Megabus.com adds Philadelphia-D.C. line, from the Daily Pennsylvanian.
We learn from a Megabus spokesperson that their vehicles use "less than a pint of fuel per passenger mile".
For those of you who don't have the misfortune of knowing this, there are eight pints in a gallon. So these busses get better than eight passenger-miles to the gallon!
Since most cars in the US get at least 20 miles or more to the gallon, this is really nothing to be proud of.
(I'm guessing that busses are actually more fuel-efficient than cars, at least if they run sufficiently full.)
Showing posts with label measurement. Show all posts
Showing posts with label measurement. Show all posts
16 March 2010
18 February 2009
Check your units!
From today's New York Times, real estate section, referring to rural Normandy:
But, on average, real estate prices here generally range from 1,500 to 2,000 euros ($1,940 to $2,585) a square foot and a typical three-bedroom house sells for 250,000 euros ($323,165), according to Manuela Marques, a broker with Objectif Pierre, a local real estate agency.Of course, this doesn't check out, unless a typical three-bedroom house is around 150 square feet (and Normandy has suddenly turned into Manhattan). The resolution is that that's a price per square meter, which is how a French real estate broker would quote things.
19 August 2008
Trying to explain the Olympic gymnastics tiebreaker
Nastia Liukin of the USA wins silver on the uneven bars; He Kexin of China wins gold. This is news because the two of them had the same score. I've seen a lot of bad explanations of how the tiebreaker works, and implications that it involves some Big Scary Mathematics.
The way gymnastics scoring currently works is that each contestant receives a score for the difficulty of their routine (I think this is open-ended), called the "A score", which is essentially the sum of the difficulties of the various things they attempted to do. Then six judges give a score out of 10, in multiples of 0.1, for how well they did it; the lowest and highest scores are thrown out and the other four are averaged, and this is the "B score". The two scores are added to give the score for that routine.
Both Liukin and He received 16.725 points -- so they're tied, right? Wrong. The first tiebreaker, in this case, is that the contestant who had the higher A score wins -- which rewards the contestant that attempts a more difficult routine. But both had A score 7.700, B score 9.025.
The impression I got (watching NBC's broadcast last night) is that if there's still a tie, then the B scores given by the four middle judges are looked at individually. In this case, for He the six judges gave 9.3, 9.1, 9.1, 9.0, 8.9, 8.9; for Liukin they were 9.3, 9.1, 9.0, 9.0, 9.0, 8.8. In both cases the middle four scores add up to 36.1. The lowest of these scores (so the second-lowest of the original scores) is thrown out. This leaves 27.2 for He, 27.1 for Liukin, so He wins. See the tiebreaker page at the official Beijing Olympics site; there's no explanation here, but he various numbers shown there seem to bear it out. Note that instead of reporting a score of x, they sometimes use 10-x, which is the number of points deducted from the highest possible B score, which is 10.0. This explains the phrasing in some sources that refers to an "average of deductions".
I'm not sure what the logic behind this is. At first I thought that it rewarded inconsistency -- the competitor who has their scores more tightly clustered will probably have a higher second-lowest score. But this isn't the right interpretation, because the scores weren't received on different routines, but on different people's measurements of the same routine -- so does the tiebreaker reward having a routine which is hard to score? Also, it was stated many times that there are no ties in the current scoring system, but what would have happened had He and Liukin received identical scores from each judge?
The math here isn't that hard; I think the big flaw was that nobody seemed to know what the rules were.
The way gymnastics scoring currently works is that each contestant receives a score for the difficulty of their routine (I think this is open-ended), called the "A score", which is essentially the sum of the difficulties of the various things they attempted to do. Then six judges give a score out of 10, in multiples of 0.1, for how well they did it; the lowest and highest scores are thrown out and the other four are averaged, and this is the "B score". The two scores are added to give the score for that routine.
Both Liukin and He received 16.725 points -- so they're tied, right? Wrong. The first tiebreaker, in this case, is that the contestant who had the higher A score wins -- which rewards the contestant that attempts a more difficult routine. But both had A score 7.700, B score 9.025.
