## 11. MNEMONICS

#### Subsections

- 11. mnemonics - general
- 11.1 mnemonics
- 11.2 mathematics
- 11.3 computer science
- 11.4 physics
- 11.5 chemistry
- 11.6 biology and medicine
- 11.7 earth sciences
- 11.8 miscellany

### 11.2 MATHEMATICS

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mathematics
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    Pi: Pi = 3.141592653589793238462643383279..................

    From: mshapiro@netlink.nix.com (Michael Shapiro)

    Now I will a rhyme construct
    By chosen words the young instruct.
    Cunningly devised endeavor,
    Con it and remember ever.
    Widths of circle here you see.
    Sketched out in strange obscurity.

    From: stephan@artn.iit.edu (Stephan Meyers)
    Sir, I send a rhyme excelling
    In sacred truth and rigid spelling
    Numerical sprites elucidate
    for me the lexicon's full weight.
    If nature gain, who can complain
    tho' Doc Johnson fulminate.

    From: c1prasad@watson.ibm.com (prasad)
    Sir, I bear a rhyme excelling
    In mystic force and magic spelling;
    Celestial sprites elucidate
    All my own striving can't relate.

    From: gsc@cairo.anu.edu.au (Sean Case)

     A.C. Orr, in: Literary Digest, vol. 32 (1906), p. 84
    Now I, even I, would celebrate in rhymes inept,
    the great immortal Syracusan rivall'd nevermore
    who in his wondrous lore passed on before
    left men his guidance how to circles mensurate.

    Americans can spell "rivall'd" as "rivaled", which works a lot better.

    From:bhuntley@tsegw.tse.com (Brian Huntley):
     How I want a drink, alcoholic of course,
    after the heavy chapters involving quantum mechanics.

    The next 9 digits are given by :
    "All of thy geometry, Herr Planck, is fairly hard."
            - Sir James Jeans

    From: Joona I Palaste <palaste@cc.helsinki.fi>

    How I need a drink, alcoholic of course, after the least valuable
    discovery anybody important has or had anywhere made.

    From: chergarj@cs.com (Chergarj)

    A shortened version:
    How I need a drink, alcoholic of course, after the summer.

    From: J B Youles <john.youles@dial.pipex.com>
    (It is assumed that you know the first digit).

    "I wish I could determine pi
    Eureka! cried the great inventor
    Christmas pudding, Christmas pie
    Is the problem's very centre."

    From: s6sj7gt@aol.com (Mike Keith)
    "May I have a large container of coffee?"
    "Cream and sugar?"

    From: jeyadev@wrc.xerox.bounceback.com (Surendar Jeyadev)

      How I wish I could recollect
      Of circle round
      The exact relation
      Archimede derived.

    From: Jimmy Hoeks <jhoeks@objectmastery.com>

     Here is a mnemonic (from that terrific magazine, Omni, somewhere in the
    late 70s or early 80s) to calculate the circumference of a circle. Not only
    that, but it helps you memorise Pi to five decimals. Best of all, it's a
    limerick

    If you cross a circle with a line
    Which hits the centre and runs from spine to spine
    And the line's length is d
    The circumference will be d times 3.14159

    From: cdsmith <cdsmith@hawaii.rr.com>

    See,  I have a rhyme assisting
    My fevered brain its tasks resisting

    From ian@iglou.com Sat Dec 23 03:25:11 1995
    http://users.aol.com/s6sj7gt/mikerav.htm Poe, E.: Near A Raven

    The poem below, which bears an uncanny similarity to a certain famous poem
    by Edgar Allen Poe, is my latest and most difficult attempt at constrained
    writing. Constrained writing is the art of constructing a work of prose or
    poetry that obeys some artificially-imposed constraint. For example, there
    are two published novels from which the letter 'e' is absent - Gadsby, by
    Ernest Vincent Wright (1938), and La Disparition by George Perec (still in
    print, and even available in a very recent English translation (A Void,
    translated by Gilbert Adair) that also obeys the constraint!).

    Your mission, should you decide to accept it, is to figure out the
    constraint imposed on this poem. The answer is given after the end, so if
    you want to try to figure it out, just look at the beginning of the poem.

