diff --git a/doc/emacs-notes.org b/doc/emacs-notes.org index 86fba32..827f772 100644 --- a/doc/emacs-notes.org +++ b/doc/emacs-notes.org @@ -185,6 +185,1621 @@ Tangling with =C-c C-v t=. ** Reproducible Research +* Emacs Calc Tutorials + +By Andrew Hyatt, found here: https://github.com/ahyatt/emacs-calc-tutorials. + +** LICENSE + +#+BEGIN_EXAMPLE + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. + +#+END_EXAMPLE + +** README + +#+BEGIN_EXAMPLE +This repository contains tutorials about emacs calc originally writen on the +Emacs community on Google+. + +The best way to read is probably just to open the org files directly, which +Github will display correctly. + +If anyone would like to correct anything, add any tutorials, or request +anything, the normal Github bug / request / or pull request process will work. + +#+END_EXAMPLE + +** Algebra + +I think it's time to write about one of the amazing things that calc can do: +algebra! + +Before we get into how to solve equations, I just want to write about on some +cool things you can do with the calc display. + +Let's say you have a formula you want to work with =a + sqrt(b) = 5=. Let's enter +that into calc: + +#+BEGIN_EXAMPLE +M-x calc +'a + sqrt(b) = 5 (' starts algebraic mode). + +Result: +1: a + sqrt(b) = 5 +#+END_EXAMPLE + +Well, that's not so surprising, that's what we put in. Kind of disappointing, +though. Is that it calc? We love your brains, but what about your looks? That's +important too! + +#+BEGIN_EXAMPLE +d B (turn on calc-big-language mode) + +Result: + ___ +1: a + V b = 5 +#+END_EXAMPLE + +Hey, that's an ASCII square-root symbol. What other cool things can you do here? + +#+BEGIN_EXAMPLE +a^2 + +Result: + + 2 +1: a + +3:4 (enter the fraction 3/4) + +Result: + + 3 +1: - + 4 +#+END_EXAMPLE + +Here's how to get back: +#+BEGIN_EXAMPLE +d N (calc-normal-language) +#+END_EXAMPLE + +And an alternative, in which all operators are explicitly represented as +functions: + +#+BEGIN_EXAMPLE +1: a + sqrt(b) = 5 (re-enter the formula) +d U (calc-unformatted-language) + +Result: +1: eq(add(a, sqrt(b)), 5) +#+END_EXAMPLE + +But, wait, did you think that's all? What if you wanted to enter that equation +in Mathematica? + +#+BEGIN_EXAMPLE +d M (calc-mathematica-language) + +Result: + +1: a + Sqrt[b] == 5 +#+END_EXAMPLE + +Ooh! Calc! Do c++ next! + +#+BEGIN_EXAMPLE +d C (calc-c-language) + +1: a + sqrt(b) == 5 +#+END_EXAMPLE + +Latex! + +#+BEGIN_EXAMPLE +d L (calc-latex-language) + +Result: + +1: a + \sqrt{b} = 5 +#+END_EXAMPLE + +I could keep going, but trust me, there's more. And you can even define your own +languages by constructing syntax tables, but I won't get into that now. + +** Bit Manipulation + +Quick! What bits are set on the number 925817? What, are you going to convert it +to binary and note positions of 1s? Ha! I laugh at such primitive techniques. + +#+BEGIN_EXAMPLE +M-x calc +925817 +b u (unpack the bits into a vector) + +Result +1: [0, [3 .. 6], 13, [17 .. 19]] +#+END_EXAMPLE + +How many bits is that? + +#+BEGIN_EXAMPLE +v # (count the number of items in a vector) + +Result: +1: 9 +#+END_EXAMPLE + +This is convenient! So yes, calc has some nice functions for binary numbers. The +interesting thing about calc's binary number functions aren't just that you can +do bitwise operations such as AND and OR, but it has the notion of a word size +that it works with. Well, it'd have to do things like NOT. + +Let's check it out. First, we'll see what the number 925817 looks like in binary. + +#+BEGIN_EXAMPLE +925817 +d 2 + +Result: +1: 2#11100010000001111001 +#+END_EXAMPLE + +This is nice, but it'd be better to see the whole word. + +#+BEGIN_EXAMPLE +d z (Display leading zeroes) + +Result: +1: 2#00000000000011100010000001111001 +#+END_EXAMPLE + +Ah, that's more like it. The word size by default is 32 bits, as you can see. +Or, wait, can you see? Hard to count. Let's verify it. + +#+BEGIN_EXAMPLE +d 0 (go back to base-10 mode) +0 (we start with 0) +b n (calculate the not) + +Result: +1: 4294967295 +#+END_EXAMPLE + +Now we already know how to count the 1's... + +#+BEGIN_EXAMPLE +b u v # + +Reuslt: + +1: 0000000032 +#+END_EXAMPLE + +Whoops, looks like we still have leading 0s. But we've confirmed it, so let's just let it go for now. + +Now, let's see what the number 925817 is if you reverse all the bits. I can't +take credit for this particular bit of cleverness, this technique comes straight +from calc's info pages. + +#+BEGIN_EXAMPLE +d z (get rid of leading 0s) +925817 +b u (unpack into a vector) +31 - (tranform each bit position by subtracting it from 31, the tab just switches the items around on the stack) +b p (repack the vector) + +Result: +1: 2651090944 +#+END_EXAMPLE + +Woody Allen once praised New York by saying how he loves that you can go to +Chinatown and eat a crab in the middle of the night, but in reality what kind of +crazy person would need to do that? I feel the same way about all these +features. Will I really ever need to reverse the bits of a number? Not sure, but +I do love the way that calc has me covered for whatever I really want to do. + +By the way, want to go to 64-bit mode? Just change the word size. + +#+BEGIN_EXAMPLE +b w 64 (change the word size to 64) +#+END_EXAMPLE + +Now let's reverse the bits of 925817 again to see what we get. It'll be +amusingly huge! + +#+BEGIN_EXAMPLE +925817 +b u (unpack into a vector) +63 - (tranform each number by subtracting it from 31, the tab just switches the items around on the stack) +b p (repack the vector) + +Result: +1: 11386348903201767424 +#+END_EXAMPLE + +Ah, that's what it was. I was just about to give that same answer myself. + +One more cool thing. If you give a negative word size, calc will interpret +binary number as 2's complement numbers. For example: + +#+BEGIN_EXAMPLE +b w 32 (set the word size to 32) +2 (just to choose a simple number) +b n (bitwise not) + +Result: +1: 4294967293 +#+END_EXAMPLE + +And now with 2's complement! + +#+BEGIN_EXAMPLE +b w -32 (set the word size to -32, in other words, a 2's complement version of 32 bit) +2 +b n + +Result: +1: -3 +#+END_EXAMPLE + +Hope this helps you twiddle those bits in all the ways that make you happy. + +** Calculus + +Quick, integrate =2x + sin(y)=! Well, frankly, it's been so long since I've done +calculus by hand I can't remember anymore. Well, knowing calculus is good, but +knowing calc is even more useful! + +#+BEGIN_EXAMPLE +M-x calc +'2x + sin(y) (The single quote enters algebraic mode) +a i y (Calculate the integral with respect to y) + +Result +1: 2 x y - 180 cos(y) / pi +#+END_EXAMPLE + +You can also integrate over specific regions by using C-u a i, whereupon it will +prompt you for the start and end point of the integration. + +As the manual mentions, the results are often not as simplified as they could +be. Calc is impressive, but it isn't as sophisticated as Mathematica. + +An example of some issues are if we just take the derivative of the integral we +just calculated. We should get back to our original formula. + +#+BEGIN_EXAMPLE +a