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#1




Why is 40 fahrenheit equal to 40 celsius?
It seems counterintuitive to me that the two measurements eventually become equal even though I understand that they clearly do.
Is there a simple explanation (beyond the math simply adding up) as to why this is the case? 
#2




The Master speaks.
So it's just a coincidence. Note that the real point of correspondence is probably not exactly 40.00 degrees. 
#3




A picture might help?.
Basically, they have to be the same at some value since two nonparallel lines have to intersect somewhere. (and by the same logic, they can only have the same value once). 
#4




Not really. The 0 point of the Celsius scale is the freezing point of water, the 0 point of Fahrenheit is the freezing point of a specific mixture of brine. (And, as someone very intelligent once noted, is colder than it ever gets in Denmark, eliminating the need for negative numbers in logbooks). So, the 0 point in Fahrenheit is lower than the 0 in Celsius, but since degrees are smaller in Fahrenheit, Celsius eventually catches up. That it does so at a nice round number is just coincidence.
Last edited by Silophant; 11112013 at 11:40 PM. Reason: Ninja'd, by someone who actually managed to look up the SD column in question! 


#5




There really isn't any explanation beyond "the math"  if (by definition) 0C=32F and 100C=212F that's just where the lines cross, as here:
http://nuclearimaging.info/site_con...to_celcius.png Last edited by zombywoof; 11112013 at 11:47 PM. 
#6




When you have two different scales with units of different "sizes", there will always be one point where they have the same value. For many circumstances, this value is zero because we are making 'absolute' measurements. For example, a length of zero is zero in any unit.
The Celsius and Fahrenheit scales, however, do not place their zero points at absolute zero, and they actually place their zero points at different temperatures from each other. Zero Celsius is the freezing point of normal water, but Fahrenheit chose his zero point based on the lowest temperature he could achieve from a salt and water mixture. As for why they eventually have the same temp, think of it like this: Start from the freezing point of water (0 C and 32 F) and start moving down the scale toward colder temperatures. For every decrease of 1 degree C, you have to decrease by 1.8 F. So after a decrease of 10 C, you have a decrease of 18 F. The temperature is now 10 C or 14 F (because 3218=14). After a total decrease of 20 C, you have a decrease of 36 F. The temperature is now 20 C or 4 F. The Fahrenheit numbers are dropping at a faster rate, but the Celsius number had a 'head start' by being at 0 initially instead of 32. Eventually, the Fahrenheit value will 'catch up' with the Celsius value, at 40 degrees. With Kelvin temperatures, a change of 1 K is equal to a change of 1 C, so those two temperatures will never have the same value, they will always be offset by 273. There is, however, a temperature where the Kelvin temp and the Fahrenheit temp have the same value. Finding this value is left as an exercise for the reader. 
#7




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#8




To be fair, it's a little unsettling that the point is exactly 40 and not 39.2817 or +pi or some other value. But since the Fahrenheit scale is already incredibly artificial, it's not so surprising after all.

#9




No, that's the Rankine scale. The Reamour scale is an octagesimal scale: the freezing point of water is 0ºRm, and the boiling point is 80º.



#10




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Note that minus forty is an exact equivalence assuming that "freezing point" and "boiling point" mean the same thing for the definition of the two scales: if zero matches 32 and 100 matches 212, then 40 matches 40 and not so much as a nanodegree the more or less. Why must there be an equivalent point? Given that they don't both start from absolute zero, the fact that they go up at different rates mean that they must cross over at some point: 100 Fahrenheit is not as hot as 100 Celsius, but 100 Fahrenheit is not as cold as 100 Celsius, so somewhere in between X Fahrenheit must be neither colder nor hotter than X Celsius. 
#11




Footnote: Reaumur and Fahrenheit also cross over, of course; the figure is the less friendly but still exact 25.6 degrees.

#12




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There's a lot of agreement that one scale would be better than two, and Celsius is the logical candidate (being more widely used). But the Fahrenheit scale has some advantages: The range 0 to 100 covers the typical range of climate experienced by the vast majority of humans. And a difference of one degree F is about the minimum increment that matters. Quote:

#13




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To show this, consider what would happen if the relationship between C and F was the approximate formula you can use to quickly transform one to the other without getting bogged down in the math  take the temperature in Celsius, double, and add 30. It gets you within a couple of degrees over the temperature range people usually live in. For that rule, the temperature at which both scales are the same is 30, another nice round number. 
#14




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Therefore the ratio of one degree to the other is 5:9 There's maybe 1 in 5 odds that the point where they cross would be an integer in both scales. Every fifth C degree is an even F degree. The joke goes that Fahrenheit wanted a scale anybody could recreate; he was using ice and salt to get the lowest possible temperature that gets you, and labelled that zero. Then he used human body temperature to mark the 100, but all that fiddling with cold gave him a slight fever. However, more likely is that he used freezing and lowest possible temperature and then divided the scale into halves over and over until he had 32 divisions. I suspect the scale has been redefined so exactly 212 is the boiling point where maybe it should be like 212.1234 or something. Last edited by md2000; 11122013 at 09:12 AM. 