The impression I got (watching NBC's broadcast last night) is that if there's still a tie, then the B scores given by the four middle judges are looked at individually. In this case, for He the six judges gave 9.3, 9.1, 9.1, 9.0, 8.9, 8.9; for Liukin they were 9.3, 9.1, 9.0, 9.0, 9.0, 8.8. In both cases the middle four scores add up to 36.1. The lowest of these scores (so the second-lowest of the original scores) is thrown out. This leaves 27.2 for He, 27.1 for Liukin, so He wins. See the tiebreaker page at the official Beijing Olympics site; there's no explanation here, but he various numbers shown there seem to bear it out. Note that instead of reporting a score of x, they sometimes use 10-x, which is the number of points deducted from the highest possible B score, which is 10.0. This explains the phrasing in some sources that refers to an "average of deductions".
I'm not sure what the logic behind this is. At first I thought that it rewarded inconsistency -- the competitor who has their scores more tightly clustered will probably have a higher second-lowest score. But this isn't the right interpretation, because the scores weren't received on different routines, but on different people's measurements of the same routine -- so does the tiebreaker reward having a routine which is hard to score? Also, it was stated many times that there are no ties in the current scoring system, but what would have happened had He and Liukin received identical scores from each judge?
The math here isn't that hard; I think the big flaw was that nobody seemed to know what the rules were.
20 June 2008
Gallons per mile?
Experts find key to saving fuel: say gallons per mile.
I'll summarize: d/dx 1/x = -1/x2.
Research has been done that shows that people believe that an improvement of 1 mpg will always save them the same amount of gas. But this is obviously false, as some simple arithmetic shows. Let's say I drive 12,000 miles a year. (Why 12,000? Because everything that follows will work out to be integers.) If I improve from 15 mpg to 16 mpg, I go from using 800 gallons of gas a year to 750, a 50-gallon reduction. But if I improve from 24 mpg to 25 mpg, I go from using 500 gallons of gas a year to 480, a 20-gallon reduction.
A driver driving m miles per year in a car getting x miles per gallon will of course use m/x gallons of gas; the derivative of this is -m/x2. So if you get x miles per gallon already, improving by one mile per gallon saves m/x2 gallons. (I'm assuming here that 1 is small compared to x.)
The article claims that this means people wanting to get better gas mileage, if they have multiple vehicles, should always target the least efficient vehicle -- but that's going too far. It might be cheaper to get a 1-mpg improvement for less fuel-efficient cars. There's no reason that the cost of a car should be linear in the number of miles per gallon it gets, all else being held constant.
Note that I'm also not saying the cost of a car should be linear in the number of gallons per mile it gets! In fact this would be impossible, because it would predict that cars that get zero gallons per mile could be made for a finite amount of money.
"Gallons per mile" is kind of an annoying unit, though, because all cars get less than 1. Perhaps "gallons per 100 miles" would be a good way to go, with most cars measuring between perhaps 3 and 6 on this scale. And people can picture driving 100 miles. (For example, if they have a ten-mile commute each way, it's five round-trips to work.) But on the other hand, there's a temptation to not have to deal with decimals, and there's a big difference between 4 gallons per 100 miles and 5 gallons per 100 miles. Perhaps "gallons per 1000 miles" works nicely; typical values are now 2-digit integers, and rounding to the nearest integer gives roughly the same precision as the current system.
(Readers from other countries: please spare me the "in my country we measure fuel economy in liters per 100 km" comments. I know this.)
I'll summarize: d/dx 1/x = -1/x2.
Research has been done that shows that people believe that an improvement of 1 mpg will always save them the same amount of gas. But this is obviously false, as some simple arithmetic shows. Let's say I drive 12,000 miles a year. (Why 12,000? Because everything that follows will work out to be integers.) If I improve from 15 mpg to 16 mpg, I go from using 800 gallons of gas a year to 750, a 50-gallon reduction. But if I improve from 24 mpg to 25 mpg, I go from using 500 gallons of gas a year to 480, a 20-gallon reduction.
A driver driving m miles per year in a car getting x miles per gallon will of course use m/x gallons of gas; the derivative of this is -m/x2. So if you get x miles per gallon already, improving by one mile per gallon saves m/x2 gallons. (I'm assuming here that 1 is small compared to x.)
The article claims that this means people wanting to get better gas mileage, if they have multiple vehicles, should always target the least efficient vehicle -- but that's going too far. It might be cheaper to get a 1-mpg improvement for less fuel-efficient cars. There's no reason that the cost of a car should be linear in the number of miles per gallon it gets, all else being held constant.