          Poe, E.
       Near A Raven

    Midnights so dreary, tired and weary.  Silently pondering volumes extolling
    all by-now obsolete lore.  During my rather long nap - the weirdest tap!
    An ominous vibrating sound disturbing my chamber's antedoor.
        "This", I whispered quietly, "I ignore".

    Perfectly, the intellect remembers: the ghostly fires, a glittering ember.
    Inflamed by lightning's outbursts, windows cast penumbras upon this floor.
    Sorrowful, as one mistreated, unhappy thoughts I heeded:
      That inimitable lesson in elegance - Lenore -
        Is delighting, exciting...nevermore.

    Ominously, curtains parted (my serenity outsmarted), And fear overcame my
    being - the fear of "forevermore".  Fearful foreboding abided, selfish
    sentiment confided, As I said, "Methinks mysterious traveler knocks afore.
        A man is visiting, of age threescore."

    Taking little time, briskly addressing something: "Sir," (robustly) "Tell
    what source originates clamorous noise afore?  Disturbing sleep unkindly,
    is it you a-tapping, so slyly?  Why, devil incarnate!--" Here completely
    unveiled I my antedoor-- Just darkness, I ascertained - nothing more.

    While surrounded by darkness then, I persevered to clearly comprehend.
      I perceived the weirdest dream...of everlasting "nevermores".  Quite,
    quite, quick nocturnal doubts fled - such relief! - as my intellect said,
      (Desiring, imagining still) that perchance the apparition was uttering a
    whispered "Lenore".
        This only, as evermore.

    Silently, I reinforced, remaining anxious, quite scared, afraid,
      While intrusive tap did then come thrice - O, so stronger than sounded
    afore.  "Surely" (said silently) "it was the banging, clanging window
    lattice."
      Glancing out, I quaked, upset by horrors hereinbefore,
        Perceiving: a "nevermore".

    Completely disturbed, I said, "Utter, please, what prevails ahead.
      Repose, relief, cessation, or but more dreary 'nevermores'?"  The bird
    intruded thence - O, irritation ever since! -
      Then sat on Pallas' pallid bust, watching me (I sat not, therefore),
        And stated "nevermores".

    Bemused by raven's dissonance, my soul exclaimed, "I seek intelligence;
    Explain thy purpose, or soon cease intoning forlorn 'nevermores'!"
    "Nevermores", winged corvus proclaimed - thusly was a raven named?
      Actually maintain a surname, upon Pluvious seashore?
        I heard an oppressive "nevermore".

    My sentiments extremely pained, to perceive an utterance so plain,
      Most interested, mystified, a meaning I hoped for.  "Surely," said the
    raven's watcher, "separate discourse is wiser.
      Therefore, liberation I'll obtain, retreating heretofore -
        Eliminating all the 'nevermores' ".

    Still, the detestable raven just remained, unmoving, on sculptured bust.
      Always saying "never" (by a red chamber's door).  A poor, tender
    heartache maven - a sorrowful bird - a raven!
      O, I wished thoroughly, forthwith, that he'd fly heretofore.
        Still sitting, he recited "nevermores".

    The raven's dirge induced alarm - "nevermore" quite wearisome.
      I meditated: "Might its utterances summarize of a calamity before?"  O, a
    sadness was manifest - a sorrowful cry of unrest;
      "O," I thought sincerely, "it's a melancholy great - furthermore,
        Removing doubt, this explains 'nevermores' ".

    Seizing just that moment to sit - closely, carefully, advancing beside it,
      Sinking down, intrigued, where velvet cushion lay afore.  A creature,
    midnight-black, watched there - it studied my soul, unawares.
      Wherefore, explanations my insight entreated for.
        Silently, I pondered the "nevermores".

    "Disentangle, nefarious bird! Disengage - I am disturbed!"
       Intently its eye burned, raising the cry within my core.  "That
    delectable Lenore - whose velvet pillow this was, heretofore,
      Departed thence, unsettling my consciousness therefore.
        She's returning - that maiden - aye, nevermore."

    Since, to me, that thought was madness, I renounced continuing sadness.
      Continuing on, I soundly, adamantly forswore: "Wretch," (addressing
    blackbird only) "fly swiftly - emancipate me!"