#15




Here is the thought exercise that the two degrees must match at some point.
Let's start with the boiling point of water 212F and 100C and travel to absolute zero 459.67F and 273.15C. Since the Fahrenheit scale starts higher and ends lower, at some point they must read the same. Imagine two cars on a straight interstate, one starts 212 miles from the state line and finishes 459.67 miles beyond it. The other car starts 100 miles from the state line and finishes 273.15 miles beyond it. No matter the speed they drive, if they stop for gas or eat ofr have a flat tire, at some point, the cars have to be next to each other. 
#16




Mention of 40° always reminds of Jack London's story when it was colder than 50°F (45.6°C):
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#17




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Since we're on this topic, a little bit of trivia for ya: the freezing temperature of pure water is not exactly 0 °C. It is very close to 0 °C, but it is not exactly 0 °C. In addition, the boiling point of pure water at standard pressure is not exactly 100 °C. It is close to 100 °C, but it is not exactly 100 °C. 
#18




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Fahrenheit originally had 3 points of reference: colder than it ever got in Denmark (0 degrees), the freezing point of water (roughly 30 degrees), and human body temperature (roughly 90 degrees). Then, Fahrenheit decided to scale each of these old degrees up (to get rid of some pesky fractional values), leading to a freezing point at 32 and a human body temperature of 96 degrees. It was just kind of coincidence that the boiling point of water happened to be roughly 180 degrees above the freezing mark at 212 degrees. Of course, those early measurements of both freezing points and human body temperatures were a bit in error, so the scale was later redefined so that 32 degrees was precisely the freezing point of water and 212 the boiling point of water. And at that point, the 180 degree difference was firmly established. In other words, if human body temperature was different and/or if the thermometers of the day were more precise, the scaling would have been different, which is an interesting concept in itself. Last edited by Great Antibob; 11122013 at 11:07 AM. 
#19




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Besides I think that on a cold winter's day the temperature could well drop below 18 C somewhere in Denmark (also outside of Greenland). 


#20




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#21




Yes, it is very arbitrary. Denmark because that's where Fahrenheit lived.
And you need a zero point. At the time, they had no clue what the actual lowest possible temperature was. So, they arbitrarily picked a value lower than the lowest recorded value in Denmark to avoid negative numbers. 
#22




[QUOTE=CalMeacham;16840997]It's not that surprising. Fahrenheit chose a scale of 180 degrees between freezing and boiling. The Centigrade/Celsius scale chose 100 degrees of difference between the same two points. When both scales used nice whole numbers for both freezing and boiling points, it became likely that the intersection point between these two nonparallel lines was going to be, if not a whole number itself, then some simply fraction. [quote]
Nope. It all has to do with the slopes of the two lines, and you can get any number of different slopes with "nice whole numbers". 
#23




[QUOTE=John Mace;16841499][QUOTE=CalMeacham;16840997]It's not that surprising. Fahrenheit chose a scale of 180 degrees between freezing and boiling. The Centigrade/Celsius scale chose 100 degrees of difference between the same two points. When both scales used nice whole numbers for both freezing and boiling points, it became likely that the intersection point between these two nonparallel lines was going to be, if not a whole number itself, then some simply fraction.
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#24




[QUOTE=CalMeacham;16841511][QUOTE=John Mace;16841499]
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Actually, 1 in 4? (I.e if Freezing/boiling had been 33/213F, the crossover point would not have been integer. C= 5(F32)/9; for C=F, this works when the offset works  let X be Fahrenheit freezing offset. C=5(Fx)/9 crosspoint is where C=F, so solve for x  F=5(Fx)/9, or 4F=5x, F=(5/4)x when F is the crossover. So crosover is an integer if 5x/4 is an integer, if x is divisible by 4, x being the offset between F and C in the scales. For example, if freezing in F was 28 degrees (boiling 208) then the conversion is C=5(F28)/9 the common point is F=C, so F=5(F28)/9 or 4F=140 crossover F=35 Last edited by md2000; 11122013 at 01:41 PM. 


#25




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How do you feel about the Electoral College? 
#26




Because math.

#27




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Though it is a good point that Fahrenheit's range of 0100 is a more practically useful one for human experience.
__________________
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#28




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To be fair, one needs to read your typo correctly ("some simple fraction" and not "simply some fraction") in order for it to make sense. So, if that's what you meant by "read it more carefully", one might wonder why you didn't write it more carefully. Especially since most people on this MB aren't going to know what a "simple fraction" is, and so wouldn't know how to correct the typo. Besides, had the answer been 39.3125, do you really think that poster you responded to would have remarked about how strange it was? 
#29




Hah! For some human experience, I suppose. This old chestnut never fails to make me laugh.



#30




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Last edited by Jragon; 11122013 at 08:39 PM. 
#31




I hadn't heard that one before, seems a close relative of "a third of an inch"

#32




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#33




At some point, Fahrenheit became tied to Celsius. They kept the traditional 32 degree freezing point on Fahrenheit, and then defined the boiling point using the notquite arbitrary value of 32+180 = 212, which roughly aligned with Fahrenheit's original scheme.
I assume this definition was made in part to ensure an exact conversion between the two scales of temperature (similar to an inch being redefined as exactly 2.54 cm.). Fahrenheit has the advantage of 0 being approximately how cold it gets and 100 being approximately how hot its gets in many parts of the world (New England in particular). It has a bit of a "false decimal" feel to it, even though it is awkward for scientific use. 
#34




Which IIRC is (very) roughly a centimeter.



