: An ordered set <5 dogs, 2 houses, 3 apples, 4 oranges> is a ratio if it represents a structure, so that <5 dogs, 2 houses, 3 apples, 4 oranges> = <10 dogs, 4 houses, 6 apples, 8 oranges> = <15 dogs, 6 houses, 9 apples, 12 oranges> = …, where k=2, 3,…, respectively. Using a colon notation, we get 5 dogs : 2 houses : 3 apples : 4 oranges = 10 dogs : 4 houses : 6 apples : 8 oranges = 15 dogs : 6 houses : 9 apples : 12 oranges = … The chain of equalities may be continued further using arbitrary values of k≠0. In this example the main property of ratios leads to the following equalities: 2 houses • 6 apples = 4 houses • 3 apples = 12 apple-houses, 6 apples • 12 oranges = 8 oranges • 12 apples = 72 apple-oranges etc.
Recipes provide good examples of ratios. Thus, a recipe that reads "For serving two persons take 2 pound rabbit, ½ cup flour, 1 tablespoon butter, and 1cup red wine", may be written as the ratio 2 persons : 2 lb : ½ cup : 1 tablespoon : 1 cup. This ratio tells us that depending on the number of persons served, the amounts of each product should be increased or decreased proportionally.
Two-element ratio related to direct variation of two quantities is called a rate. For example, <126 miles, 3 gallons> =126 miles : 3 gallons is a rate of gasoline consumption. A rate with the second element equals to one is called a unit rate. Thus, this example may be written as 126 miles : 3 gallons = 42 miles : 1 gallon, with the latter rate being the unit rate.
Rates and other two-element ratios without units of measurement possess the following property of fractions: they do not change their meaning if their elements are multiplied or divided by any non-zero number. In particular, they may be expressed in lower terms. For example, the following ratios are equivalent: 126:3 = 42:1. Nevertheless, rates or two-element ratios are not fractions, because they do not possess all of the fractions' properties. For instance, ratios cannot be added or subtracted; if we formally add or subtract them as fractions, the result may or may not make sense as a ratio. —Preceding unsigned comment added by Hostosv ( talk • contribs) 01:01, 5 November 2007 (UTC)
ų —Preceding unsigned comment added by 41.242.171.21 ( talk) 11:38, 17 August 2008 (UTC)
Current definition is very bad. It mentions the word proportional which leads to circular definition. Somebody provided a better one above:
The ratio of two numbers of is value of one number in terms of the other, and is expressed as the quotient of their measures. A ratio is a general means of comparing any two numbers in a multiplicative sense.
I believe this one also has an issue, as it defines "ratio of numbers" and isn't it supposed to be a "ratio of quantities" per discussion above? By the way Rate also seems to have a broken lead section, it contradicts this article. Could someone comment or correct? I'm not feeling "bold" enough because of my poor English. -- Kubanczyk 15:25, 11 October 2007 (UTC)
So if you have two ratios, 1:2000 and 1:4000, which one is "higher"? —The preceding unsigned comment was added by 69.157.57.16 ( talk • contribs) .
The article had gotten quite long considering there were no references cited. I've added some older sources on the assumption that there haven't been a lot of changes to the subject in the last hundred years. It will take some time to go through the article section by section to see what needs to be further referenced, what should be deleted as OR, what should be expanded based on the material in the sources, and what is OK as is. I'm leaving the references needed tag until this is all sorted out.-- RDBury ( talk) 21:45, 4 November 2009 (UTC)
Paul Beardsell, what statement do you wish to add (or remove) to the article to explain your understanding of the word "ratio"? -- Robin ( talk) 00:56, 28 December 2009 (UTC)
Lets say I'm dealing in apples and oranges, and I am in debt apples but have a surplus of oranges.
I may have a ratio of (-2 apples / 3 oranges), and a ratio of (-3 apples / 2 oranges). Which is the larger ratio of apples to oranges?
If thought about as a fraction then -2/3 = -.666, and -3/2 = -1.5.
Therefore, -2/3 is a bigger ratio of apples to oranges because it is 'less negative' compared with -1.5.
However, if thought about in absolute terms, there are more apples to oranges in the -3/2 ratio.
Can ratios work with one (or more) parts of the ratio being negative? Or are ratios strictly absolute?
71.142.81.237 08:11, 22 February 2007 (UTC)Dave A
This article needs much work. I've fiddled around with it a bit whilst watching TV, but it needs restructuring. I suggest a brief lead, followed by the simple examples for those who come here wondering what the word means, or how to use the concept, with the technical definitions and philosophy of rationality at the end. What does anyone else think? Thanks to 24.51.192.180 for removing the bit I didn't like but wasn't brave enough to remove, and to Anonymous Dissident for improving my wording. Dbfirs 23:16, 25 January 2010 (UTC)
Thanks to RDBury for improving the article, including removing my heading that turned out to be OR (though I thought when I used it that I could find someone else who called it "Normal Form"). I've restored the content of the paragraph because it can be found in most elementary texts on ratio. Dbfirs 23:24, 23 February 2010 (UTC)
Right now (19:27, 11 January 2010 (UTC)), the article completely seems to lack creferences to commensurability issues. This is a pity; at least, the historical relation between ratios of commensurable entities and rational numbers ought to be explained. IMHO, the explanation of the term "rational" is clearly of encyclopedial interest. JoergenB ( talk) 19:26, 11 January 2010 (UTC)
I find the opening sentences to be somewhat confusing, particularly to a person who is looking for a basic understanding of ratio. The first sentence definition makes sense and serves as an adequate definition of ratio: "In mathematics, a ratio expresses the magnitude of quantities relative to each other." That's clear.
But, the opening goes on: "Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second..." What does that mean? Right now, the graphic example given next to the opening paragraph is a "4:3" ratio. A reader would presumably look over at that example and try to puzzle out the opening. Using the second sentence definition, that means "the ratio of 4 to 3 indicates how many times 4 is contained in 3." What?? The Penny Encyclopedia is cited for this, but I looked at the entry linked at the bottom of the page, and I don't see this idea mentioned prominently. It's a long article, so it might be buried in there somewhere, but in general the source seems to go more with the definition of the first sentence, i.e., a ratio compares the relative magnitude of two things, which means 4:3 is the same as 3:4, it's just the order of the things expressed (width:height vs. height:width) has changed -- so why the focus on which quantity is "contained" in which other quantity?
The opening continues: "and may be expressed algebraically as their quotient." (I don't disagree with this, but it seems to focus on only two-term ratios that represent fractional relationships, which is only one class of ratio -- is that appropriate for a general opening?) And then "Example: For every Spoon of sugar, you need 2 spoons of flour ( 1:2 )" This isn't a very good example for what was just stated (quotient relationships), since expressing this ratio as 1/2 is potentially misleading. In terms of "spoons," there is 1/2 as much sugar as flour, but -- as is clear from some confusion expressed in earlier Talk Page discussion -- this is not the only possible fractional relationship to be derived from such a ratio. If the ratio clearly represented a part-to-whole relationship (as many ratios do, such as "3 students compared to the entire class of 12 students," or 3:12), it would make sense to represent it as a quotient (3/12, or 1/4). In the case of the example provided, however, the application of a quotient as mentioned in the previous sentence is ambiguous. 140.247.240.127 ( talk) 22:08, 19 July 2010 (UTC)
Please clarify the first sentence under Number of Terms to say something like,
"In general, when comparing the quantities of a two-quantity ratio, this can be expressed as a fraction derived from the ratio. For example, in a ratio of 2:3, the amount/size/volume/number of the first quantity will be 2/3 that of the second quantity. This pattern also holds in ratios with more than two terms; however, a ratio with more than two terms cannot be converted into a single fraction, where a single fraction can represent only one part of the ratio."