d y (Calculate the derivative with respect to y) + +Result: +1: 2 x + 3.14159265358 sin(y) / pi +#+END_EXAMPLE + +Clearly this should be 2x + sin(y), but calc may have made an error. + +OK, let's make calc do something cool so we can forget this unfortunate +incident. Hey, how about making a Taylor series of a function? + +#+BEGIN_EXAMPLE +'2x + sin(y) (re-enter the formula) +a t y 6 (Calculate the Taylor series of a term, over y, for 6 terms) + +Result: +1: 2 x + y - y^3 / 6 + y^5 / 120 - y^7 / 5040 + y^9 / 362880 +#+END_EXAMPLE + +This isn't a bad approximation, see [[https://www.google.com/search?q=y+-+y%5E3+%2F+6+%2B+y%5E5+%2F+120+-+y%5E7+%2F+5040+%2B+y%5E9+%2F+362880][Google’s answer]] for comparison. + +So, yes, calc can do college-level math, even if the answers aren't perfectly +simplified. It's not Mathematica, but it is free and integrated into emacs, so +it's definitely nice to have. + +** Date + +Ever want to know how many seconds old David Hasselhoff is? calc can do many +things, but it doesn't know much about Hasselhoff, so first I do a query on +Google for [david hasselhoff]. I get a knowledge card on the right saying he was +born July 17, 1952. It doesn't give a time, so we'll just assume it was at +midnight. + +#+BEGIN_EXAMPLE +M-x calc +t N (put the current time on the stack) +' (press ' to enter algebraic mode, then you input the date). +- (subtract the two to get the number of days David has been alive) +24 (we're going to multiply by 24, the number of hours in a day) +60 (the number of minutes in an hour) +60 (the number of seconds in a minute) +* +* +* + +Final result: +1: 1910255938.01 +#+END_EXAMPLE + +There you have it, he's... wait, how many seconds? That's really hard to read. + +Back into calc! + +#+BEGIN_EXAMPLE +d g (toggle digit grouping) + +The final final result: +1: 1,910,255,938.01 +#+END_EXAMPLE + +Ah, that's a 1.9 billion seconds. Sweet! + +** Financial.org + +I recently chatted with emacspeak creator T.V. Raman, and told him I was +writing a series of short tutorials about calc. He is really a calc fanatic, and +told me a story in which he astounded a loan officer by calculating scheduled +loan payments with just a few keystrokes in calc. Raman is living proof that +calc is a useful tool for so many situations, and it always pays to have emacs +running. He also mentioned that he found the explanation in the calc tutorial +about the financial functions to be the clearest he's ever read. + +So, yes, calc can do finance. Let's say that you were sitting in front of a loan +officer, and she told you that for your loan of $500,000, you need to pay in 30 +installments with a 5% interest rate. How much do you need to pay each month? +Wait a second! Stop right there, loan officer! I have calc! + +#+BEGIN_EXAMPLE +M-x calc +500000 (the amount of the loan) +30 (the number of payments) +'5% (equivalent to typing 0.05) +b M (calc-fin-pmt, computing the amount of periodic payments to amortize a loan) + +Result: +1: 25,000 +#+END_EXAMPLE + +OK, but that's a bit obvious, since $25,000 is just 5% of $500,000. If the +number of payments was much smaller, we'd get a larger value. Let's take another +question: if you wanted to only pay $10,000 in each installment? How many +installments would it take to pay off the loan? + +#+BEGIN_EXAMPLE +'5% +10000 (the payment we want to make) +500000 (the loan amount) +b # (calc-fin-nper, calculate the number of installments needed) + +Result +1: nper(0.05, 10,000, 500,000) +#+END_EXAMPLE + +What? Oh, I see, I