Note that I'm also not saying the cost of a car should be linear in the number of gallons per mile it gets! In fact this would be impossible, because it would predict that cars that get zero gallons per mile could be made for a finite amount of money.
"Gallons per mile" is kind of an annoying unit, though, because all cars get less than 1. Perhaps "gallons per 100 miles" would be a good way to go, with most cars measuring between perhaps 3 and 6 on this scale. And people can picture driving 100 miles. (For example, if they have a ten-mile commute each way, it's five round-trips to work.) But on the other hand, there's a temptation to not have to deal with decimals, and there's a big difference between 4 gallons per 100 miles and 5 gallons per 100 miles. Perhaps "gallons per 1000 miles" works nicely; typical values are now 2-digit integers, and rounding to the nearest integer gives roughly the same precision as the current system.
(Readers from other countries: please spare me the "in my country we measure fuel economy in liters per 100 km" comments. I know this.)
10 April 2008
Dimensionally inconsistent(?) spam
Received at my Penn e-mail address today: spam with the subject line "Increase girth and inches in one easy step!"
Presumably "inches" means "inches of length". (I'll leave it to you to figure out what length they're trying to increase.)
But I couldn't help but notice that they really should have said "girth" and "length", naming both the quantities. (Or "inches" and "inches", naming both the dimensions, but that would be silly and redundant.)
Presumably "inches" means "inches of length". (I'll leave it to you to figure out what length they're trying to increase.)
But I couldn't help but notice that they really should have said "girth" and "length", naming both the quantities. (Or "inches" and "inches", naming both the dimensions, but that would be silly and redundant.)
23 December 2007
Reciprocal fuel economy
Eric de Place notes:
The idea is that chopping off the low-fuel-economy tail of the distribution (by legal means) would be a much easier way to reduce oil consumption than trying to make very-high-fuel-economy cars.
But not all incremental achievements are created equal. It was probably a lot harder to get from 1 mpg to 2 mpg than it will be to get from 100 mpg to 101 mpg.
Also, note that a pair of cars that get, say, 20 mpg and 50 mpg will average "35 mpg" in the way that the new regulations for average mileage of a automaker's fleet are written; but for each car to go 100 miles, it'll take a total of seven gallons of fuel, for a fuel economy of 200/7 = 28.6 mpg. (This is the harmonic mean of 20 and 50.) The regulations aren't necessarily flawed -- they probably should be stated in terms of the measures of fuel economy that are most commonly used -- but there's room for possible misunderstanding.
Another place I can think of where the "natural" units are the reciprocal of the ones that are habitually used is in statistical mechanics; there are tons of formulas there that have temperature in the denominator, and for the purposes of statistical mechanics it makes more sense to use inverse temperature. (I've written about this before, I think; it basically comes out of the fact that the partition function involves inverse temperature.) Are there others?
(I found this from Marginal Revolution.)
You save more fuel switching from a 15 to 18 mpg car than switching from a 50 to 100 mpg car.This sounds counterintuitive at first. But the "natural" units for fuel consumption, at least in this case, are not distance per unit of fuel but units of fuel per distance. In some parts of the word fuel usage is given in liters per 100 km; let's say we were to give fuel usage in gallons per 100 miles. (The constant "100" is just there to make the numbers reasonably sized.) Then switching from a 15 mpg car to an 18 mpg car is switching from a car that gets 6.67 gal/100 mi to 5.56 (lower is better); switching from a 50 mpg car to a 100 mpg car is switching from a car that gets 2.00 gal/100 mi to 1.00. (Another interesting consequence -- switching from 50 mpg to 100 mpg has the same effect as switching from 100 mpg to ∞ mpg, i. e. a car that uses no fuel at all.)
The idea is that chopping off the low-fuel-economy tail of the distribution (by legal means) would be a much easier way to reduce oil consumption than trying to make very-high-fuel-economy cars.
But not all incremental achievements are created equal. It was probably a lot harder to get from 1 mpg to 2 mpg than it will be to get from 100 mpg to 101 mpg.
Also, note that a pair of cars that get, say, 20 mpg and 50 mpg will average "35 mpg" in the way that the new regulations for average mileage of a automaker's fleet are written; but for each car to go 100 miles, it'll take a total of seven gallons of fuel, for a fuel economy of 200/7 = 28.6 mpg. (This is the harmonic mean of 20 and 50.) The regulations aren't necessarily flawed -- they probably should be stated in terms of the measures of fuel economy that are most commonly used -- but there's room for possible misunderstanding.