      "Respite, respite, detestable raven - and discharge me, I implore!"
        A ghostly answer of: "nevermore".

    " 'Tis a prophet? Wraith? Strange devil? Or the ultimate evil?"
      "Answer, tempter-sent creature!", I inquired, like before.  "Forlorn,
    though firmly undaunted, with 'nevermores' quite indoctrinated,
      Is everything depressing, generating great sorrow evermore?
        I am subdued!", I then swore.

    In answer, the raven turned - relentless distress it spurned.
      "Comfort, surcease, quiet, silence!" - pleaded I for.  "Will my (abusive
    raven!) sorrows persist unabated?
      Nevermore Lenore respondeth?", adamantly I encored.
        The appeal was ignored.

    "O, satanic inferno's denizen -- go!", I said boldly, standing then.

      "Take henceforth loathsome "nevermores" - O, to an ugly Plutonian shore!
    Let nary one expression, O bird, remain still here, replacing mirth.

      Promptly leave and retreat!", I resolutely swore.
        Blackbird's riposte: "nevermore".

    So he sitteth, observing always, perching ominously on these doorways.
      Squatting on the stony bust so untroubled, O therefore.  Suffering stark
    raven's conversings, so I am condemned, subserving,
      To a nightmare cursed, containing miseries galore.
        Thus henceforth, I'll rise (from a darkness, a grave) -- nevermore!

                -- Original: E. Poe
                -- Redone by measuring circles.

    Solution:

    Despite the rather difficult constraint (to be revealed shortly), observe
    how this revised version of "The Raven" duplicates the story, tone, and
    rhyme scheme of the original fairly closely (including the internal rhymes
    in the first and third line of each stanza). The only major concession to
    the form is that the original has six lines per stanza, with the fourth and
    fifth lines usually being very similar. Due to the nature of the constraint
    I imposed (revealed in the next paragraph), this would have been nearly
    impossible to do. Therefore, this version eliminates the similar line in
    each stanza.

    Give up? Hint: Start at the very beginning (with the word 'Poe') and write
    next to each word the number of letters it contains. Put a decimal point
    after the first digit. Look at the first few digits (or more if, like me,
    you know the first several hundred by heart).  Are you impressed yet?

    Even given the rather difficult constraint, I was able to match the
    original very closely in spots. The very first line, although its meter is
    wrong, is surprisingly close. Others which are very close, even to the
    point of using many of the same words, are stanza 4 line 5, stanza 6 line
    3, stanza 7 line 4, and stanza 15, line 1.

    Note the use of the term "blackbird" a couple of times. Though not,
    strictly speaking, correct (a raven is a black bird, not a blackbird), the
    term is particularly appropriate. It is a subtle reference to George
    Perec's La Disparition, which contains another written-with-constraints
    version of "The Raven" - in this case the constraint being "write it in
    French without using the letter 'e'".  In the English translation of La
    Disparition by Gilbert Adair, the poem is faithfully translated into
    English, also without using letter 'e'. The English version of the poem is
    titled (wait for it...) Black Bird!

    The poem encodes the first 740 decimals of pi. The encoding rule is this: a
    word of N letters represents the digit N if N<9, the digit 0 if N=10, and
    two adjacent digits if N>10 (e.g., a 12-letter word represents the digit
    '1' followed by '2').

    A much less well-known example is this nice poem by Joseph Shipley (1960):

         But a time I spent wandering in bloomy night;
         Yon tower, tinkling chimewise, loftily opportune.
         Out, up, and together came sudden to Sunday rite,
         The one solemnly off to correct plenilune.

    I believe that "Near a Raven" establishes the world record for length of a
    pi mnemonic. I would be glad to hear of other wordy attempts, either in
    prose or poetry. Perhaps someone would like to attempt a short story or a
    novel?!

    From: s6sj7gt@aol.com (Mike Keith)

    I have just finished composing a short story that sets a new world record
    for the length of a pi mnemonic: 3835 decimals!

    Check it out, at

    http://users.aol.com/s6sj7gt/cadenza.htm

    You may recognize the first section, a pi-digits version of Edgar Allen
    Poe's "The Raven" that I wrote about a year ago [See above]. The story
    takes off from there, in a somewhat science-fictiony vein.

