11. MNEMONICS

Subsections

11.2 MATHEMATICS

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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 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#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 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#NoSpam.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#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 g५ttlich!
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 a-walc'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 ॆ noite, escuridॅo na cidade pobre"

sem = 3 letters
o = 1 letter
fogo = 4 letters
ॆ = 1 letter
noite = 5 letters
escuridॅo = 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 journ़es de 1830 ont renvers़e 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.prai-jei.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: "ञऐझ२ऩ५" <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 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#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 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#NoSpam.panix.com (danny burstein):

 Soh-Kah-Toa 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 (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#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 CAST-iron 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.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#NoSpam.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.

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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:
        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#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 


mathematics
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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
...)

mathematics
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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

mathematics
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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.

mathematics
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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!)

mathematics
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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

mathematics
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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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