Another place I can think of where the "natural" units are the reciprocal of the ones that are habitually used is in statistical mechanics; there are tons of formulas there that have temperature in the denominator, and for the purposes of statistical mechanics it makes more sense to use inverse temperature. (I've written about this before, I think; it basically comes out of the fact that the partition function involves inverse temperature.) Are there others?
(I found this from Marginal Revolution.)
21 November 2007
Acres are strange.
Canada to Announce Vast New Park, from tomorrow's NYT.
The size of the park is referred to as "25.5 million acres", which seems kind of silly to me. The whole point of an acre is that it measures areas which are too large for, say, square feet and too small for square miles. I have no idea how large 25.5 million acres is, until I convert it to square miles -- 40,000 square miles. That's approximately the area of Pennsylvania, or five times the area of New Jersey. If the park were circular, it would have a radius of 112 miles -- that's kind of a useful way to picture it, since that says that if you were in the center of the park the borders would be over a hundred miles away. I have some idea what a hundred miles looks like.
But that relies on the fact that an area is the square of a distance. An acre is 43,560 square feet, or 1/640 of a square mile. What's the square root of an acre? 208.7 feet, which isn't any conventional length unit. The history is that an acre is a rectangle one furlong by one chain, or so Wikipedia says, so 208.7 feet is the geometric mean of a furlong (660 feet, or 1/8 mile) and a chain (66 feet, or 1/80 mile), or √10 chains. The weird definition is agricultural -- "[t]he acre was selected as approximately the amount of land tillable by one man behind an ox in one day", and it's easier to plow a long, narrow rectangle than a square. But haven't we moved past this?
Of course, in the end trying to rationalize the customary measurement system is silly. I suspect many of you are just saying "why don't you Americans use metric already?" In fact, one of my students, who is not American, actually wrote this once on a homework assignment, in his solution to a problem which applied calculus to physics where measurements were given in customary units.
The size of the park is referred to as "25.5 million acres", which seems kind of silly to me. The whole point of an acre is that it measures areas which are too large for, say, square feet and too small for square miles. I have no idea how large 25.5 million acres is, until I convert it to square miles -- 40,000 square miles. That's approximately the area of Pennsylvania, or five times the area of New Jersey. If the park were circular, it would have a radius of 112 miles -- that's kind of a useful way to picture it, since that says that if you were in the center of the park the borders would be over a hundred miles away. I have some idea what a hundred miles looks like.
But that relies on the fact that an area is the square of a distance. An acre is 43,560 square feet, or 1/640 of a square mile. What's the square root of an acre? 208.7 feet, which isn't any conventional length unit. The history is that an acre is a rectangle one furlong by one chain, or so Wikipedia says, so 208.7 feet is the geometric mean of a furlong (660 feet, or 1/8 mile) and a chain (66 feet, or 1/80 mile), or √10 chains. The weird definition is agricultural -- "[t]he acre was selected as approximately the amount of land tillable by one man behind an ox in one day", and it's easier to plow a long, narrow rectangle than a square. But haven't we moved past this?
Of course, in the end trying to rationalize the customary measurement system is silly. I suspect many of you are just saying "why don't you Americans use metric already?" In fact, one of my students, who is not American, actually wrote this once on a homework assignment, in his solution to a problem which applied calculus to physics where measurements were given in customary units.
05 November 2007
A cold lottery
British lottery games cause confusion over negative numbers. A winter-themed scratch-off lottery game required people to be able to compare two numbers to determine if they won; the numbers were "temperatures", and some of them were negative. The game was pulled from the shelves.
I'm not crazy enough to say that we should just use Kelvins so that we wouldn't have this problem. But temperature is special this way. There are two examples of negative numbers that "ordinary" people have to deal with -- cold temperatures and debts. But the difference between owing money and not owing money is much larger than the difference between "positive" and "negative" temperature.
(In statistical physics, inverse temperature comes up a lot. This only makes sense if one is using absolute temperature.)
I'm not crazy enough to say that we should just use Kelvins so that we wouldn't have this problem. But temperature is special this way. There are two examples of negative numbers that "ordinary" people have to deal with -- cold temperatures and debts. But the difference between owing money and not owing money is much larger than the difference between "positive" and "negative" temperature.
(In statistical physics, inverse temperature comes up a lot. This only makes sense if one is using absolute temperature.)
15 September 2007
just noticeable difference of temperature?
Down with the metre and litre, claims that the sizes of metric units are unintuitive: "On the other hand, a degree celsius is too large and imprecise. By contrast, the Fahrenheit scale was custom made to measure weather phenomena: it has human scale."
A celsius degree is 1.8 times the size of a Fahrenheit degree.
Do people who claim this seriously think that they can tell the difference between, say, 61 degrees Fahrenheit and 62.8 degrees Fahrenheit? I don't think they could, and so I would claim that even the Celsius degree is small enough for "everyday" purposes. (In weather forecasts given in Fahrenheit one often refers to, say, the "low seventies" or the "mid-sixties" which seems to imply a resolution of about three or four degrees.) I claim that in both scales, one degree is less than the just noticeable difference for atmospheric temperatures, although I can't quickly find out if the people who study this back me up.
(One thing I do like about using the Fahrenheit scale for weather is that almost all weather I experience is between about 0 degrees and 100 degrees. In some tellings of the story, that's said to be deliberate. There is something weird about negative temperatures, but I'm not quite crazy enough to just start stating all temperatures in Kelvins.)
A celsius degree is 1.8 times the size of a Fahrenheit degree.
Do people who claim this seriously think that they can tell the difference between, say, 61 degrees Fahrenheit and 62.8 degrees Fahrenheit? I don't think they could, and so I would claim that even the Celsius degree is small enough for "everyday" purposes. (In weather forecasts given in Fahrenheit one often refers to, say, the "low seventies" or the "mid-sixties" which seems to imply a resolution of about three or four degrees.) I claim that in both scales, one degree is less than the just noticeable difference for atmospheric temperatures, although I can't quickly find out if the people who study this back me up.
(One thing I do like about using the Fahrenheit scale for weather is that almost all weather I experience is between about 0 degrees and 100 degrees. In some tellings of the story, that's said to be deliberate. There is something weird about negative temperatures, but I'm not quite crazy enough to just start stating all temperatures in Kelvins.)
Why g ~ π2
The acceleration due to gravity, at the surface of the Earth, is about 9.81 m/s2. (If you are some of my students, you think it's 10, which is confusing for a moment. Fortunately none of my students thought it was 32.)
π2 = 9.87.
The approximate numerical equality of these numbers is not a coincidence.
I was reminded of this by Mark Dominus' post John Wilkins invents the meter, which I found via his post The Wilkins pendulum mystery resolved. In 1668, John Wilkins defined the meter to be essentially the length of the "seconds pendulum", i. e. the pendulum whose period is two seconds (the "mystery" there is that since one wants a pendulum with a light cord and a heavy bob, one has to take into account the moment of inertia of the heavy spherical bob to define this correctly). This turns out to be about 39.1 inches.
A meter is 39.37 inches.
Indeed, originally the length of the seconds pendulum was going to be the length of the meter, but the slightly different suggestion was adopted instead that the meter would be one part in 107 of the distance from the North Pole to the Equator via Paris. (Now, in fact, the meter is defined by assuming the second known and stating the speed of light.) Wikipedia tells me that these definitions were adopted in 1790, 1791, and 1983 respectively; there are others intermediate between the last two.)
The period of a pendulum is approximately T = 2π(L/g)1/2, where L is its length and g is the acceleration due to gravity. If we set T = 2 and L = 1, and solve for g, we get g = π2.
I suspect that the reason the seconds pendulum wasn't adopted is that the formula for the period involves the small-angle approximation; in reality the period of a pendulum depends not only on its length and on the acceleration due to gravity but also on the angle through which it swings. The period is given by
and so the fractional magnitude of the error is about 1/4 sin2 (θ/2); if θ is, say, one degree this is one part in about fifty thousand, or nearly two seconds a day. That error would become an error in the definition of the meter, and perhaps the Powers that Were thought that was a bit too much. (I'm not sure how accurate surveying was at the time, though, so I can't comment on the accuracy of their eventual definition based on the size of the Earth.)
π2 = 9.87.
The approximate numerical equality of these numbers is not a coincidence.
I was reminded of this by Mark Dominus' post John Wilkins invents the meter, which I found via his post The Wilkins pendulum mystery resolved. In 1668, John Wilkins defined the meter to be essentially the length of the "seconds pendulum", i. e. the pendulum whose period is two seconds (the "mystery" there is that since one wants a pendulum with a light cord and a heavy bob, one has to take into account the moment of inertia of the heavy spherical bob to define this correctly). This turns out to be about 39.1 inches.