I'm requesting this clarification because I often find that my students think that ratios are the same thing as fractions. While this is clearly demonstrated in the Fraction and Proportion subheadings, the Number of Terms text muddies and confuses this important distinction.
Thanks
66.245.6.251 ( talk) 02:54, 1 January 2011 (UTC)
Is an expression like "2mg substance per 50 ml water" a ratio? If so, some changes are needed. If not, what is it? 118.107.149.10 ( talk) 01:51, 23 June 2011 (UTC)
In antiquity writers such as Vitruvus went back as far as the historian Herodotus checking for ratios between the unit fractions used up until medieval times for calculation and unit measures and discovered that the body measures which were the basis for Egyptian inscription grids were expanded to the agricultural measures used for Egyptian and Mesopotamian fields, and further expanded into architectural proportions based on structural loads and spans and distance measures such as the surveyed length of a days march or sail. The proportion of foot to remen can be either 4:5 making it the hypotenuse or 3:4 making it the side of a right triangle. If the remen is the hypotenuse of a 3:4:5 triangle then the foot is one side and the quarter another so the proportions are 3:4 quarter to foot, 4:5 foot to remen and 3:5 quarter to Remen. The quarter is 1/4 yard. The foot is 1/3 yard. The remen is
The remen may also be the side of a square whose diagonal is a cubit The proportion of remen to cubit is 4:5
The table below demonstrates a harmonious system of proportion much like the musical scales, with fourths and fifths, and other scales based on geometric divisions, diameters, circumferences, diagonals, powers, and series coordinated with the canons of architectural proportion, Pi, phi and other constants..
In Mesopotamia and Egypt the Remen could be divided into different proportions as a similar triangle with sides as fingers, palms, or hands. The Egyptians thought of the Remen as proportionate to the cubit or mh foot and palm.
They used it as the diagonal of a unit rise or run like a modern framing square. Their related seked gives a slope. Its convenient to think of remen as intermediate to both large and small scale elements.
Even before the Greeks like Solon, Herodotus, Pythagorus, Plato, Ptolomy, Aristotle, Eratosthenes, and the Romans like Vitruvius, there seems to be a concept that all things should be related to one another proportionally.
Its not certain whether the ideas of proportionality begin with studies of the elements of the body as they relate to scaling architecture to the needs of humans, or the divisions of urban planning laying out cities and fields to the needs of surveyors.
In all cultures the canons of proportion are proportional to reproducable standards.
In ancient cultures the standards are divisions of a degree of the earths circumference into mia chillioi, mille passus, and stadia.
Stadia, are used to lay out city blocks, roads, large public buildings and fields
Fields are divided into acres using as their sides, furlongs, perches, cords, rods, fathoms, paces, yards, cubits, and remen which are proportional to miles and stadia
Buildings are divided into feet, hands, palms and fingers, which are also systematized to the sides of agricultural units.
Inside buildings the elements of the architectural design follow the canons of proportion of the the inscription grids based on body measures and the orders of architectural components.
In manufacturing the same unit fraction proportions are systematized to the length and width of boards, cloth and manufactured goods.
The unit fractions used are generally the best sexigesimal factors, three quarters, halves, 3rds, fourths, fifths, sixths, sevenths, eighths, tenths, unidecimals, sixteenths and their inverses used as a doubling system
Greek Remen generally have long, median and short forms with their sides related geometrically as arithmetric or geometric series based on hands and feet.
Roman Remen generally have long, and short forms with their sides related geometrically as arithmetric or geometric series based on fingers palms and feet.
By Roman times the Remen is standardized as the diagonal of a 3:4:5 triangle with one side a palmus and another a pes. The Remen and similar forms of sacred geometry formed the basis of the later system of Roman architectural proportions as described by Vitruvius.
Generally the sexagesimal (base-six) or decimal (base-ten) multiples have Mesopotamian origins while the septenary (base-seven) multiples have Egyptian origins.
Unit | Finger | Culture | Metric | Palm | Hand | Foot | Remen | Pace | Fathom |
---|---|---|---|---|---|---|---|---|---|
(1 ŝuŝi | 1 (little finger) | Mesop | 14.49 mm | .2 | 0.067 | 0.05 | |||
1 ŝushi | 1 (ring finger) | Mesop | 16.67 mm | .2 | 0.67 | 0.05 | |||
1 shushi | 1 (ring finger) | Mesop | 17 mm | .2 | 0.67 | 0.05 | |||
1 digitus | 1 (long finger) | Roman | 18.5 mm | .25 | 0.0625 | 0.04 | |||
1 dj | 1 (long finger) | Egyptian | 18.75 mm | .25 | 0.0625 | 0.04 | |||
1 daktylos | 1 (index finger) | Greek | 19.275 mm | .2 | 0.067 | 0.04 | |||
1 uban | 1 (index finger) | Mesop | .2 | .2 | 0.067 | 0.04 | |||
1 finger | 1 (index finger) | Old English | 20.32 mm | .2 | 0.067 | 0.045 | |||
1 inch | (thumb) | English | 25.4 mm | 0.083 | .067 | ||||
1 uncia | (thumb or inch) | Roman | 24.7 mm | .25 | 0.083 | .067 | |||
1 condylos | 2 (daktylos) | Greek | 38.55 mm | .5 | 2 | .1 | |||
1 palaiste, palm | 4 (daktylos) | Greek | 77.1 mm | 1 | 0.25 | .2 | |||
1 palaistos, hand | 5 (daktylos) | Greek | 96.375 mm | 1 | 0.333 | .25 | |||
1 hand | 5 (fingers) | English | 101.6mm | 1 | 0.333 | .25 | |||
1 dichas, | 8 (daktylos) | Greek | 154.2 mm | 2 | 0.5 | .4 | |||
1 spithame | 12 (daktylos) | Greek | 231.3 mm | 3 | .75 | .6 | |||
1 pous, foot of 4 palms | 16 (daktylos) | Ionian Greek | 296 mm | 4 | 1 | .8 | |||
1 pes, foot | 16 (digitus) | Roman | 296.4 mm | 4 | 1 | .8 | |||
1 uban, foot | 15 (uban) | Mesop | 300 mm | 3 | 1 | .75 | |||
1 bd, foot | 16 (dj) | Egyptian | 300 mm | 4 | 1 | .8 | |||
1 foote(3 hands) | 15 (fingers) | Old English | 304.8 mm | 3 | 1 | .75 | |||
1 foot, (12 inches) | 16 (inches) | English | 308.4 mm | 3 | 1 | .75 | |||
1 pous, foot of 4 palms | 16 (daktylos) | Attic Greek | 308.4 mm | 4 | 1 | .8 | |||
1 pous, foot of 3 hands | 15 (daktylos) | Athenian Greek | 316 mm | 4 | 1 | .8 | |||
1 pygon, remen | 20 (daktylos) | Greek | 385.5 mm | 5 | 1.25 | 1.25 | 1 | ||
1 pechya, cubit | 24 (daktylos) | Greek | 462.6 mm | 6 | 1.5 | 1.1 | |||
1 cubit of 17.6" 6 palms | 25 (fingers) | Egyptian | 450 mm | 6 | 1.5 | 1.3 | |||
1 cubit of 19.2" 5 hands | 25 (fingers) | English | 480 mm | 5 | 1.62 | 1.3 | |||
1 mh royal cubit | 28 (dj) | Egyptian | 525 mm | 7 | 2.33 | 1.4 | |||
1 bema | 40 (daktylos) | Greek | 771 mm | 10 | 2.5 | 2 | |||
1 yard | 48 (finger) | English | 975.36 mm | 12 | 3 | 2.4 | |||