    From: wald@math.uconn.edu (Kevin Wald)

    It occurred to me that the technique used in the The Raven version for
    representing 0, using 10-letter words, is a trifle inelegant; ideally, one
    should use zero-letter words. Alas, these are in short supply in written
    English and the best examples, numbers written in Arabic numerals, have a
    tendency not to come up in poetry. Nonetheless, taking advantage of a
    different commonly-used symbol, I've just completed the following (a
    translation of Sappho's "Hymn to Aphrodite"):

       Now I pray, O queen Aphrodite on ornate chair,
       Sly, death-shunning thunderer-progeny,
       Devastate not my own emotions with aching or sorrow;

       Come the way formerly you, my plaints detecting,
       Heard & in hurrying downward left
       A begetter's mansion. A golden cabriolet

       You harnessed; posthaste did finches impel 't &
       Wings vibrated by & enveloped Midgard
       From firmament down unto lower midranges of sky, &

       Arrived speedily. O milady, holy & eterne in splendor,
       Smiled ye & inquired wherefore lamenting resounds,
       Whence my distress, &

       For what, signally, I'm heart-mad.
       "Whom am I t' ensnare & seduce?
       Whoever currently troubles ye, O poet?

       Rebuffer & offering-dumper shall I set to pursuing ye now, &
       Giving thence many gifties; & transform now-unloving maid
       Into adorer (& unwilling wooer, maybe)." &

       Speed likewise to me now, I entreat; my heart set again
       Woelessly free, & whatever I so heartily wish achieved p.d.q.,
       Fulfill that thing, & be Psappho's ally.

    From: thomas@melchior.frmug.fr.net (Thomas Quinot)
     For PI, we have in France : Here is the full mnemonic, from Helen
    A. Merrill's Mathematical Exurcsions (Dover, 1957), reprinted in
    Dr. Crypton's Mind Benders from Science Digest (St. Martin's Press, 1981).

    Que j'aime a faire apprendre un nombre utile aux sages Immortel Archimede,
    artiste, ingenieur Qui de ton jugement peut priser la valeur ?  Pour moi
    ton probleme eut de pareils avantages.

    From: Daniel Kobler <kobler@dma.epfl.ch>
    1.  Que j'aime a faire apprendre un nombre utile aux sages.

    2.  Glorieux Archimede, artiste ingenieux !
    3.  Toi, de qui Syracuse, aime encore la gloire,
    4.  Soit ton nom conserve par de savants grimoires.

    5.  Jadis, mysterieux, un probleme existait.
    6.  Tout l'admirable procede (l'oeuvre etonnante !)
    7.  Que Pythagore decouvrit aux anciens Grecs :

    8.  O quadrature ! Vieux tourment du philosophe ! Sibylline rondeur !
    9.  Trop longtemps vous avez defie Pythagore et ses imitateurs !

    10. Comment integrer l'espace plan circulaire ?
    11. Thales tu tomberas ! Platon tu desesperes !

    12. Apparait Archimede :

    13. Archimede inscrira dedans un hexagone :
    14. Appreciera son aire fonction du rayon ;
    15. Pas trop ne s'y tiendra !
    16. Dedoublera chaque element anterieur,
    17. Toujours de l'orbe calculee approchera ;
    18. Laquelle limite donne l'arc,
    19. La longueur de cet inquietant cercle,

    20. Ennemi trop rebelle !

    21. Professeur, enseignez son probleme avec zele ...

    You can change lines 11 et 12 to
    11'. Former un triangle auquel il equivaudra ?
    12'. Nouvelle invention :

    and lines 18 and 19 to
    18'. Definira limite ; enfin, l'arc,
    19'. le limiteur de cet inquietant cercle

    In Dutch: Mag 't kind 't paard roskammen en voeren?

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    From: Joe Fineman <jcf@TheWorld.com>
     e: To destroy a building we detonate a quantity of hydrogen bombs.  (count
    the letters of each word)

    From: Joona I Palaste <palaste@cc.helsinki.fi>

    We require a mnemonic to remember e whenever we scribble math.

    From: "Prai Jei" <pvstownsend@prai-jei.fsnet.co.uk>

    In seeking a mnemonic, we composed a sentence of sensible words.