also go the message: "Payment too small to cover interest +rate: 10000". Oh, right, 5% of $500,000 is already $25,000, so we'd never pay it +off at that rate. What if we payed $50,000 instead? + +#+BEGIN_EXAMPLE +'5% +50000 (the payment we want to make) +500000 (the loan amount) +b # + +Result: +1: 14.2066908 +#+END_EXAMPLE + +So, it would take just over 14 payments to pay off the loan. + +OK, one more cool one: Let's say you meet an investment banker who gives you the +following deal. I've got a investment for you, she says. Just give me $100,000 +and I'll give you $10,000 at the end of each year for the next 12 years. +Assuming the interest rate will stay at 3% for the next 12 years. Is it a good +deal? + +Hey, what are you asking me for? I have no idea! Calc knows, though, because it +can tell you the break-even point for the cost of an investment that gives +periodic payments. + +#+BEGIN_EXAMPLE +'3% (the interest rate) +12 (the number of payments) +10000 (the payment you get each time) +b P (calc-fin-pv, calculate the "present value" of the investment, the break-even point for the investment) + +Result: +1: 99,540.0399357 +#+END_EXAMPLE + +In other words, the break-even point for the initial cost is $99,540. If the +investment costs more than this, it's no good at that assumed interest rate. +Better reject the deal. Trust calc more than any investment banker. + +This is just a small sampling of some of the financial calculations that calc +can perform. The next time you are making an investment, fire up calc. You'll +not only have confidence in the deal, you may just amaze someone with the power +of emacs, just like T.V. Raman did. + +** Fractional Arithmetic + +This one is pretty short, but it's about one of my favorite features of calc: +the ability to handle fractions as fractions instead of rendering them as real +numbers. + +Quick, what's =5/8 + 9/21=? + +Um, ok... better start multiplying things... wait, let's just tell calc to do +it. + +#+BEGIN_EXAMPLE +M-x calc +5:8 (this is how you enter a fraction) +9:21 ++ + +Result: +1: 59/56 +#+END_EXAMPLE + +So easy! If we want to convert it to a float you can do this: + +#+BEGIN_EXAMPLE +c f (convert to +float) + +Result: + +1: 1.05357142857*10.^0 +#+END_EXAMPLE + +And if you want it back as a fraction, then just do: + +#+BEGIN_EXAMPLE +c F (convert to fraction) + +Result: + +1: 59/56 +#+END_EXAMPLE + +That's so awesome! + +You could also enter fractions this way: + +#+BEGIN_EXAMPLE +m f (set fraction mode, integer division will result in fractions) +5 +8 +/ + +Result: + +1: 5/8 +#+END_EXAMPLE + +Now you can live in the nice world of fractions as much as you like. It's a nice +world, full of pleasant to look at integers taking up little horizontal space + +** HEX + +OK, seems like there's interest in some quick calc tips. Here's today's: + +How to convert decimal to hexidecimal. Let's say you want to convert number +12345 to hex. + +#+BEGIN_EXAMPLE +M-x calc +d 6 (sets the number radix to 16, meaning all output will be in hex) +10#12345 (inputs the number 12345 in base 10) + +The output reads: +1: 16#3039 +#+END_EXAMPLE + +The answer is therefore =0x3039=. + +And then you can do a =d 0= to set the number radix back to normal, base 10. + +Here's how to do the other way. Let's convert =0xABCDEF= to base 10. + +#+BEGIN_EXAMPLE +M-x calc +16#ABCDEF + +The output reads: +1: 11259375 +#+END_EXAMPLE + +** More on Algebra + +Jim is 42 years old. He has one brother, and their total age is 100. What is the +brother's