1 xylon | 72 (daktylos) | Greek | 1.3878 m | 18 | 4.55 | 3.64 | |||
1 passus pace | 80 (digitus) | Roman | 1.542 m | 20 | 5 | 4 | 1 | ||
1 orguia | 96 (daktylos) | Greek | 1.8504 m | 24 | 6 | 5 | 1 | ||
1 akaina | 160 (daktylos) | Greek | 3.084 m | 40 | 10 | 8 | 2 | ||
1 English rod | 264 (fingers) | English | 5.365 m | 66 | 16.5 | 13.2 | 1 | ||
1 hayt | 280 (dj) | Egyptian | 5.397 m | 70 | 17.5 | 14 | 3 | ||
1 perch | 1,056 (fingers) | English | 20.3544 m | 264 | 66 | 53.4 | 11 | ||
1 plethron | 1,600 (daktylos) | Greek | 30.84 m | 400 | 100 | 80 | 20 | ||
1 actus | 1,920 (digitus) | Roman | 37.008 m | 480 | 120 | 96 | 24 | 20 | |
khet side of 100 royal cubits | 2,800 (dj) | Egyptian | 53.97 m | 700 | 175 | 140 | 35 | ||
iku side | 3,600 (ŝushi) | Mesop | 60m | 720 | 240 | 180 | 48 | 40 | |
acre side | 3,333 (daktylos) | English | 64.359 m | 835 | 208.71 | 168.9 | |||
1 stade of Eratosthenes | 8,400 (dj) | Egyptian | 157.5 m | 2100 | 525 | 420 | 84 | 70 | |
1 stade | 8,100 (shushi) | Persian | 162 m | 2700 | 900 | 525 | 85 | ||
1 minute | 9,600 (daktylos) | Egyptian | 180 m | 2400 | 600 | 480 | 96 | 80 | |
1 stadion 600 pous | 9,600 (daktylos) | Greek | 185 m | 2400 | 600 | 480 | 96 | 80 | |
1 stadium625 pes | 9,600 (daktylos) | Roman | 185 m | 2400 | 625 | 500 | 100 | ||
1 furlong 625 pes | 10,000 (digitus) | Roman | 185.0 m | 2640 | 660 | 528 | 132 | 88 | |
1 furlong 600 pous | 9900 (daktylos) | English | 185.0 m | 1980 | 660 | 528 | 132 | 88 | |
1 Olympic Stadion 600 pous | 10,000 (daktylos) | Greek | 192.8 m | 2500 | 625 | 500 | 100 | ||
1 furlong 625 fote | 10,000(fingers) | Old English | 203.2 m | 2500 | 635 | 500 | 100 | ||
1 stade | 11,520 (daktylos) | Persian | 222 m | 2880 | 720 | 576 | 144 | 120 | |
1 cable | 11,520 (daktylos) | English | 222 m | 2880 | 720 | 576 | 144 | 120 | |
1 furlong 660 feet | 10,560 (inches) | English | 268.2 m | 2640 | 660 | 528 | 132 | 110 | |
1 diaulos | 19,200 (daktylos) | Greek | 370 m | 4800 | 1,200 | 960 | 192 | 160 | |
1 English myle | 75,000(fingers) | Old English | 1.524 km | 15000 | 5,000 | 4000 | 800 | ||
1 mia chilioi | 80,000 (daktylos) | Greek | 1.628352 km | 20,000 | 5,000 | 1000 | |||
1 mile | 84,480 (fingers) | English | 1.628352 km | 21,120 | 5,280 | 4224 | 1056 | 880 | |
1 dolichos | 115,200 (daktylos) | Greek | 2.22 km | 28,800 | 7,200 | 5760 | 4800 | ||
1 stadia of Xenophon | 280,000 (daktylos) | Greek | 5.397 km | 70,000 | 17,500 | 1400 | 3500 | ||
1/10 degree | 560,000 (daktylos) | Greek | 10.797 km | 140,000 | 35,000 | 2800 | 7000 | ||
1 schϓnus | 576,000 (daktylos)Z | Greek | 11.1 km | 144,000 | 36,000 | 288000 | 28800 | 24000 | |
1 stathmos | 1,280,000 (daktylos) | Greek | 24.672 km | 320,000 | 80,000 | 64000 | 16000 | ||
1 degree | 5,760,000 (digitus) | Roman | 111 km | 1,440,000 | 360,000 | 288000 | 72000 | 60000 |
For variant, the stadion at Olympia measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as short as 157.5 m up to 222 m, but it is usually stated as 185 m.
The Greek root stadios means 'to have standing'. Stadions are used to measure the sides of fields.
In the time of Herodotus, the standard Attic stadion used for distance measure is 600 pous of 308.4 mm equal to 185 m. so that 600 stadia equal one degree and are combined at 8 to a mia chilioi or thousand which measures the boustredon or path of yoked oxen as a distance of a thousand orguia, taken as one orguia wide which defines an aroura or thousand of land and at 10 agros or chains equal to one nautical mile of 1850 m.
Several centuries later, Marinus and Ptolemy used 500 stadia to a degree, but their stadia were composed of 600 Remen of 370 mm and measured 222 m, so the measuRement of the degree was the same.
The same is also true for Eratosthenes, who used 700 stadia of 157.5 m or 300 Egyptian royal cubits to a degree, and for Aristotle, Posidonius, and Archimedes, whose stadia likewise measured the same degree.
The 1771 Encyclopædia Britannica mentions a measure named acæna which was a rod ten (Greek) feet long used in measuring land. — Preceding unsigned comment added by 142.0.102.117 ( talk) 20:48, 18 May 2014 (UTC)
Another question. So a ratio can never be expressed as a percentage? —The preceding unsigned comment was added by 202.4.4.48 ( talk • contribs) .
I think that a ratio is always 100% of everything you are talking about. For example, if you have a 2:1 ratio of apples to oranges then two thirds or approximately 67% of your fruit are apples and one third or 33% are oranges, for a total of 100% or three thirds.-- Dwetherow 05:18, 23 February 2007 (UTC)
Maps present another interesting example. A map ratio of 1:100 sensibly presented as a percentage would be 1%. Meaning a distance on the map is 1% of the distance in the real world. It makes no sense to add the distance on the map to the distance in the real world, and use this combined 'real' and 'virtual' distance in any calculation. —Preceding unsigned comment added by 89.242.145.251 ( talk) 17:43, 14 February 2010 (UTC)
The article begins by declaring a ratio to be a linear relationship. What about, say, the ratio of a square's perimeter to its area? That's nonlinear; is it a ratio? --VP 38.113.17.3 21:41, 17 April 2006 (UTC)
in which case they become non linear since they are exponential. Further you can change the rate of increase at an increasing rate over time introducing a fourth dimension. The ancient problems of squaring a circle, doubling a cube and trisecting an angle were solvable so long as you didn't add constraints such as limiting their construction to ruler and compass. 142.0.102.93 ( talk) 19:04, 23 May 2014 (UTC)
I have some confusion over ratios and fractions - In the opening statement, the example 2:3 is used and is described as a whole consisting of 5 parts. In the first example, the ratio 1:4 refers to four parts in the whole. Which is the correct description of a ratio? This has always confused me. Stating the question in other terms - if I have a solution consisting of 1 part X and 3 parts Y, do I describe the ratio as 1:3 or 1:4? —Preceding unsigned comment added by 67.161.203.22 ( talk • contribs)
I'm a HS teacher, and have always taught that fractions are synonymous with ratios; that the ratio 2:3, for example, is the quotient of 2 divided by 3 or 2/3. Under this interpretation, a ratio would be "a fraction turned on its side." This is in many textbooks, for example Dolciani "Algebra-Structure and Method." I'd be interested in seeing a reference with an alternative interpretation, making 1/2 not equal to 1:2. While on the subject: Dolciani defines a proportion as "an equation that states that two ratios are equal." So, 2:3 = 4:6 would be a proportion. Splendiff 23:42, 6 June 2007 (UTC)
The ratio of two numbers of is value of one number in terms of the other, and is expressed as the quotient of their measures. A ratio is a general means of comparing any two numbers in a multiplicative sense.