    From: Jean Debord <JDebord@compuserve.com>
    A french riddle to remember the digits of "e" :

    Tu aideras a rappeler ta quantite a beaucoup de docteurs amis (You will
    help to remember your quantity to many friend doctors) I have found them in
    the last issue (October 1998) of "Pour la science" (french edition of
    "Scientific American").

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    From: "¼»óÇö" <mathmaniac@hanmail.net>

     Reading the following, It would help to know Korean counting system:

    Korean Counting System

    Number 1 2 3 4 5 6 7 8 9 Korean hana dul set net daseot yeoseot ilgop
    yeodeol ahop Sino-K il i sam sa o yuk chil pal gu

    And for zero, there is no Korean word for that, but there are two
    Sino-Korean* reading: yeong and gong *Sino-Korean: Reading of Chinese
    letters in Korean fashion.

    Isn't it fairly nice that there are two readings for every number?  I think
    Korean counting is a ideal system to make mnemonics!

    Note. Since Korean is non-European language, it is hard to give an
    one-to-one literal translation. And sentences for mnemonics are usually
    very skewed, therefore it is impossible to give an literal
    translation. (However, native speaker of Korean will understand every
    proper meanings and silly nuances immediately...)

    Root 3: I think this is the best one I've ever heard.

    There is a mnemonic to memorize a value of root 3 in Korea:

    han chi se du go o go in ne 1.  7 3 2 0 5 0 1 4

    This sounds like 'hana chil set dul gong o gong il net', (especially when
    you ignore the last consonants or vowel!)  meaning '1 7 3 2 0 5 0 1 4' in
    Korean counting.

    What this sentence means is quite meaningless: (Root 3) is coming after
    counting one chi* (of whatever) *chi: Korean traditional measuring unit for
    length.

    After counting one chi (of whatever), root 3 will come to you. :)

    Root 2: This one is fairly good, though digits aren't many.

    wan ne wan ne dul il se 1.  4 1 4 2 1 3

    For sure, this sounds like 'hana net hana net dul il set'.  which means '1
    4 1 4 2 1 3' in Korean counting.

    This sentence means: Coming! Coming! (something coming is) two!

    After chanting this, the result is 'coming' of the root 'two'. :)

    If I got more of these stuffs, I would send it, too.

    P.S: Was it interesting? Perhaps it is boring for someone who knows nothing
    about Korean... But I hope you enjoy this one.

    PPS: I hope to recieve your short answer. Is my English O.K.?  This one is
    my nearly first attempt to write an E-mail in English...

    From Seo SangHyeon (living in the city of Uijongbu, Korea)

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    From: "Chiem Whua Ma" <sdragon@flash.net>
     My father learned this on in Hong Kong and I can't believe it hasn't
    made it's way here sooner.

    The mnemonic doesn't hold in English, but it's only needed for the
    placement of the functions which is easily remembered.

    (This MUST be viewed in a non-proportional font):
            -----------------
            |               |
            |  SIN-----COS  |
            |    \     /    |
            |     \   /     |
            |      \ /      |
            |  TAN--1--COT  |
            |   |  / \  |   |
            |   | /   \ |   |
            |   |/     \|   |
            |  SEC     CSC  |
            |               |
            -----------------

    (SIN TAN SEC on left, CO-functions on right, 1 in the middle)

    Using this chart (I just look at it in my head) you can remember the
    following things:

    Across the 1:
    	1/SIN=CSC or 1/CSC=SIN
    	1/TAN=COT or 1/COT=TAN
    	1/SEC=COS or 1/COS=SEC

    Down any triangle:
    	SIN^2+COS^2=1
    	TAN^2+1 =SEC^2
                1+COT^2=CSC^2

    Up any triangle:
    	SEC^2-1 =TAN^2 or 1+TAN^2=SEC^2
    	CSC^2-1 =COT^2 or CSC^2-COT^2=1
    	    1-SIN^2=COS^2 or 1-COS^2=SIN^2

    A function and its two nearest CLOCKWISE or COUNTERCLOCKWISE neighbors
    around any edge of the square:
    	(listed starting at tan going clockwise)
    		TAN=SIN/COS
    		SIN=COS/COT
    		COS=COT/CSC
    		CSC=SEC/TAN
    		SEC=TAN/SIN
    	(listed starting at tan going counter-clockwise)
    		TAN=SEC/CSC
    		SEC=CSC/COT
    		CSC=COT/COS
    		COS=SIN/TAN
    		SIN=TAN/SEC

    A function and its two neighbors around any edge of the square:
    	(listed starting at tan going clockwise)
    		TAN=SIN*SEC
    		SIN=COS*TAN
    		COS=COT*SIN
    		CSC=COT*SEC

SEC=TAN*CSC

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    Here are some phrases used to remember SIN, COS, and TAN.  (SIN =
    Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A).

    From: dannyb@panix.com (danny burstein):

     Soh-Kah-Toa Sine=opposite/hypotenuse, etc.

    From: stephan@artn.iit.edu (Stephan Meyers)

     Some officers add curly auburn hair to offer attraction

    From: kcousins@awadi.com.au (Kevin Cousins)

     Sydney Opera House: Costs are higher than originally anticipated.

    From: ahcson@ccwf.cc.utexas.edu (Tree Pig)

     how about Oscar Had A Hit Of Acid?  write the first letter of each word
    along with the letters SCT like : S OH (sine = opposite/hypotenuse) C AH
    (cosine = adjacent/hypotenuse) T OA (tangent = opposite/adjacent)

    From: Alan Meban <AMEBAN@bfsec.bt.co.uk>
     Two Old Angels Skipped Over Heaven Carrying Ancient Harps

    From: pdundas@bfsec.bt.co.uk (Paul Dundas)

     Two Old Angels Skipped Over Heaven Carrying A Harp

    From: pyotr@chinook.halcyon.com (Peter D. Hampe)

     Oscar Had A Heap Of Apples - you just have to remember the sine, cosine,
    tangent progression on your own.

    From: Andrew Rogers (rogers@sasuga.hi.com):

     Saddle Our Horses, Canter Away Happily, To Other Adventures.

    From: cs92dy@cen.ex.ac.uk sin/cos etc.
      Silly old Henry, caught Albert Hugging/Humping two old Aunts.

    From: heath@pi.cs.fsu.edu0 (Taliver B Heath)

     Oscar had a hairy old ass.

    From: robin sewoke <rsewoke@cwcom.net>
     (T)ommy (O)n (A) (S)hip (O)f (H)is (C)aught (A) (H)addock

    T = O/A S = O/H C=A/H

          SOHCAHTOA (sock-a-toe-a)

          The Cat Sat
          On An Orange
          And Howled Hard

          Some Old Hulks
          Carry A Huge
          Tub Of Ale

          Silly Old Hitler
          Caused Awful Headaches
          To Our Airmen

          Some Old Hag
          Cracked All Her
          Teeth On Asparagus

          Some Old Hairy
          Camels Are Hairier
          Than Others Are

          Silly Old Harry
          Caught A Herring
          Trawling Off America

          SOPHY, CADHY, TOAD

    From: mau059@clss1.bangor.ac.uk (D.M.Rigby)

     Smiles Of Happiness Come After Having Tankards Of Ale!!!

    From: John Jetmore <jj33@evansville.edu>

     I was taught the following phrase to remember SIN, COS, and TAN
    relationships:

    "The Old Arab Sat On His Camel And Hiccupped"

    From: raistlin@mentor.cc.purdue.edu (Paul)

     For remembering the sign of trig functions in the quadrants:

    All Suckers Take Calculus: in quadrants one through four

                    S | A
                    ---|---
                    T | C

    All=sin, cos, and tan are all posative Suckers=sine positive (others
    negative) Take=tangent positive (others negative) Calculus=cosine positive
    (others negative)

    From: royl@zen.icl.co.uk (Roy Lakin)
    I was taught it as a CAST-iron rule
                       ^
                       |
                       |
                       |             ^ positive
                    S  |  A          |
                    ---+-----------> | 0
                    T  |  C          |
                                     v negative

    taking quadrant 1 (all) covering positive X and Y

    From: dloucks@primenet.com (Donovan Loucks)

       Signs of trignometric functions in the four quadrants:
          Aunt Sally Tickles Cannibals
          Admiral Spock Tickles Cabbages
          After Saturday, Tommy Croaked
          Atra Shaved Timmy Closer

    From: "Forrest Davie" <fdavie@calpoly.edu>
          All stoner's take crack.

    From: Vinod Bamalwa <ncb@giascl01.vsnl.net.in>
     Perp=Perpendicular /|
    hyp=hypotenuese (hyp)/ |
     (perpendicular) base=base /___|
    				Base

    Sine=Perp/hyp Cos=Base/hyp Tan=perp/base

    In one single rhyme it can be summarised as: Some people have curly brown
    hair turned permanantly black.  Sin= p/h cos=b/h Tan=p/b

    From: Jan OR Christiane Woloniecki <janandchris@northrock.bm>
    Scruffy Old He Cats Are Hungrier Than Other Animals (Rules of Triganometry)

    For positive or negative signs: All Sausages Taste Cool (or, very UK this)
    All Trains Stop (at) Crewe

    From: Ben Bullock <ben@hayamasa.demon.co.uk>
     All Sadists Teach Chemistry

    From: Stephen Tonkin <sft@nospam.demon.co.uk> Trig ratios from my father in
    law: Some Orifices Have Curly Auburn Hair To Obscure Approach.

    From: "Wyburn J (SoTech - M & S)" <jwyburn1@glam.ac.uk>
    Spite Or Homesickness Caused Adolf Hitler To Occupy Austria.

mathematics
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    From: Sanya Rajan <sanya_rajan@intekom.co.za>

    I've got a mnemonic to remember SIN, COS and TAN

    Silly Old Hens,
    Cackle And Howl,
    Till Old Age.

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    From: "Matthew Burakowski" <mburakow@stevens-tech.edu>
    Another mnemonic for remembering sin, cos, tan...

    Some old hippy
    Caught another hippy
    Tripping on acid

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    From: Jim Hollerman <jhollerm@usd.edu>
     I don't have a better one for the roots of quadratics, but I learned the
    sine-cosine song for the sum and difference formulae.  (I'll describe it
    here, but it works better if you can hear the chant.)

    You memorize the formulae for the sine of a sum or difference on the first
    line and the cosine on the second.  The chant goes "sine cosine cosine sine
    cosine cosine sign sine sine" (the last three are a triplet -- done in the
    same time as two of the previous) then fill in the angle names alternately
    and the + and - signs as appropriate.  (That's the purpose of the 'sign' --
    to remind you that if the angles are added, then the products of trig
    functions are subtracted.)

    I also learned a cute, no-brainer method of remembering the second
    derivative test.  You'll see the trick if you draw a smiley face with +'s
    for eyes and a frowning face with -'s for eyes.  (I don't really like to
    teach this one, as I think that the students are better off understanding
    what the sign of the second derivative tells us about the first, and what
    that entails about the concavity of the function.  I usually mention it
    during the review for the final exam, rather than the chapter test that
    includes the second derivative test.

mathematics
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    Weber Tracy L (tweber@cc.brynmawr.edu):

     "Please excuse my dear aunt Sally" or "PEMDAS" Default operator precedence
    () ^ * / + -

    From: g4klx@g4klx.demon.co.uk (Jonathan Naylor)
    I was taught a longer version at school:

    "Brackets of my dear aunt Sally"

    Which nicely included the fact that brackets and "of" were higher in
    precedence that * / + -. Being a bunch of nasty snivelling (sp?) ten year
    olds, we changed it to "Bollocks of my dear aunt Sally". For our American
    readers, Bollocks == Gonads. Not biologically correct but who cares ?

    From: magyar@hss.caltech.edu (Ted Turocy)

     Please excuse my dear aunt Sally parentheses exponents multiplication
    division addition subtraction

    From: dloucks@primenet.com (Donovan Loucks)
    Porno Pictures Make Dad Act

    Silly (algebraic order of operations)

    From: "Martin Kimber" <mkimber@ntlworld.com>
    Brackets           Blue
    Order              Ovaries
    Division           Disgust
    Multiplitcation    My
    Addition           Anal
    Subtraction        Sultanas

    It didn't win best team name in our pub quiz,
    but it got the biggest laugh.

