In the comments to the post about the cartoon with the cosine pun, many people recalled the mnemonics that they were taught to remember how sine, cosine, and tangent were defined. In the comments, Rob Grigjanis mentioned the mnemonic he learned for the color spectrum as “Richard Of York Gave Battle In Vain” and that reminded me of this story that I have written about earlier that happened when my older daughter was in third grade.

She came home from school one day and told me excitedly how the teacher had explained how white light was made up of different colors. The teacher had also told her that the great scientist who discovered this was Roy G. Biv! To say I was surprised is putting it mildly. I tried to gently correct her about who the scientist was without seeming to disparage her teacher, but my daughter was skeptical about what I was telling her. Who was she more likely to believe: her teacher, a fount of authoritative knowledge, or her dopey old father, often prone to making jokes? She was too young to appreciate the implausibility argument that it was highly improbable that the scientist who discovered the color spectrum just happened to have a name that matched the initial letters of the colors in the right order.

Growing up Sri Lanka, sophisticated mnemonics such as these were not a thing and I did not recall that we were taught any for the trigonometric ratios or indeed for anything else. I found those trig definitions pretty easy to remember. For things that were more complicated, we just made a crude mnemonic by making the sequence of first letters into a word. We learned the order of the colors by saying ‘vibgyor’ pronounced phonetically, so that it sounded vaguely Hungarian. Roy G. Biv never made an appearance. Another one was ‘bodmas’, for the order in which mathematical operations had to be done in an expression that combined many operations. It stood for ‘brackets, of, division, multiplication, addition, subtraction’.

The fact that I still remember them testifies to the power of such devices to remember things.


  1. brucegee1962 says

    The most elaborate one I have come across is
    “On old Olympus’ tiny tops
    A Finn and German viewed some hops”

    which is supposed to help you remember the cranial nerves:
    I. Olfactory II. Optic III. Oculomotor IV. Trochlear V. Trigeminal VI. Abducens VII. Facial VIII. Auditory (Vestibulocochlear) IX. Glossopharyngeal X. Vagus XI. Spinal Accessory XII. Hypoglossal

  2. sonofrojblake says

    A (to me) surprisingly large part of infantry training involves mnemonics (or as one of the training corporals had it, “pneumonics”, and yes, he spelled it as well as said it that way). It’s a testament to their power that I can still remember PREWAR (Preparation for battle, Reaction to effective enemy fire, Enemy location, Winning the firefight, Attack, Reorg) and PAWPERSO (Protection, Ammunition, Weapon, Personal Camoflage , Equipment, Radios, Special Equipment, Orders) and others, a quarter century on from when I last picked up an L85A1.

  3. Rob Grigjanis says

    sonofrojblake @3: I thought all you needed in the Army was “If it moves, salute it. If it doesn’t move, paint it”.

  4. Pierce R. Butler says

    Rob Grigjanis @ # 4: If it moves, salute it…

    Traditionally a Navy doctrine.

  5. anat says

    sonofrojblake @3, I remember that one, but it takes me forever to remember what each letter stands for (especially #4 and #6). So not all that effective?

  6. moarscienceplz says

    When I first heard about Roy G. Biv, I was kind of shocked. People needed a mnemonic aid to remember the colors in a rainbow? I don’t even remember how I learned it, it just seemed obvious. A box of eight crayons always came in rainbow order (with also brown and black), plus I knew that red plus yellow made orange so putting orange between red and yellow seemed logical; same for yellow, green, and blue. Learning that indigo was considered a major color seemed unnecessary, to this day I suspect it was included simply to provide another vowel for the mnemonic.
    Around age eight, my dad introduced me to the resistor color code (using colored bands on the resistor body to represent numerals in the Ohms value of the resistor). This really nailed down the rainbow order for me (minus indigo).

  7. billseymour says

    moarscienceplz @7 mentioned the resistor color code.  I was a wires-and-pliers guy years ago (my first vocation), and I learned what, nowadays, I should probably introduce with trigger warning:  “Bad Boys Rape Our Young Girls But Violet Gives Willingly.”