Rather than thinking of a ratio as a special case of a fraction, think of the ratio as the way numbers were compared in a multiplicative sense, before fractions assumed their full power.Ratios are more flexible than fractions, because they can be used to compare part to part, such as often used in chemistry or maths (like a 3:4:5 triangle), or part to whole, as in a fraction. The techniques for manipulating fractions are much more powerful though (I don't think I've ever tried to add dissimilar ratios), so we use fractions most of the time now. Trishm 04:53, 18 June 2007 (UTC)
The example given under concentration not only makes no sense, it's incorrect. 1:5 means 1 part TO 5 parts (i.e. 1 part of X added to 5 parts Y) and should not be confused with 1 in 5 (which means 1 part in 5 parts TOTAL). The same is true for smaller ratios such as 1:100 which is not the same as 1% but actually, in terms of concentration, refers to 1 part added to 100 parts which equates to 0.91%. An easy way to understand it is to look at a 1:1 mixture. Using Splendiff's explanation above, this would be equivalent to 1/1 or 100%. When in fact it represents a 50% mixture of one component in the other or 1/2. I'm not sure how they teach these concepts in high school, but I teach it this way to our pharmacy students - and we're pretty picky with life-threatening concentration calculations. PharmaG ( talk) 14:03, 15 July 2010 (UTC)
Hi there,
I am confused the following line in the article "There is often confusion between dilution ratio (1:n meaning 1 part solute to n parts solvent) and dilution factor (1:n+1) where the second number (n+1) represents the total volume of solute + solvent. "
I thought n was already solute + solvent as the example (1mL+4mL water = 5 has shown). That line just adds more confusion. About the difference between dilution ratio and dilution factor; here is what I know. When in biology, we are ask to prepare a 1:100 dilution - I assume that this is the Dilution Ratio The Dilution Factor - for me, it is the 100 above. So if I write 1:a dilution ratio, then a is the dilution factor. For example, a 7.56 M of acid following a 1:100 dilution ratio, the answer would be .0756M which is easily obtained by having 7.56/100 where the denominator is the dilution factor. Of course one may argue that the same result can be obtain by having the stock concentration * Dilution ratio. Essentially, we are adding 1mL of acid + 99 mL of water to dilute the acid.
Would like an academic to review my workings. Flowright138 (talk) (contributions) 10:28, 14 March 2012 (UTC)
::Now the acidity of the oceans may be affected by the levels of atmospheric carbon in the greenhouse gas emissions so that's another factor to take into account, also winds tend to pile the seas up in the direction of the prevailing wind and relieve them in the opposite direction but weather events such as el Nino can reverse the prevailing winds affecting sea levels. Also surface water near land is attracted more strongly gravitationally than surface water over great depths. The dilution ratio thus has to take into account state, relative frozen or liquid height when floating, temperature, pressure,gravitational attraction, acidity, lateral loading from wind and all of these factors become variables in your dilution ratio equation. Given a body of water the size of the earths oceans its probably also necessary to consider the relative humidity of that portion of the water which is in suspension in the atmosphere, and perhaps also tidal forces.Your formula will eventually have as many or more variables than the computation of seismic forces caused by the changed loading on the mantle.
Metaphysical Engineering (
talk)
19:17, 26 May 2014 (UTC)
Is a 3-4-5 triangle a ratio? Are the number of terms limited to two, or does that merely define the dimension of the ratio? Are irrational numbers such as Pi and Phi legitimate ratios where they aren't defined by whole numbers but rather the ratio of a circles radius to its circumference. Can anything expressible as a fraction be considered a ratio? How about continuous fractions? Are they ratios? — Preceding unsigned comment added by 142.0.102.9 ( talk) 16:40, 5 June 2014 (UTC)
142.0.102.55 ( talk) 18:41, 6 July 2015 (UTC)
MostSome members in
Category:Engineering ratios are not
dimensionless, e.g.,
Carrier to noise density ratio.
Fgnievinski (
talk)
06:52, 21 July 2015 (UTC)
A different though related problem is Category:Statistical ratios, which contains many "rates" that are clearly not dimensionless and not even named ratios (contrary to the misleading engineering ratio above). Fgnievinski ( talk) 03:03, 22 July 2015 (UTC)
Two sources: Fgnievinski ( talk) 05:17, 22 July 2015 (UTC)
Another quote: "Ratio as a Rate. The first type [of ratio] defined by Freudenthal, above, is known as rate, and illustrates a comparison between two variables with difference units. (...) A ratio of this sort produces a unique, new concept with its own entity, and this new concept is usually not considered a ratio, per se, but a rate or density.", "Ratio and Proportion: Research and Teaching in Mathematics Teachers" [3]. Fgnievinski ( talk) 05:48, 22 July 2015 (UTC)
So ratios are not necessarily dimensionless; non-dimensionless ratios are called rates; and dimensionless ratios are... proportions/scales? Fgnievinski ( talk) 06:06, 22 July 2015 (UTC)
::::::Ratio should remain a broad concept article, but I have no objection to having sections within the article addressing things like geometry, numerical analysis, arithmetic and geometric sequences, dimensionality where for example we might discuss a rate that changes over time, or whose properties change at some nano scale
Metaphysical Engineering (
talk)
00:54, 28 July 2015 (UTC)
Just to explain why 2 edits have been struck. Doug Weller ( talk) 13:31, 30 July 2015 (UTC)
While the statements made in a recent edit concerning expressing ratios as decimal fractions are certainly mathematically correct, I question whether this is actually done in practice (for instance, you never see the aspect ratio of a TV screen expressed as 1.3333...). It is possible that this is a cultural difference and that such expressions are more common in different parts of the world. If this is the case, it should be brought up on this talk page so that we can decide how best to put that information in the article. I reverted the edit so that a discussion of its intent could take place here. Bill Cherowitzo ( talk) 04:40, 27 September 2015 (UTC)
I feel like the 4:3 image at the top of the page is unclear. Which of the rectangles in that image is 4:3? The inner one or the outer one? Margalob ( talk) 22:21, 5 June 2016 (UTC)
If you were drawing a map and were using the ratio 1cm:20km how many cm would 22km be? 1.1? —The preceding unsigned comment was added by 81.178.228.183 ( talk • contribs) .
someone added the word 'chicken' to the start of the page. it wasn't in context and i assume it was a mistake so i removed it. if you're terribly fond of chickens and find this edit to be offensive, i apologize.
gba 05:11, 12 February 2007 (UTC)
I'm sorry. I don't edit and don't know what the standards are involved. I just wanted to point out something I think needs correction:
Under: Ratios and fractions
"a) If you have three apples for every four oranges then you have a 3:4 ratio b) If you want to determine what fraction of the total fruit will be apples or oranges then you add the parts of the ratio to determine the total fruit, in this case: 3+4=7 c) The total fruit becomes the common denominator and the parts of the ratio become the numerators, in this case: 3/7 of the fruit are apples and 1/7 are oranges d) The fractions implied in a ratio will always total one whole (or 100% of the fruit), in this case: 3/7 + 4/7 = 7/7 = 1"
Specifically "c) The total fruit becomes the common denominator and the parts of the ratio become the numerators, in this case: 3/7 of the fruit are apples and 1/7 are oranges" I believe the "1/7 are oranges" should read "4/7 are oranges"
24.61.93.51 15:30, 17 March 2007 (UTC)peter
RATIO
A ratio is an ordered finite set of quantities provided two sets are equivalent when their correspondent elements are proportional. For example, <a, b c, d,…> = <A, B, C, D,…> if A=ka, B=kb, C=kc, … for some k≠0. The equality sign is usually used in this case to designate equivalence of the two sets.