age? OK, this isn't a very hard problem, but let's just introduce calc +algebra by solving it. + +#+BEGIN_EXAMPLE +M-x calc +'42 + x = 100 (' to enter algebraic input) +a S x (solve for x) + +Result: +1: x = 58 +#+END_EXAMPLE + +Let's make this harder. Jim and Dan's ages sum to 100. Jim is 5 years older than +Dan. How old are they? + +#+BEGIN_EXAMPLE +'[j + d = 100, d + 5 = j] +a S j,d + +Result: +1: [j = 52.5, d = 47.5] +#+END_EXAMPLE + +Nice! + +And of course it can give you more than just numerical solutions: + +#+BEGIN_EXAMPLE +'sin(x) + tan(y) = pi / 2 +a S y (solve for y) + +Result: +1: y = arctan(pi / 2 - sin(x)) +#+END_EXAMPLE + +Sometimes there are more than one solution. For example: +#+BEGIN_EXAMPLE +'x^2 = 25 +a S x + +Result: +1: x = 5 +#+END_EXAMPLE + +Wait, what happened to -5! That's a valid solution, why didn't calc tell us +about it? What's happening here is that calc is telling us about the first valid +thing it can find, which is basically how it operates. But you can always get +everything: + +#+BEGIN_EXAMPLE +'x^2 = 25 +a P x (find the polynomial solutions) + +Result: +1: [5, -5] +#+END_EXAMPLE + +Sometimes there aren't a finite number of results because you aren't dealing +with polynomials. You can just get a generalized solution: + +#+BEGIN_EXAMPLE +'sin(x)^2 = 25 +H a S x (solve for x, giving the generalized solution) + +Result: +1: x = arcsin(5 s1) (-1)^n1 + 180 n1 +#+END_EXAMPLE + +This uses the calc notation =n1=, which you just means any integer. You can also +see another notation =s1= which means any sign. In this case =5 s1= means that that +number can be 5 or -5. + +Looking at how awesome calc is, it's just a shame I never knew about it in high +school... + +** Pi and Precision + +This one's about p and P and mostly about pi. + +First, let's pi it up: + +#+BEGIN_EXAMPLE +M-x calc +P (this gives you pi) + +Result: +1: 3.14159265359 +#+END_EXAMPLE + +Well, I guess that's a reasonable pi. But, c'mon, this is calc. Can't we get a +bit more digits? How about 100? + +#+BEGIN_EXAMPLE +p 100 (sets precisions to 100) +P (need to ask calc again for pi, it doesn't recalculate) + +Result: +1: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068 +#+END_EXAMPLE + +Well, but actually evaluating it robs it of its never-ending charm. Let's just +use it as a variable. How about calculating the area of a circle with a 5 km +radius? + +#+BEGIN_EXAMPLE +'5000 m +2 +^ +'pi (enter pi as a variable) +* + +We get: +1: 25000000 m^2 pi +#+END_EXAMPLE + +Yeah, sure that’s what I said I wanted, but I’ve changed my mind - now I want a number. + +#+BEGIN_EXAMPLE += + +1: 78539816.3397448309615660845819875721049292349843776455243736148076954101571552249657008706335529267 m^2 +#+END_EXAMPLE + +Whoops, looked like I forgot to set the precision back to normal. And I can't +read this. Let's make it a bit nicer. + +#+BEGIN_EXAMPLE +Control-_ (normal emacs undo) +p 7 +d g (turn digit grouping on) += + +Result: +1: 7.853983e7 m^2 +#+END_EXAMPLE + +Oh, that's because I didn't have enough precision to render it without resorting +to scientific notation. Let's just bump the precision up again. + +#+BEGIN_EXAMPLE +Control-_ (undo, since we have to redo the pi conversion with more precision) +p 10 += + +Result: +1: 78,539,816.35 m^2 +#+END_EXAMPLE + +Ah, that's better. + +** Random + +I use calc whenever I need a random number. The interface is easy and the random +numbers are (supposedly) high quality. + +So, let's start with something simple: A random number between 0 and 100: + +#+BEGIN_EXAMPLE +M-x calc +100 (the upper bound, all values will be between 0 and this) +k r (creates a random number between 0 and the number on the stack) + +Result: +1: 66 (of course, yours will be different) +#+END_EXAMPLE + +I want another one! +#+BEGIN_EXAMPLE +k a (creates another number with the same upper bound as the last) +#+END_EXAMPLE + +Now that I’ve had a taste of that sweet sweet randomness, I want a vector of 50! + +#+BEGIN_EXAMPLE +100 (the upper bound, again) +50 (the number to generate) +k h (generate a vector of 50 random numbers between 0 and 100) + +1: [60, 72, 61, 74, 77, 97, 10, 90, 8, 29, 82, 81, 51, 58, 7, 88, 99, 1, 37, 89, 93, 84, 52, 94, 2, 35, 5, 48, 87, 47, 14, 6, 79, 18, 67, 76, 70, 9, 43, 65, 69, 23, 55, 11, 53, 78, 50, 30, 13, 42] +#+END_EXAMPLE + +OK, that's nice. But how about a number between 0 and 1? + +#+BEGIN_EXAMPLE +1.0 +k r + +Result: +1: 0.636988102539 +#+END_EXAMPLE + +OK, how about number between -50 and 50? For that we need to use what calc calls +an interval form: + +#+BEGIN_EXAMPLE +[ (Starts interval form) +50 (You can't just type -50 in calc) +n (negate, givint -50) +.. (the middle part of the interval form) +50] (closing the interval form) +#+END_EXAMPLE + +What you see now in calc is: +#+BEGIN_EXAMPLE +[-50 .. 50] +#+END_EXAMPLE +And you could have just typed it in with: +#+BEGIN_EXAMPLE +'[-50 .. 50] +#+END_EXAMPLE +which would be a lot easier, really. + +#+BEGIN_EXAMPLE +k r +#+END_EXAMPLE +This produces a random number from the bounds of the interval, in this case both +-50 and 50 are possible, if you wanted them to be exlusive bounds, you'd use the +form =(-50 .. 50)=. + +Finally, you can re-arrange a list: +#+BEGIN_EXAMPLE +'[1 2 3 4] (our starting vector) +-1 (signals to use the vector above, could also be the size of the vector) +k h + +Result: +1: [3, 1, 4, 2] +#+END_EXAMPLE + +But =k a= will not give you more variants, unfortunately. + +** Strings + +Did you know you could work with strings in calc? For an example, let's find out +what "Hello world" is in binary: + +#+BEGIN_EXAMPLE +M-x calc +d 2 (change the to binary mode) +"Hello world (Enter the string "Hello world" which turns into a vector of numbers) + +Result: +1: [2#1001000, 2#1100101, 2#1101100, 2#1101100, 2#1101111, 2#100000, 2#1110111, 2#1101111, 2#1110010, 2#1101100, 2#1100100] +#+END_EXAMPLE + +And similarly, we can convert back. If someone gave you the binary number: +=01001000011011110110110001100001= and asked what the string was, I'd have no +idea... but calc knows: + +#+BEGIN_EXAMPLE +d " (changes to string mode) +C-x b scratch (whaaa, leave calc?) +01001000011011110110110001100001 (enter the number we're parsing) +C-a (go to the start of the line) +C-x ( (start a macro) +2# (prefix the number with a binary indicator) +C-u 8 C-f (Jump forward 8 characters) + (insert a space to separate the numbers) +C-x ) (end the macro) +C-x e (repeat the macro) +e e (repeat twice twice more) +C- (set mark) +C-a (goto beginning of line) +C-x g (copy region into calc) + +Result: + +1: "Hola" +#+END_EXAMPLE + +And there you have it! Maybe there is an easier way to convert from the giant +binary number to a vector of bytes, but I don't know it yet. + +** Time + +Hey, what's the time? It's time to get ill! No, actually I meant the time in +seconds since the epoch. Yesterday I went over doing math with time, which is +fun but not something I use everyday. Much more useful is converting to and from +Unix timestamps. + +Let's start by getting the time now in