    I once made one up for the order in which sharps appear in key signatures in printed music:  “Foxy Call Girls Disdain All Empty Beds.”  (Real musicians probably know a much better one.)

  8. Tethys says

    I never learned trigonometry, so didn’t connect the cartoon and cosign/ sine pun.

    I don’t recall if I ever learned the spectrum mnemonic, as already noted, it’s easy enough to get the correct order by starting with primary red and adding the correct secondary of orange, primary yellow, etc..

    In biology we learned ‘King Phillip cried out for good spaghetti’ to remember the proper sequence of kingdom, phylum, class, order, family, genus, species.

    The other one I still remember is used for reading sheet music. Every good boy deserves fudge stands for the correct order of the notes, and corresponds with the order of lines on a treble staff.

  9. says

    Another one was ‘bodmas’, for the order in which mathematical operations had to be done in an expression that combined many operations.

    See also, FOIL: First, Outside, Inside, Last [ (a+b)^2 = a^2 + 2ab + b^2 ].

    The one I remember from high school band class is the order of sharps and flats because it uses the same words in reverse:

    Sharps: Father Charles Goes Down And Ends Battle

    Flats: Battle Ends And Down Goes Charles’ Father

    And it’s not a mnemonic, but an easy way to remember the structure of the periodic table and the s, p, d and f (sharp, principle, diffuse and fundamental) orbital levels is add four twice, insert after the first:


    If elements up to 140 are ever synthesized, we’ll likely see 2,6,10,14,18.

    As for Roy G. Biv, They Might Be Giants said it best.

  10. anat says

    I learned Roy Gbiv at the age of 5, a few months before my first experience of color mixing (which was my first experience with 2 flavors/colors or ice-cream).

  11. DrVanNostrand says

    The mnemonic I always remember is from a parody video. For the biological taxonomy levels: Phylum, Class, Order, Family, Genus, Species. The mnemonic was “Please Come Over For Gay Sex”, the joke being that it was highly inappropriate for middle/high schoolers. That said, having been a teenage boy at one point, I think it would’ve been a very effective mnemonic in my high school biology class.

  12. billseymour says

    Intransitive’s mnemonic for sharps and flats definitely beats mine, and it works backwards for the flats.  That’s elegant.

    Intransitive wins, I lose.  (I like losing when it means that I’ve learned something.)

  13. Bruce says

    So much effort to memorize seven color names. Yet so little analysis or discussion on if there even should be seven or six. Six is logical from three primary colors sensed by human eye receptors, plus the three obvious blends of them. Seven is only because Isaac Newton was a mystic, who agreed with JK Rowling that seven is the most powerful magical number. I find seven unpersuasive.

  14. Rob Grigjanis says

    Bruce @17:

    Seven is only because Isaac Newton was a mystic, who agreed with JK Rowling that seven is the most powerful magical number

    He actually started with five, but added orange and indigo to match the number of musical notes in the major scale. I wouldn’t call that mystical.

  15. says

    A mnemonic for sine and cosine? That’s just crazy talk. I just picture a unit circle in my head, and my brain gestalts sine being this one* and cosine being that one†.

    * “This one” being the one parallel to the y-axis, but my brain doesn’t think of that in that literal way, it just knows it as the one.

    † “That one” being the one along the x-axis, but my brain doesn’t think of that in that literal way, it just knows that’s the one.

  16. sonofrojblake says

    @RG, 4:
    Yeah that’s Navy -- the way I heard it was “if it moves, salute it. If it doesn’t salute back, pick it up. If you can’t pick it up, paint it Hadmralty Grey”

  17. Ridana says

    The staff lines and spaces I learned as Every Good Boy Does Fine, and FACE, which wasn’t really an acronym. I don’t think we were ever taught any math mnemonics.
    Roy G. Biv may not be necessary to recall the spectrum order, but it’s way faster for me than processing “what’s between red and yellow” or “is green a shorter or longer wavelength than orange?” since I don’t work with those to the point of it being second nature. Even if I did, I always second-guess myself and have to go through the steps every time to be sure I’m not making a stupid mistake. I don’t know if that’s lessons learned from making stupid mistakes all the time, or just OCD.
    I was many years old before I heard of HOMES as the mnemonic for the Great Lakes. I learned it from crosswords that kept using it in clues and I had no idea what they were talking about. It’s only good for remembering all five, but not their relative positions. I guess you could go with SHMEO, since Michigan and Huron are hydrologically one lake.
    I don’t need a mnemonic to recall the phone number I grew up with. I’m sure that for whatever reason, I’ll remember it until I die, even if I forget my own name.

  18. Holms says

    Similar to moarscienceplz #7, but about planetary order. Being thirsty for astronomy knowledge as far back as I can remember, I knew the order of the planets going back to primary school years and so was greatly surprised to hear from adults, and sometimes even actual astronomers, that they used mnemonics.

    But the oddest mnemonic I have ever heard was the one I was taught -- and still remember -- for the first 20 elements. Similar to Mano’s ‘vibgyor’ pronounced phonetically, it was simply the first 20 atomic symbols pronounced phonetically. H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca, pronounced aitch helly beb k’nov nina m’gal sips clarka (the apostrophes denote a schwa).

  19. Kimpatsu5001 says

    Kids Prefer Cheese Over Fried Green Spinach for Linnaean taxonomy. (Kingdom, Phylum, Class, Order, Family, Genus, Species)

  20. mnb0 says

    “I found those trig definitions pretty easy to remember.”
    Every year several of my pupils are happy with sos cas toa (the English version of this was mentioned in that previous thread.
    But now I wonder: why should anyone learn the colours of a rainbow? In the correct order, on top of it? What’s the use of it? I’m a teacher math and physics and I never cared.

  21. Tethys says

    Colour theory is not about rainbows, it’s about the interactions of the visible spectrum of light. The order is due to visible light for humans spanning the wavelengths between infra-red to ultra-violet.

  22. Rob Grigjanis says

    mnb0 @24: I don’t think there is much use for mnemonics for people who work in the fields they apply to. So, people working on Solar System topics don’t need

    My Very Energetic Mother Just Served Us Nine Pizzas

    but they can be handy for non-specialists chatting about such stuff. I certainly never needed Richard Of York Gave Battle In Vain, but it sounds cool, and it’s true!

  23. garnetstar says

    My Ph.D. adviser had to make a mnemonic to remember the names and order of the 14 lanthanide elements in the periodic table. I kept it, and made a new one of my own for the 14 actinide elements. And yes, I do still remember both mnemomics! That does work.

  24. consciousness razor says

    The staff lines and spaces I learned as Every Good Boy Does Fine, and FACE, which wasn’t really an acronym.

    I learned that when I was young too.* It leaves something to be desired…. Now do bass clef, tenor clef, alto clef, etc. And what’s on the fourth ledger line above the treble clef? How about the space beneath the third line below it?

    Maybe it helped a little when I was first starting out, but now it’s pretty much just a piece of useless trivia for me. All I do is look at the notation, and I just know what I’m looking at, without having to think about it or do a calculation or derive it somehow from something else.

    Same thing with the circle of fifths/fourths (or the “order” of sharps and flats, which is related). I have a mental picture of where things go on the circle, and that’s basically all there is to it. It’s sort of an improvement, in the sense that I can start from anywhere and go around in either direction, since this isn’t tied to a sequence of words (with a “first” word and “last” word) that are supposed to have a meaning in English. Because it’s not a line segment and doesn’t have endpoints. It’s a circle. Big difference.

    *Also, the one for bass clef lines (going up) was “good boys do fine always.” I’m sure there was something for the bass clef spaces too, but ironically I can’t remember what the mnemonic was supposed to be….

  25. Numenaster, whose eyes are up here says

    I haven’t seen this one for taxonomy mentioned yet, but it’s the one I learned in summer classes from our science museum: King Philip Comes Over For Good Spices

  26. KG says

    How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics!

  27. Rob Grigjanis says

    It enables a numskull to memorize a quantity of numerals

    (Euler’s number)

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