The quantities may or may not have units of measurement. Colon is usually used as separator, for example, a:b:c:d:… or A:B:C:D…
Main property of ratios: For any two pairs of corresponding elements, say b, d and B, D, the following equality is held: bD=dB.
Example: An ordered set <5 dogs, 2 houses, 3 apples, 4 oranges> is a ratio if it represents a structure, so that <5 dogs, 2 houses, 3 apples, 4 oranges> = <10 dogs, 4 houses, 6 apples, 8 oranges> = <15 dogs, 6 houses, 9 apples, 12 oranges> = …, where k=2, 3,…, respectively. Using a colon notation, we get 5 dogs : 2 houses : 3 apples : 4 oranges = 10 dogs : 4 houses : 6 apples : 8 oranges = 15 dogs : 6 houses : 9 apples : 12 oranges = … The chain of equalities may be continued further using arbitrary values of k≠0. In this example the main property of ratios leads to the following equalities: 2 houses • 6 apples = 4 houses • 3 apples = 12 apple-houses, 6 apples • 12 oranges = 8 oranges • 12 apples = 72 apple-oranges etc.
Recipes provide good examples of ratios. Thus, a recipe that reads "For serving two persons take 2 pound rabbit, ½ cup flour, 1 tablespoon butter, and 1cup red wine", may be written as the ratio 2 persons : 2 lb : ½ cup : 1 tablespoon : 1 cup. This ratio tells us that depending on the number of persons served, the amounts of each product should be increased or decreased proportionally.
Two-element ratio related to direct variation of two quantities is called a rate. For example, <126 miles, 3 gallons> =126 miles : 3 gallons is a rate of gasoline consumption. A rate with the second element equals to one is called a unit rate. Thus, this example may be written as 126 miles : 3 gallons = 42 miles : 1 gallon, with the latter rate being the unit rate.
Rates and other two-element ratios without units of measurement possess the following property of fractions: they do not change their meaning if their elements are multiplied or divided by any non-zero number. In particular, they may be expressed in lower terms. For example, the following ratios are equivalent: 126:3 = 42:1. Nevertheless, rates or two-element ratios are not fractions, because they do not possess all of the fractions' properties. For instance, ratios cannot be added or subtracted; if we formally add or subtract them as fractions, the result may or may not make sense as a ratio. —Preceding unsigned comment added by Hostosv ( talk • contribs) 01:01, 5 November 2007 (UTC)
ų —Preceding unsigned comment added by 41.242.171.21 ( talk) 11:38, 17 August 2008 (UTC)
Current definition is very bad. It mentions the word proportional which leads to circular definition. Somebody provided a better one above:
The ratio of two numbers of is value of one number in terms of the other, and is expressed as the quotient of their measures. A ratio is a general means of comparing any two numbers in a multiplicative sense.
I believe this one also has an issue, as it defines "ratio of numbers" and isn't it supposed to be a "ratio of quantities" per discussion above? By the way Rate also seems to have a broken lead section, it contradicts this article. Could someone comment or correct? I'm not feeling "bold" enough because of my poor English. -- Kubanczyk 15:25, 11 October 2007 (UTC)
So if you have two ratios, 1:2000 and 1:4000, which one is "higher"? —The preceding unsigned comment was added by 69.157.57.16 ( talk • contribs) .
The article had gotten quite long considering there were no references cited. I've added some older sources on the assumption that there haven't been a lot of changes to the subject in the last hundred years. It will take some time to go through the article section by section to see what needs to be further referenced, what should be deleted as OR, what should be expanded based on the material in the sources, and what is OK as is. I'm leaving the references needed tag until this is all sorted out.-- RDBury ( talk) 21:45, 4 November 2009 (UTC)
Paul Beardsell, what statement do you wish to add (or remove) to the article to explain your understanding of the word "ratio"? -- Robin ( talk) 00:56, 28 December 2009 (UTC)
Lets say I'm dealing in apples and oranges, and I am in debt apples but have a surplus of oranges.
I may have a ratio of (-2 apples / 3 oranges), and a ratio of (-3 apples / 2 oranges). Which is the larger ratio of apples to oranges?
If thought about as a fraction then -2/3 = -.666, and -3/2 = -1.5.
Therefore, -2/3 is a bigger ratio of apples to oranges because it is 'less negative' compared with -1.5.
However, if thought about in absolute terms, there are more apples to oranges in the -3/2 ratio.
Can ratios work with one (or more) parts of the ratio being negative? Or are ratios strictly absolute?
71.142.81.237 08:11, 22 February 2007 (UTC)Dave A
This article needs much work. I've fiddled around with it a bit whilst watching TV, but it needs restructuring. I suggest a brief lead, followed by the simple examples for those who come here wondering what the word means, or how to use the concept, with the technical definitions and philosophy of rationality at the end. What does anyone else think? Thanks to 24.51.192.180 for removing the bit I didn't like but wasn't brave enough to remove, and to Anonymous Dissident for improving my wording. Dbfirs 23:16, 25 January 2010 (UTC)
Thanks to RDBury for improving the article, including removing my heading that turned out to be OR (though I thought when I used it that I could find someone else who called it "Normal Form"). I've restored the content of the paragraph because it can be found in most elementary texts on ratio. Dbfirs 23:24, 23 February 2010 (UTC)
Right now (19:27, 11 January 2010 (UTC)), the article completely seems to lack creferences to commensurability issues. This is a pity; at least, the historical relation between ratios of commensurable entities and rational numbers ought to be explained. IMHO, the explanation of the term "rational" is clearly of encyclopedial interest. JoergenB ( talk) 19:26, 11 January 2010 (UTC)
I find the opening sentences to be somewhat confusing, particularly to a person who is looking for a basic understanding of ratio. The first sentence definition makes sense and serves as an adequate definition of ratio: "In mathematics, a ratio expresses the magnitude of quantities relative to each other." That's clear.
But, the opening goes on: "Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second..." What does that mean? Right now, the graphic example given next to the opening paragraph is a "4:3" ratio. A reader would presumably look over at that example and try to puzzle out the opening. Using the second sentence definition, that means "the ratio of 4 to 3 indicates how many times 4 is contained in 3." What?? The Penny Encyclopedia is cited for this, but I looked at the entry linked at the bottom of the page, and I don't see this idea mentioned prominently. It's a long article, so it might be buried in there somewhere, but in general the source seems to go more with the definition of the first sentence, i.e., a ratio compares the relative magnitude of two things, which means 4:3 is the same as 3:4, it's just the order of the things expressed (width:height vs. height:width) has changed -- so why the focus on which quantity is "contained" in which other quantity?