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    From: boingo@agora.rdrop.com (Capuchin=Jeme A Brelin)

     Quotient rule for derivatives ala Cab Calloway: Hodehi minus hideho over hoho.

    From: RM Mentock <mentock@mindspring.com>

     My brother gave me this one from his math professor.  It is a mnemonic for
    the quotient rule, called the Heidi Ho, or Cab Calloway, mnemonic.  Hi
    represents the numerator (high), Ho the denominator (low), and De is the
    derivative operator.

    Ho De Hi minus Hi De Ho over Ho Ho

    Sometimes it's called the Santa Claus mnemonic.

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    From: ssw@hamlet.umd.edu (Susan Schwartz Wildstrom)
     My friend and colleague, Lynn Gruner (who teaches BC Calculus with me at
    Walt Whitman HS in Bethesda, MD) has altered the quotient rule song that
    we received some years back.  Her version (sung to OLD MACDONALD'S FARM)
    goes like this:
            Lo-de-hi less hi-de-lo   EIEIO
            Then draw the line and down below   EIEIO
            With a dx here and a dy there
            Here a slope, yes there's hope, you can cope
            Denominator squared will go   EIEIO

    I composed a chain rule "song" to the tune of Allouette, but it's too
    long to be of much value as a mnemonic.  The point of the song certainly
    underscores how the chain rule works, but it's not one you'd be likely to
    remember.

            On another mathematical subject, Lynn also uses EIEIO as a
    mnemonic for extracting roots and when the absolute value symbols are
    required in the answer  Even Index, Even In yielding Odd  (exponents).

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    From: Robert Bellamy (Cssna206@aol.com)

    The numerator is called  hi.
    The demoniator is called  ho.
    The derative is called  d
    The derivative of the fraction is as follows-
    ho  d(hi) minus hi  d(ho) over ho ho

    yd(x)-xd(y)/Ysquare

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    From:  Duran Castore <duran_castore@yahoo.com>
     sin 2a = 2 * sin a * cos a    --  2sicko
     cos 2a = (cos a)^2 - (sin a)^2   --  coas2si2
      (no hint for signal, but is obvious that is "-", for cos^2 + sin^2 = 1
    ...)

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    From: David Vivash <PMA98DAV@shef.ac.uk>
     I remember one my physics teacher taught me (I still use it... but that
    probably says more about me than the mnemonic)

    Is dc negative?

    Means Integrate Sine / Differentiate cos gives negative

mathematics
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    From: Susan Schwartz Wildstrom <ssw@csc.umd.edu>
     A student of mine learned a song (from her mother) that helps her remember
    it. It is sung to the tune of Pop Goes the Weasel

            X equals negative B
            Plus or minus square root
            of B squared minus four A C
            All over two A.

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    From: Jeff <munchcruncher@nospam.msn.com>
     When I was in Jr. High and first learning about the trig functions, I
    thought of Howard Cosell. "Cosell is an a**hole" for cos=a/h. I never got
    sine and cosine confused since.

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    From: John Harper <harper@kauri.vuw.ac.nz>
     For those wishing to remember which is the domain and which the range:

    ^ y
    |
    |-----\___
    |  _   \__|~@@@@@@@
    | |_|   \    ~~@@@@@@
    |____   /       ~~@@@@@@@
    |____| /
    |-----/
    |
    +-------------------> x
      Home on the Range

    (Acknowledgements to whoever drew this on a men's room wall in the U of
    Chicago mathematics department many years ago, which is where I saw it.
    Few graffiti one sees in such places are so useful!)

mathematics
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    From: "Wyburn J (SoTech - M & S)" <jwyburn1@glam.ac.uk>

    May I submit the following of my own devising?

    MATRICES: Multiply Appropriate Two Row Into Column, Evaluate Sum

    MOM'S ACE BRA: Matrices Only Multiply Should A's Columns Equal B's Rows...
    Actually

next page | Index | Comments and Contributions

#### Subsections

- 11. mnemonics - general
- 11.1 mnemonics
- 11.2 mathematics
- 11.3 computer science
- 11.4 physics
- 11.5 chemistry
- 11.6 biology and medicine
- 11.7 earth sciences
- 11.8 miscellany

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