A meter is 39.37 inches.
Indeed, originally the length of the seconds pendulum was going to be the length of the meter, but the slightly different suggestion was adopted instead that the meter would be one part in 107 of the distance from the North Pole to the Equator via Paris. (Now, in fact, the meter is defined by assuming the second known and stating the speed of light.) Wikipedia tells me that these definitions were adopted in 1790, 1791, and 1983 respectively; there are others intermediate between the last two.)
The period of a pendulum is approximately T = 2π(L/g)1/2, where L is its length and g is the acceleration due to gravity. If we set T = 2 and L = 1, and solve for g, we get g = π2.
I suspect that the reason the seconds pendulum wasn't adopted is that the formula for the period involves the small-angle approximation; in reality the period of a pendulum depends not only on its length and on the acceleration due to gravity but also on the angle through which it swings. The period is given by
and so the fractional magnitude of the error is about 1/4 sin2 (θ/2); if θ is, say, one degree this is one part in about fifty thousand, or nearly two seconds a day. That error would become an error in the definition of the meter, and perhaps the Powers that Were thought that was a bit too much. (I'm not sure how accurate surveying was at the time, though, so I can't comment on the accuracy of their eventual definition based on the size of the Earth.)
06 July 2007
liquor comes in fifths, but not tenths
I bought a fifth of vodka to bring to a party tonight. (Why, you ask? They said to bring something. And there often comes a moment towards the end of the evening where I'm thinking "damn, these people should have bought more vodka".) A fifth used to be a fifth of a gallon; now it's 750 mL. A fifth of a gallon is 756 mL, so the name makes sense. I'm kind of curious as to why this is a traditional unit, though. How Many?: A Dictionary of Units of Measurement (which is tremendously interesting, especially when you have other things you should be doing) says that it's an American version of a traditional British unit called the "bottle", which was one-sixth of an Imperial gallon, or 758 milliliters. The fact that an Imperial gallon is very nearly six-fifths of a U.S. gallon is apparently a coincidence.
While I was at the liquor store I noticed that they also sold vodka in 375 mL bottles. To my surprise, this is not called a "tenth". There are 28,800 google hits for "fifth of vodka" and 2 google hits for "tenth of vodka". The aforementioned unit dictionary mentions that a "half bottle of champagne" (375 mL) is called a "fillette".
Some people believe that a fifth and a liter are the same thing.
Another common size is the 1.75-liter bottle, often called a handle, and that size makes no sense at all; it's not two fifths, it's not a half-gallon, it's not all that round of a number in the metric system. I would have expected the "larger" size to be 1.5 liters (two fifths) or 2 liters. I thought it might be something to do with European law, but European law says that spirits must be sold in bottles of 0.02, 0.03, 0.04, 0.05, 0.10, 0.20, 0.5, 1, 1.5, 2, 2.5, or 3 liters. Notice that neither .75 nor 1.75 appears here. From what I can gather, the reason for these laws is so that a company can't decrease the size of their bottle slightly and sell it for the same price, so price hikes are actually visible to the consumer. 0.75 liters is on the list of allowed bottle sizes for wine, though.
While I was at the liquor store I noticed that they also sold vodka in 375 mL bottles. To my surprise, this is not called a "tenth". There are 28,800 google hits for "fifth of vodka" and 2 google hits for "tenth of vodka". The aforementioned unit dictionary mentions that a "half bottle of champagne" (375 mL) is called a "fillette".
Some people believe that a fifth and a liter are the same thing.
Another common size is the 1.75-liter bottle, often called a handle, and that size makes no sense at all; it's not two fifths, it's not a half-gallon, it's not all that round of a number in the metric system. I would have expected the "larger" size to be 1.5 liters (two fifths) or 2 liters. I thought it might be something to do with European law, but European law says that spirits must be sold in bottles of 0.02, 0.03, 0.04, 0.05, 0.10, 0.20, 0.5, 1, 1.5, 2, 2.5, or 3 liters. Notice that neither .75 nor 1.75 appears here. From what I can gather, the reason for these laws is so that a company can't decrease the size of their bottle slightly and sell it for the same price, so price hikes are actually visible to the consumer. 0.75 liters is on the list of allowed bottle sizes for wine, though.
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