The opening continues: "and may be expressed algebraically as their quotient." (I don't disagree with this, but it seems to focus on only two-term ratios that represent fractional relationships, which is only one class of ratio -- is that appropriate for a general opening?) And then "Example: For every Spoon of sugar, you need 2 spoons of flour ( 1:2 )" This isn't a very good example for what was just stated (quotient relationships), since expressing this ratio as 1/2 is potentially misleading. In terms of "spoons," there is 1/2 as much sugar as flour, but -- as is clear from some confusion expressed in earlier Talk Page discussion -- this is not the only possible fractional relationship to be derived from such a ratio. If the ratio clearly represented a part-to-whole relationship (as many ratios do, such as "3 students compared to the entire class of 12 students," or 3:12), it would make sense to represent it as a quotient (3/12, or 1/4). In the case of the example provided, however, the application of a quotient as mentioned in the previous sentence is ambiguous. 140.247.240.127 ( talk) 22:08, 19 July 2010 (UTC)
Please clarify the first sentence under Number of Terms to say something like,
"In general, when comparing the quantities of a two-quantity ratio, this can be expressed as a fraction derived from the ratio. For example, in a ratio of 2:3, the amount/size/volume/number of the first quantity will be 2/3 that of the second quantity. This pattern also holds in ratios with more than two terms; however, a ratio with more than two terms cannot be converted into a single fraction, where a single fraction can represent only one part of the ratio."
I'm requesting this clarification because I often find that my students think that ratios are the same thing as fractions. While this is clearly demonstrated in the Fraction and Proportion subheadings, the Number of Terms text muddies and confuses this important distinction.
Thanks
66.245.6.251 ( talk) 02:54, 1 January 2011 (UTC)
Is an expression like "2mg substance per 50 ml water" a ratio? If so, some changes are needed. If not, what is it? 118.107.149.10 ( talk) 01:51, 23 June 2011 (UTC)
In antiquity writers such as Vitruvus went back as far as the historian Herodotus checking for ratios between the unit fractions used up until medieval times for calculation and unit measures and discovered that the body measures which were the basis for Egyptian inscription grids were expanded to the agricultural measures used for Egyptian and Mesopotamian fields, and further expanded into architectural proportions based on structural loads and spans and distance measures such as the surveyed length of a days march or sail. The proportion of foot to remen can be either 4:5 making it the hypotenuse or 3:4 making it the side of a right triangle. If the remen is the hypotenuse of a 3:4:5 triangle then the foot is one side and the quarter another so the proportions are 3:4 quarter to foot, 4:5 foot to remen and 3:5 quarter to Remen. The quarter is 1/4 yard. The foot is 1/3 yard. The remen is
The remen may also be the side of a square whose diagonal is a cubit The proportion of remen to cubit is 4:5
The table below demonstrates a harmonious system of proportion much like the musical scales, with fourths and fifths, and other scales based on geometric divisions, diameters, circumferences, diagonals, powers, and series coordinated with the canons of architectural proportion, Pi, phi and other constants..
In Mesopotamia and Egypt the Remen could be divided into different proportions as a similar triangle with sides as fingers, palms, or hands. The Egyptians thought of the Remen as proportionate to the cubit or mh foot and palm.
They used it as the diagonal of a unit rise or run like a modern framing square. Their related seked gives a slope. Its convenient to think of remen as intermediate to both large and small scale elements.
Even before the Greeks like Solon, Herodotus, Pythagorus, Plato, Ptolomy, Aristotle, Eratosthenes, and the Romans like Vitruvius, there seems to be a concept that all things should be related to one another proportionally.
Its not certain whether the ideas of proportionality begin with studies of the elements of the body as they relate to scaling architecture to the needs of humans, or the divisions of urban planning laying out cities and fields to the needs of surveyors.
In all cultures the canons of proportion are proportional to reproducable standards.
In ancient cultures the standards are divisions of a degree of the earths circumference into mia chillioi, mille passus, and stadia.
Stadia, are used to lay out city blocks, roads, large public buildings and fields
Fields are divided into acres using as their sides, furlongs, perches, cords, rods, fathoms, paces, yards, cubits, and remen which are proportional to miles and stadia
Buildings are divided into feet, hands, palms and fingers, which are also systematized to the sides of agricultural units.
Inside buildings the elements of the architectural design follow the canons of proportion of the the inscription grids based on body measures and the orders of architectural components.
In manufacturing the same unit fraction proportions are systematized to the length and width of boards, cloth and manufactured goods.
The unit fractions used are generally the best sexigesimal factors, three quarters, halves, 3rds, fourths, fifths, sixths, sevenths, eighths, tenths, unidecimals, sixteenths and their inverses used as a doubling system
Greek Remen generally have long, median and short forms with their sides related geometrically as arithmetric or geometric series based on hands and feet.
Roman Remen generally have long, and short forms with their sides related geometrically as arithmetric or geometric series based on fingers palms and feet.
By Roman times the Remen is standardized as the diagonal of a 3:4:5 triangle with one side a palmus and another a pes. The Remen and similar forms of sacred geometry formed the basis of the later system of Roman architectural proportions as described by Vitruvius.
Generally the sexagesimal (base-six) or decimal (base-ten) multiples have Mesopotamian origins while the septenary (base-seven) multiples have Egyptian origins.
Unit | Finger | Culture | Metric | Palm | Hand | Foot | Remen | Pace | Fathom |
---|---|---|---|---|---|---|---|---|---|
(1 ŝuŝi | 1 (little finger) | Mesop | 14.49 mm | .2 | 0.067 | 0.05 | |||
1 ŝushi | 1 (ring finger) | Mesop | 16.67 mm | .2 | 0.67 | 0.05 | |||
1 shushi | 1 (ring finger) | Mesop | 17 mm | .2 | 0.67 | 0.05 | |||
1 digitus | 1 (long finger) | Roman | 18.5 mm | .25 | 0.0625 | 0.04 | |||
1 dj | 1 (long finger) | Egyptian | 18.75 mm | .25 | 0.0625 | 0.04 | |||
1 daktylos | 1 (index finger) | Greek | 19.275 mm | .2 | 0.067 | 0.04 | |||
1 uban | 1 (index finger) | Mesop | .2 | .2 | 0.067 | 0.04 | |||
1 finger | 1 (index finger) | Old English | 20.32 mm | .2 | 0.067 | 0.045 | |||
1 inch | (thumb) | English | 25.4 mm | 0.083 | .067 | ||||
1 uncia | (thumb or inch) | Roman | 24.7 mm | .25 | 0.083 | .067 | |||
1 condylos | 2 (daktylos) | Greek | 38.55 mm | .5 | 2 | .1 | |||
1 palaiste, palm | 4 (daktylos) | Greek | 77.1 mm | 1 | 0.25 | .2 | |||
1 palaistos, hand | 5 (daktylos) | Greek | 96.375 mm | 1 | 0.333 | .25 | |||
1 hand | 5 (fingers) | English | 101.6mm | 1 | 0.333 | .25 | |||
1 dichas, | 8 (daktylos) | Greek | 154.2 mm | 2 | 0.5 | .4 | |||
1 spithame | 12 (daktylos) | Greek | 231.3 mm | 3 | .75 | .6 | |||
1 pous, foot of 4 palms | 16 (daktylos) | Ionian Greek | 296 mm | 4 | 1 | .8 | |||
1 pes, foot | 16 (digitus) | Roman | 296.4 mm | 4 | 1 | .8 | |||
1 uban, foot | 15 (uban) | Mesop | 300 mm | 3 | 1 | .75 | |||
1 bd, foot | 16 (dj) | Egyptian | 300 mm | 4 | 1 | .8 | |||
1 foote(3 hands) | 15 (fingers) | Old English | 304.8 mm | 3 | 1 | .75 | |||
1 foot, (12 inches) | 16 (inches) | English | 308.4 mm | 3 | 1 | .75 | |||
1 pous, foot of 4 palms | 16 (daktylos) | Attic Greek | 308.4 mm | 4 | 1 | .8 | |||
1 pous, foot of 3 hands | 15 (daktylos) | Athenian Greek | 316 mm | 4 | 1 | .8 | |||
1 pygon, remen | 20 (daktylos) | Greek | 385.5 mm | 5 | 1.25 | 1.25 | 1 | ||
1 pechya, cubit | 24 (daktylos) | Greek | 462.6 mm | 6 | 1.5 | 1.1 | |||
1 cubit of 17.6" 6 palms | 25 (fingers) | Egyptian | 450 mm | 6 | 1.5 | 1.3 | |||
1 cubit of 19.2" 5 hands | 25 (fingers) | English | 480 mm | 5 | 1.62 | 1.3 | |||
1 mh royal cubit | 28 (dj) | Egyptian | 525 mm | 7 | 2.33 | 1.4 | |||
1 bema | 40 (daktylos) | Greek | 771 mm | 10 | 2.5 | 2 | |||
1 yard | 48 (finger) | English | 975.36 mm | 12 | 3 | 2.4 | |||
1 xylon | 72 (daktylos) | Greek | 1.3878 m | 18 | 4.55 | 3.64 | |||
1 passus pace | 80 (digitus) | Roman | 1.542 m | 20 | 5 | 4 | 1 | ||
1 orguia | 96 (daktylos) | Greek | 1.8504 m | 24 | 6 | 5 | 1 | ||
1 akaina | 160 (daktylos) | Greek | 3.084 m | 40 | 10 | 8 | 2 | ||
1 English rod | 264 (fingers) | English | 5.365 m | 66 | 16.5 | 13.2 | 1 | ||
1 hayt | 280 (dj) | Egyptian | 5.397 m | 70 | 17.5 | 14 | 3 | ||
1 perch | 1,056 (fingers) | English | 20.3544 m | 264 | 66 | 53.4 | 11 | ||
1 plethron | 1,600 (daktylos) | Greek | 30.84 m | 400 | 100 | 80 | 20 | ||
1 actus | 1,920 (digitus) | Roman | 37.008 m | 480 | 120 | 96 | 24 | 20 | |
khet side of 100 royal cubits | 2,800 (dj) | Egyptian | 53.97 m | 700 | 175 | 140 | 35 | ||
iku side | 3,600 (ŝushi) | Mesop | 60m | 720 | 240 | 180 | 48 | 40 | |
acre side | 3,333 (daktylos) | English | 64.359 m | 835 | 208.71 | 168.9 | |||
1 stade of Eratosthenes | 8,400 (dj) | Egyptian | 157.5 m | 2100 | 525 | 420 | 84 | 70 | |
1 stade | 8,100 (shushi) | Persian | 162 m | 2700 | 900 | 525 | 85 | ||
1 minute | 9,600 (daktylos) | Egyptian | 180 m | 2400 | 600 | 480 | 96 | 80 | |
1 stadion 600 pous | 9,600 (daktylos) | Greek | 185 m | 2400 | 600 | 480 | 96 | 80 | |
1 stadium625 pes | 9,600 (daktylos) | Roman | 185 m | 2400 | 625 | 500 | 100 | ||
1 furlong 625 pes | 10,000 (digitus) | Roman | 185.0 m | 2640 | 660 | 528 | 132 | 88 | |
1 furlong 600 pous | 9900 (daktylos) | English | 185.0 m | 1980 | 660 | 528 | 132 | 88 | |
1 Olympic Stadion 600 pous | 10,000 (daktylos) | Greek | 192.8 m | 2500 | 625 | 500 | 100 | ||
1 furlong 625 fote | 10,000(fingers) | Old English | 203.2 m | 2500 | 635 | 500 | 100 | ||
1 stade | 11,520 (daktylos) | Persian | 222 m | 2880 | 720 | 576 | 144 | 120 | |
1 cable | 11,520 (daktylos) | English | 222 m | 2880 | 720 | 576 | 144 | 120 | |
1 furlong 660 feet | 10,560 (inches) | English | 268.2 m | 2640 | 660 | 528 | 132 | 110 | |
1 diaulos | 19,200 (daktylos) | Greek | 370 m | 4800 | 1,200 | 960 | 192 | 160 | |
1 English myle | 75,000(fingers) | Old English | 1.524 km | 15000 | 5,000 | 4000 | 800 | ||
1 mia chilioi | 80,000 (daktylos) | Greek | 1.628352 km | 20,000 | 5,000 | 1000 | |||
1 mile | 84,480 (fingers) | English | 1.628352 km | 21,120 | 5,280 | 4224 | 1056 | 880 | |
1 dolichos | 115,200 (daktylos) | Greek | 2.22 km | 28,800 | 7,200 | 5760 | 4800 | ||
1 stadia of Xenophon | 280,000 (daktylos) | Greek | 5.397 km | 70,000 | 17,500 | 1400 | 3500 | ||
1/10 degree | 560,000 (daktylos) | Greek | 10.797 km | 140,000 | 35,000 | 2800 | 7000 | ||
1 schϓnus | 576,000 (daktylos)Z | Greek | 11.1 km | 144,000 | 36,000 | 288000 | 28800 | 24000 | |
1 stathmos | 1,280,000 (daktylos) | Greek | 24.672 km | 320,000 | 80,000 | 64000 | 16000 | ||
1 degree | 5,760,000 (digitus) | Roman | 111 km | 1,440,000 | 360,000 | 288000 | 72000 | 60000 |
For variant, the stadion at Olympia measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as short as 157.5 m up to 222 m, but it is usually stated as 185 m.
The Greek root stadios means 'to have standing'. Stadions are used to measure the sides of fields.
In the time of Herodotus, the standard Attic stadion used for distance measure is 600 pous of 308.4 mm equal to 185 m. so that 600 stadia equal one degree and are combined at 8 to a mia chilioi or thousand which measures the boustredon or path of yoked oxen as a distance of a thousand orguia, taken as one orguia wide which defines an aroura or thousand of land and at 10 agros or chains equal to one nautical mile of 1850 m.
Several centuries later, Marinus and Ptolemy used 500 stadia to a degree, but their stadia were composed of 600 Remen of 370 mm and measured 222 m, so the measuRement of the degree was the same.
The same is also true for Eratosthenes, who used 700 stadia of 157.5 m or 300 Egyptian royal cubits to a degree, and for Aristotle, Posidonius, and Archimedes, whose stadia likewise measured the same degree.
The 1771 Encyclopædia Britannica mentions a measure named acæna which was a rod ten (Greek) feet long used in measuring land. — Preceding unsigned comment added by 142.0.102.117 ( talk) 20:48, 18 May 2014 (UTC)
Another question. So a ratio can never be expressed as a percentage? —The preceding unsigned comment was added by 202.4.4.48 ( talk • contribs) .