seconds since the epoch: + +#+BEGIN_EXAMPLE +M-x calc +t N (get the time now) +t U (convert the time to seconds since the epoch) + +Result: +1: 1359424746 +#+END_EXAMPLE + +Oh, and you want to insert that into your last used buffer? + +#+BEGIN_EXAMPLE +y (that doesn't mean "yes", that means yank into the last buffer) +#+END_EXAMPLE + +Done! Just to be complete, let's convert another date we have to input: + +#+BEGIN_EXAMPLE +'<12:00pm Jul 4, 1776> (single quote to enter algebraic mode, then the date) +t U (converts the time to seconds since the epoch) +#+END_EXAMPLE + +But wait, what will happen? This is considerably before the epoch. + +#+BEGIN_EXAMPLE +Result: +1: -6106003200 +#+END_EXAMPLE + +Oh calc, you never let me down. + +Let's do the other way. Remember the Billenium? + +#+BEGIN_EXAMPLE +1e9 +t U (converts the time in seconds since the epoch to text) + +Result: +1: <9:46:40pm Sat Sep 8, 2001> +#+END_EXAMPLE + +Wow, I never realized how close the Billenium was to September 11th. Kind of spooky... + +** Unit Conversion + +You load 16 tons, and what do you get? I mean, in kilograms. + +#+BEGIN_EXAMPLE +M-x calc +' 16 tons (' to enter algebraic mode, so you can type out the units) +u c kg (u c for "unit convert", and kg being the target unit). + +Result: +1: 14514.95584 kg +#+END_EXAMPLE + +Calc treats units as special. If you added something, such as: + +#+BEGIN_EXAMPLE +3 ++ + +Result: +1: 14514.95584 kg + 3 +#+END_EXAMPLE + +But you can remove the units from the above using: +#+BEGIN_EXAMPLE +u r (remove units) + +Result: +1: 14517.95584 +#+END_EXAMPLE + +OK, that's all well and good. But I've always wondered how much is Grandpa +Simpson's gas mileage when he said "My car gets 40 rods to the hogshead and +that's the way I likes it." + +For that, we need to define the units. Calc knows about a lot of units, but +maybe not the rod and hogshead. In fact, in the calc info pages, defining what a +"rod" is the example for how to define your own units. Let's get started! + +#+BEGIN_EXAMPLE +'16 ft (The equivalent to one rod) +u d rod Rod (defines a new unit rod, with optional description "Rod") +#+END_EXAMPLE +Now a hogshead is a unit of measurement that varies by what liquid it contains. +I don't know what the unit is for gasoline, but let's use sherry as a +substitute, in which a hogshead is 245 liters. + +#+BEGIN_EXAMPLE +'245 liters +u d hogshead (don't bother with a description this time) +'40 rod +'1 hogshead +/ +#+END_EXAMPLE +Wait, what units should we be using? +#+BEGIN_EXAMPLE +u v (show the units table, a handy table of all units) +u c mi/gal (the units come from the unit table) + +Result: +1: 1.87280731429e-3 mi / gal +#+END_EXAMPLE + +But wait, we can do better. Why upgrade this measure to something that isn't +even standard? Miles per gallon is just a bit better than rods per hogshead (in +fact, that was what the original joke was about). + +#+BEGIN_EXAMPLE +u c si (convert everything to scientific units) + +Result: +1: 796.212244896 / m^2 +#+END_EXAMPLE + +Not that I understand this number, but at least in miles per gallon, I can see +that that's not such great fuel economy, but what you do expect from Grandpa? + +OK, one more cool thing, then I'm out of here. Calc can split up numbers into +multiple units. Here's 42 inches in feet and inches: + +#+BEGIN_EXAMPLE +'42 in +u c ft+in (Convert to a mixture of feet and inches) + +Result: +1: 3 ft + 6. in +#+END_EXAMPLE + +Calc, you're sooo coool! + * Random Notes ** How to paste then copy :NOTE: :PROPERTIES: