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Pi: Pi = 3.141592653589793238462643383279.................. From: mshapiro#NoSpam.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#NoSpam.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#NoSpam.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#NoSpam.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#NoSpam.tsegw.tse.com (Brian Huntley): How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics. September 11 September 16 The next 9 digits are given by : "All of thy geometry, Herr Planck, is fairly hard."  Sir James Jeans From: Joona I Palaste <palaste#NoSpam.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#NoSpam.cs.com (Chergarj) A shortened version: How I need a drink, alcoholic of course, after the summer. From: J B Youles <john.youles#NoSpam.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#NoSpam.aol.com (Mike Keith) "May I have a large container of coffee?" "Cream and sugar?" From: jeyadev#NoSpam.wrc.xerox.bounceback.com (Surendar Jeyadev) How I wish I could recollect Of circle round The exact relation Archimede derived. From: Jimmy Hoeks <jhoeks#NoSpam.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: Proginoskes <CCHeckman#NoSpam.gmail.com> How I wish I could calculate pi.  Christopher Heckman From: cdsmith <cdsmith#NoSpam.hawaii.rr.com> See, I have a rhyme assisting My fevered brain its tasks resisting From ian#NoSpam.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 artificiallyimposed 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 bynow 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 atapping, 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, midnightblack, 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, temptersent 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 writtenwithconstraints 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 12letter word represents the digit '1' followed by '2'). A much less wellknown 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#NoSpam.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 pidigits 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 sciencefictiony vein. From: wald#NoSpam.math.uconn.edu (Kevin Wald) It occurred to me that the technique used in the The Raven version for representing 0, using 10letter words, is a trifle inelegant; ideally, one should use zeroletter 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 commonlyused 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, deathshunning thundererprogeny, 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 heartmad. "Whom am I t' ensnare & seduce? Whoever currently troubles ye, O poet? Rebuffer & offeringdumper shall I set to pursuing ye now, & Giving thence many gifties; & transform nowunloving 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#NoSpam.melchior.frmug.fr.net (Thomas Quinot) For PI, we have in France : 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#NoSpam.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? In German: Wie? O! Dies π Machst ernstlich so vielen viele Möh! Lernt immerhin, Jönglinge, leichte Verselein, Wie so sum Beispiel dies dörfte zu merken sein. Dir, O Held, o alter Philosoph, du RiesengenieQ Wie viele Tausende bewundern Geister Himmlisch wie du und gą„«ttlich! Noch reiner in Aeonen Wird das uns strahlen, Wie im lichten Morgenrot Spanish: Con 1 palo y 5 ladrillos se pueden hacer mil cosas Bretons: Piv a zebr awalc'h dimerc'her? Ne lavaro netra, tud Breizh! From: Renan <renan.birck#NoSpam.gmail.com> Method in Portuguese to memorize pi to 8 digits. Just count the number of letters for each word in this sentence, it's a digit of PI (starts at 3, you know where the dot goes): "sem o fogo ą„ noite, escuridą„ o na cidade pobre" sem = 3 letters o = 1 letter fogo = 4 letters ą„ = 1 letter noite = 5 letters escuridą„ o = 9 letters na = 2 letters cidade = 6 letters pobre = 5 letters What it means is pretty meaningless: "Without the fire at night, darkness in the poor city". Obviously this only works in Portuguese.