I think that a ratio is always 100% of everything you are talking about. For example, if you have a 2:1 ratio of apples to oranges then two thirds or approximately 67% of your fruit are apples and one third or 33% are oranges, for a total of 100% or three thirds.-- Dwetherow 05:18, 23 February 2007 (UTC)
Maps present another interesting example. A map ratio of 1:100 sensibly presented as a percentage would be 1%. Meaning a distance on the map is 1% of the distance in the real world. It makes no sense to add the distance on the map to the distance in the real world, and use this combined 'real' and 'virtual' distance in any calculation. —Preceding unsigned comment added by 89.242.145.251 ( talk) 17:43, 14 February 2010 (UTC)
The article begins by declaring a ratio to be a linear relationship. What about, say, the ratio of a square's perimeter to its area? That's nonlinear; is it a ratio? --VP 38.113.17.3 21:41, 17 April 2006 (UTC)
in which case they become non linear since they are exponential. Further you can change the rate of increase at an increasing rate over time introducing a fourth dimension. The ancient problems of squaring a circle, doubling a cube and trisecting an angle were solvable so long as you didn't add constraints such as limiting their construction to ruler and compass. 142.0.102.93 ( talk) 19:04, 23 May 2014 (UTC)
I have some confusion over ratios and fractions - In the opening statement, the example 2:3 is used and is described as a whole consisting of 5 parts. In the first example, the ratio 1:4 refers to four parts in the whole. Which is the correct description of a ratio? This has always confused me. Stating the question in other terms - if I have a solution consisting of 1 part X and 3 parts Y, do I describe the ratio as 1:3 or 1:4? —Preceding unsigned comment added by 67.161.203.22 ( talk • contribs)
I'm a HS teacher, and have always taught that fractions are synonymous with ratios; that the ratio 2:3, for example, is the quotient of 2 divided by 3 or 2/3. Under this interpretation, a ratio would be "a fraction turned on its side." This is in many textbooks, for example Dolciani "Algebra-Structure and Method." I'd be interested in seeing a reference with an alternative interpretation, making 1/2 not equal to 1:2. While on the subject: Dolciani defines a proportion as "an equation that states that two ratios are equal." So, 2:3 = 4:6 would be a proportion. Splendiff 23:42, 6 June 2007 (UTC)
The ratio of two numbers of is value of one number in terms of the other, and is expressed as the quotient of their measures. A ratio is a general means of comparing any two numbers in a multiplicative sense.
Rather than thinking of a ratio as a special case of a fraction, think of the ratio as the way numbers were compared in a multiplicative sense, before fractions assumed their full power.Ratios are more flexible than fractions, because they can be used to compare part to part, such as often used in chemistry or maths (like a 3:4:5 triangle), or part to whole, as in a fraction. The techniques for manipulating fractions are much more powerful though (I don't think I've ever tried to add dissimilar ratios), so we use fractions most of the time now. Trishm 04:53, 18 June 2007 (UTC)
The example given under concentration not only makes no sense, it's incorrect. 1:5 means 1 part TO 5 parts (i.e. 1 part of X added to 5 parts Y) and should not be confused with 1 in 5 (which means 1 part in 5 parts TOTAL). The same is true for smaller ratios such as 1:100 which is not the same as 1% but actually, in terms of concentration, refers to 1 part added to 100 parts which equates to 0.91%. An easy way to understand it is to look at a 1:1 mixture. Using Splendiff's explanation above, this would be equivalent to 1/1 or 100%. When in fact it represents a 50% mixture of one component in the other or 1/2. I'm not sure how they teach these concepts in high school, but I teach it this way to our pharmacy students - and we're pretty picky with life-threatening concentration calculations. PharmaG ( talk) 14:03, 15 July 2010 (UTC)
Hi there,
I am confused the following line in the article "There is often confusion between dilution ratio (1:n meaning 1 part solute to n parts solvent) and dilution factor (1:n+1) where the second number (n+1) represents the total volume of solute + solvent. "
I thought n was already solute + solvent as the example (1mL+4mL water = 5 has shown). That line just adds more confusion. About the difference between dilution ratio and dilution factor; here is what I know. When in biology, we are ask to prepare a 1:100 dilution - I assume that this is the Dilution Ratio The Dilution Factor - for me, it is the 100 above. So if I write 1:a dilution ratio, then a is the dilution factor. For example, a 7.56 M of acid following a 1:100 dilution ratio, the answer would be .0756M which is easily obtained by having 7.56/100 where the denominator is the dilution factor. Of course one may argue that the same result can be obtain by having the stock concentration * Dilution ratio. Essentially, we are adding 1mL of acid + 99 mL of water to dilute the acid.
Would like an academic to review my workings. Flowright138 (talk) (contributions) 10:28, 14 March 2012 (UTC)
::Now the acidity of the oceans may be affected by the levels of atmospheric carbon in the greenhouse gas emissions so that's another factor to take into account, also winds tend to pile the seas up in the direction of the prevailing wind and relieve them in the opposite direction but weather events such as el Nino can reverse the prevailing winds affecting sea levels. Also surface water near land is attracted more strongly gravitationally than surface water over great depths. The dilution ratio thus has to take into account state, relative frozen or liquid height when floating, temperature, pressure,gravitational attraction, acidity, lateral loading from wind and all of these factors become variables in your dilution ratio equation. Given a body of water the size of the earths oceans its probably also necessary to consider the relative humidity of that portion of the water which is in suspension in the atmosphere, and perhaps also tidal forces.Your formula will eventually have as many or more variables than the computation of seismic forces caused by the changed loading on the mantle.
Metaphysical Engineering (
talk)
19:17, 26 May 2014 (UTC)
Is a 3-4-5 triangle a ratio? Are the number of terms limited to two, or does that merely define the dimension of the ratio? Are irrational numbers such as Pi and Phi legitimate ratios where they aren't defined by whole numbers but rather the ratio of a circles radius to its circumference. Can anything expressible as a fraction be considered a ratio? How about continuous fractions? Are they ratios? — Preceding unsigned comment added by 142.0.102.9 ( talk) 16:40, 5 June 2014 (UTC)
142.0.102.55 ( talk) 18:41, 6 July 2015 (UTC)
MostSome members in
Category:Engineering ratios are not
dimensionless, e.g.,
Carrier to noise density ratio.
Fgnievinski (
talk)
06:52, 21 July 2015 (UTC)
A different though related problem is Category:Statistical ratios, which contains many "rates" that are clearly not dimensionless and not even named ratios (contrary to the misleading engineering ratio above). Fgnievinski ( talk) 03:03, 22 July 2015 (UTC)
Two sources: Fgnievinski ( talk) 05:17, 22 July 2015 (UTC)
Another quote: "Ratio as a Rate. The first type [of ratio] defined by Freudenthal, above, is known as rate, and illustrates a comparison between two variables with difference units. (...) A ratio of this sort produces a unique, new concept with its own entity, and this new concept is usually not considered a ratio, per se, but a rate or density.", "Ratio and Proportion: Research and Teaching in Mathematics Teachers" [3]. Fgnievinski ( talk) 05:48, 22 July 2015 (UTC)
So ratios are not necessarily dimensionless; non-dimensionless ratios are called rates; and dimensionless ratios are... proportions/scales? Fgnievinski ( talk) 06:06, 22 July 2015 (UTC)
::::::Ratio should remain a broad concept article, but I have no objection to having sections within the article addressing things like geometry, numerical analysis, arithmetic and geometric sequences, dimensionality where for example we might discuss a rate that changes over time, or whose properties change at some nano scale
Metaphysical Engineering (
talk)
00:54, 28 July 2015 (UTC)
Just to explain why 2 edits have been struck. Doug Weller ( talk) 13:31, 30 July 2015 (UTC)
While the statements made in a recent edit concerning expressing ratios as decimal fractions are certainly mathematically correct, I question whether this is actually done in practice (for instance, you never see the aspect ratio of a TV screen expressed as 1.3333...). It is possible that this is a cultural difference and that such expressions are more common in different parts of the world. If this is the case, it should be brought up on this talk page so that we can decide how best to put that information in the article. I reverted the edit so that a discussion of its intent could take place here. Bill Cherowitzo ( talk) 04:40, 27 September 2015 (UTC)
I feel like the 4:3 image at the top of the page is unclear. Which of the rectangles in that image is 4:3? The inner one or the outer one? Margalob ( talk) 22:21, 5 June 2016 (UTC)