#35




Strictly speaking, the Celsius scale shouldn't be called that at all. Celsius' scale was reversed, with 100 degrees being the freezing point of water and 0 degrees being the freezing point. Linnaeus flipped the scale, and it became known as the Centigrade scale (and was later rerenamed the Celsius scale because centigrade was already in use in certain languages.)

#36




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Last edited by Jragon; 11132013 at 07:20 PM. 
#37




I believe it's easy to perceive the difference between water at 97 and 98 degrees F. Between 40 and 39 degrees F, probably not so much.

#38




Water, maybe, but the scale is used far more often for air temperature.

#39




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I am reminded of this constantly by aircon settings which do not allow fractional degrees. In fact I was reminded just a moment ago: Mrs. Septimus said "Cooler, please. Just one degree." I clicked the setting from 27° to 26°. After a very short time: "Warmer please." (Mrs. Septimus does have her idiosyncrasies, but I experience the same inability to finetune that setting myself.) 


#40




I get why having boiling point of water being at 100 might be great for scientific applications, but most people aren't doing scientific experiments when they use temperature, so for weather and the like it's more user friendly to fit the normal, nonextreme weather into 0100 degrees. Not needing decimals on the thermostat is an added bonus.

#41




septimus, have you and your wife ever tried a blinded experiment? Because I'll bet that she would have gone from "colder, please" to "warmer" without you even changing the thermostat at all. Besides which, most household thermostats cycle with a larger amplitude than 1 degree (on either scale), anyway, so if a person's comfort zone really were that narrow, they'd be out of luck no matter what units you use.

#42




I was in a goofy debate with a group of cohorts that the US should finally make the switch to metric.
All except Celsius. Keep that for the lab. Fahrenheit is just too damn convenient on a human level. 
#43




Only because you're used to it, Fahrenheit is extremely inconvenient to me because it doesn't tell me anything unless I convert it to Celsius first.

#44




I'm used to both (having lived in the UK and US) and I cannot think of any objective or subjective measure where Celsius isn't equal or better.



#45




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Point was, there's something to be said about a temperature scale whose 0 – 100° range relates to typical temperate climate ranges and relative correlation with the human body. That makes it more practical when I think of outdoor/external temperatures and the extremes of comfort at both ends (room temperature/nice day being ~3/4 of the way up). But yes, it's all pretty much arbitrary. Last edited by cmyk; 11152013 at 04:06 PM. 
#46




I'd like to add one of the cohorts in the debate was British. All he could do was laugh and laugh.

#47




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My mother and grandmother, on the other hand, grew up with Fahrenheit (also in Canada, mind you), which makes temperature talk between us a bit difficult. 
#48




Plus, the temperature at which water freezes is certainly something relevant to human experience. If the temperature is a little above 0 F, or a little below it, makes very little difference to me... But if it's a little above or below 0 C, that makes a huge difference. It makes sense to put such a significant temperature at the zero point.

#49




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It's because the Celsius degree increment covers a wider range of temperature change than does the Fahrenheit degree. Each Celsius degree is about 1.8 Fahrenheit degrees. Imagine two thermometer scales, C and F, next to each other. If the individual increments of the C scale are larger, and we have a "0" line anywhere near the middle of the range we're measuring, then both above and below that 0 line a given number of increments on the C scale is farther away from the 0 line than the same number of increments on the F scale. Start with 32F and notice that 0C is right next to it. The F scale at 40 below is 72 increments different from 0. Because the C scale uses larger increments, it's only changed 40 increments. Thus the magic point the scales meet is 40 below; with a different delta of relative degree size difference, that meeting point would be somewhere different, but as long as the degree sizes are not identical, two measuring systems where the 0 point is reasonably near freezing and increments are reasonably small would meet somewhere... Last edited by Chief Pedant; 11172013 at 05:57 PM. 


#50




Put another way:
We could also measure temperature by giving the difference between the Celsius and Fahrenheit measurements; call this the Indistinguishable scale, if you like. Thus, on the Indistinguishable scale, the freezing point of water would be 32  0 = 32 degrees, the boiling point of water would be 212  100 = 112 degrees, normal body temperature would be around 60 degrees, and so on. By considering that the Indistinguishable scale, like any other, will have a temperature indicated by "0 degrees", we see that there must be a temperature at which the Celsius and Fahrenheit scales agree. (Above that, the Indistinguishable scale will be positive, indicating that the Fahrenheit measure will be above the Celsius measure; below that, the Indistinguishable scale will be negative, indicating that the Fehrenheit measure will be below the Celsius measure.) Last edited by Indistinguishable; 11172013 at 06:05 PM. Reason: Ignoring any concerns about the nature of absolute zero and temperatures below it, none of which I know anything about 
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