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1/pi Les trois journą¤¼es de 1830 ont renversą¤¼e 89
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From: Joe Fineman <jcf#NoSpam.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#NoSpam.cc.helsinki.fi> We require a mnemonic to remember e whenever we scribble math. From: "Prai Jei" <pvstownsend#NoSpam.praijei.fsnet.co.uk> In seeking a mnemonic, we composed a sentence of sensible words. From: Jean Debord <JDebord#NoSpam.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: "ą¤ą¤ą¤ą„Øą¤©ą„«" <mathmaniac#NoSpam.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 SinoK il i sam sa o yuk chil pal gu And for zero, there is no Korean word for that, but there are two SinoKorean* reading: yeong and gong *SinoKorean: 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 nonEuropean language, it is hard to give an onetoone 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 Email in English... From Seo SangHyeon (living in the city of Uijongbu, Korea)
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From: "Chiem Whua Ma" <sdragon#NoSpam.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 nonproportional font):     SINCOS   \ /   \ /   \ /   TAN1COT    / \     / \    / \   SEC CSC     (SIN TAN SEC on left, COfunctions 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^21 =TAN^2 or 1+TAN^2=SEC^2 CSC^21 =COT^2 or CSC^2COT^2=1 1SIN^2=COS^2 or 1COS^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 counterclockwise) 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*SECSEC=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#NoSpam.panix.com (danny burstein): SohKahToa Sine=opposite/hypotenuse, etc. From: stephan#NoSpam.artn.iit.edu (Stephan Meyers) Some officers add curly auburn hair to offer attraction From: kcousins#NoSpam.awadi.com.au (Kevin Cousins) Sydney Opera House: Costs are higher than originally anticipated. From: ahcson#NoSpam.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#NoSpam.bfsec.bt.co.uk> Two Old Angels Skipped Over Heaven Carrying Ancient Harps From: pdundas#NoSpam.bfsec.bt.co.uk (Paul Dundas) Two Old Angels Skipped Over Heaven Carrying A Harp From: pyotr#NoSpam.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#NoSpam.sasuga.hi.com): Saddle Our Horses, Canter Away Happily, To Other Adventures. From: cs92dy#NoSpam.cen.ex.ac.uk sin/cos etc. Silly old Henry, caught Albert Hugging/Humping two old Aunts. From: heath#NoSpam.pi.cs.fsu.edu0 (Taliver B Heath) Oscar had a hairy old ass. From: robin sewoke <rsewoke#NoSpam.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 (sockatoea) 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#NoSpam.clss1.bangor.ac.uk (D.M.Rigby) Smiles Of Happiness Come After Having Tankards Of Ale!!! From: John Jetmore <jj33#NoSpam.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#NoSpam.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#NoSpam.zen.icl.co.uk (Roy Lakin) I was taught it as a CASTiron rule ^    ^ positive S  A  +>  0 T  C  v negative taking quadrant 1 (all) covering positive X and Y From: dloucks#NoSpam.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#NoSpam.calpoly.edu> All stoner's take crack. From: Vinod Bamalwa <ncb#NoSpam.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: preeti sarkar <shubhangda_me#NoSpam.yahoo.co.in> Some People Have Curly Black Hair Through Proper Brushing From: Jan OR Christiane Woloniecki <janandchris#NoSpam.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#NoSpam.hayamasa.demon.co.uk> All Sadists Teach Chemistry From: Stephen Tonkin <sft#NoSpam.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#NoSpam.glam.ac.uk> Spite Or Homesickness Caused Adolf Hitler To Occupy Austria. From: Ming Tang <project.shinkirou#NoSpam.gmail.com> Here is a mnemonic for the reciprocal trigonometric ratios: (view in a monospace font) 321 sin > csc cos > sec tan > cot By reading the three ratios vertically, you get "csc", "seo" and "cct". Notice the "csc" got all 3 letters, right, and the "se"o got the first 2 letters of "sec" right, and "c"ct got the first 1 letter of "cot" right. Therefore, when you forget some of reciprocal ratios, start by writing the following on paper: csc s c and the first letters will remind you the ratios.
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From: Sanya Rajan <sanya_rajan#NoSpam.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#NoSpam.stevenstech.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#NoSpam.usd.edu> I don't have a better one for the roots of quadratics, but I learned the sinecosine 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, nobrainer 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.
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Weber Tracy L (tweber#NoSpam.cc.brynmawr.edu): "Please excuse my dear aunt Sally" or "PEMDAS" Default operator precedence () ^ * / +  From: g4klx#NoSpam.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#NoSpam.hss.caltech.edu (Ted Turocy) Please excuse my dear aunt Sally parentheses exponents multiplication division addition subtraction From: dloucks#NoSpam.primenet.com (Donovan Loucks) Porno Pictures Make Dad Act Silly (algebraic order of operations) From: "Martin Kimber" <mkimber#NoSpam.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#NoSpam.agora.rdrop.com (Capuchin=Jeme A Brelin) Quotient rule for derivatives ala Cab Calloway: Hodehi minus hideho over hoho. From: RM Mentock <mentock#NoSpam.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#NoSpam.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: Lodehi less hidelo 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#NoSpam.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#NoSpam.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#NoSpam.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
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From: Susan Schwartz Wildstrom <ssw#NoSpam.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.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#NoSpam.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!)
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From: "Wyburn J (SoTech  M & S)" <jwyburn1#NoSpam.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
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From: G. L. Honaker, Jr., curios#NoSpam.bvub.com In the early morning, astronomers spiritualized nonmathematicians. Counting the letters of each word gives you the first seven prime numbers.
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