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From: mathwft#NoSpam.math.canterbury.ac.nz (Bill Taylor)
Here are some more. Definitely all my own work. CAPs for stress.
========================================
November 17
September 26
The Moebius strip is a pain,
When you cut it again and again,
But if you should wedge
A large disk round the edge
Then you just get a PROjective plane.
========================================
If you have a cross-CAP on your sphere,
And you give it a circle-shaped tear,
Then just shake it about
And untangle it out
And a Moebius strip will appear!
========================================
Consider the pitiful plight
Of a runner who wasn't too bright
But he sprinted so fast,
That he vanished at last
By red-shifting himself out of sight.
========================================
In the near-light speed space-ship I'm in,
I went rocketting off from my twin;
But since I'VE been away
I've aged hardly a day
And just LOOK at the state that he's in!
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April 15
September 18
(e to the i) to the pi,
And plus one leaves you nought but a sigh.
This fact amazed Euler
That genius toiler,
And still gives US pause, bye the bye.
========================================
And finally one sent to me in an email...
A mathematician named Joe,
Said "Really it just can't be so;
"My wife, for her sins,
"Is going to have twins,
"And 2 into 1 doesn't go!"
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From: Bill Taylor (W.Taylor#NoSpam.math.canterbury.ac.nz) A go-go lap dancer, a pip, Was able to peel in a zip. But she read science fiction, And died of constriction, Attempting a Mobius strip.
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From: "Helge Moulding" <hmoulding#NoSpam.excite.com> When I set k equal to 0, I can be a mathematical hero: If I should decide By k to divide, Then it's clear that 1 = 0. -- Helge "No rhyme nor reason" Moulding
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From: Larry Bavly <bavly#NoSpam.rci.rutgers.edu> A calculus student upset as could be That his antiderivative just didn't agree With the answer in the book Even after a second look Indeed it was off, but by a constant C.
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From: klein_bottle#NoSpam.hotmail.com (Jonah Edwards) If you integrate zee squared dee zee From one to the cube root of three Multiplied by cosine Of three pi over nine You get natural log of the cube root of e
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From: naphtalia_leba#NoSpam.yahoo.com The mathematician Von Blecks Derived the equation for sex. He found a good f*** Isn't patience or luck But a function of Y over X.
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From: Keith Sullivan (KSullivan#NoSpam.worldnet.att.net)
THE MAGIC OF STATISTICS
The statistician spends his days,
In figuring out the many ways,
In which a standard error can,
Enclose by bars the average man.
And having thus imprisoned him,
Perhaps at some researcher's whim,
Can with the same chicanery,
Enlarge the bars and set him free.
Or better yet, within the sample,
Locate some points with girth so ample,
That if by "choice" they were discarded,
Man and hypothesis are safeguarded.
Joe Mole <JOEMOLE#NoSpam.USCN.BITNET>
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From: Hugh Janus <Hugh_Janus#NoSpam.HotMail.Dot.Com> The mathematician Von Blecks Derived the equation for sex. He found a good fuck Isn't patience or luck But a function of Y over X.
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From PeterW (PeterW#NoSpam.lims.demon.uk)
Remember school math(s)? Remember quadratic equations?
Right! Read:- 'a2' below as "a squared"
'b2' below as "b squared" etc.
If a = b (so I say) [a = b]
And we multiply both sides by a
Then we'll see that a2 [a2 = ab]
When with ab compared
Are the same. Remove b2. OK? [a2-b2 = ab-b2]
Both sides we will factorize. See?
Now each side contains a - b. [(a+b)(a-b) = b(a-b)]
We'll divide through by a
Minus b and ol़
a + b = b. Oh whoopee! [a+b = b]
But since I said a = b
b + b = b you'll agree? [b+b = b]
So if b = 1
Then this sum I have done [1+1 = 1]
Proves that 2 = 1. Q.E.D.
From: Karen (REMOVEbruceandkaren#NoSpam.erols.com)
I lost you exactly half way
When I saw that division by a
If a=b
Than only with c
Can we demonstrate what you don't say
a less b times b plus a
= ba less b, that's ok
But divide & dump b
Is -b, see?
So c has to be b+a
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Special Category: Euclid/Euclides
From: dpbsmith#NoSpam.world.std.com (Daniel P. B. Smith)
Old Euclid drew a circle
On a sand-beach long ago.
He bounded and enclosed it
With angles thus and so.
His set of solemn greybeards
Nodded and argued much
Of arc and of circumference,
Diameter and such.
A silent child stood by them
From morning until noon
Because they drew such charming
Round pictures of the moon.
--Vachel Lindsay
OK, I cribbed them from the collection "Fantasia Mathematica," edited by
Clifton Fadiman, recently reprinted I think, which is full of stuff you
might be able to use...
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From: Prashant Upadhyaya <pupadhyaya#NoSpam.hss.hns.com> Here's a limerick ! It's called A complex PJ (Poor Joke) Do you want to hear a complex PJ ! Yes ? Ok, P + iJ ! Where is the Joke, do you ask with a start ? So listen up, it's in the imaginary part !!!
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From: dpbsmith#NoSpam.world.std.com (Daniel P. B. Smith)
And then of course, there's always the cheer:
Sine! Cosine! Cosine! Sine!
Three point one four one five nine!
Phi! Psi! Omega! Chi!
Cube root of Y cubed equals Y!
--circulated among nerdish high school students circa 1960
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From: Moshe Zadka <moshez#NoSpam.math.huji.ac.il> Using only a chalk and a board A mathematician once showed That two plus two equals five Just to keep math alive And the audience sure wasn't bored!
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Xdat315:There once was a number named pi
From: Ian Ellis <ian#NoSpam.iglou.com>
This poem was written by Eve Andersson.
There once was a number named pi
Who frequently liked to get high.
All he did every day
Was sit in his room and play
With his imaginary friend named i.
There once was a number named e
Who took way too much LSD.
She thought she was great.
But that fact we must debate;
We know she wasn't greater than 3.
There once was a log named Lynn
Whose life was devoted to sin.
She came from a tree
Whose base was shaped like an e.
She's the most natural log I've seen.
found at
http://www.math.tamu.edu/~Jiang.Chuan/projectC.html#1
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From: Swanson_D <Swanson_D#NoSpam.bls.gov> These two songs are logically equivalent. They use contrapositives, which means that the statement "If A then B" is logically equivalent to the statement "If not B, then not A." Original song: If the ocean was whiskey and I was a duck, I'd swim to the bottom and never come up. But the ocean ain't whiskey, and I ain't no duck, So I'll play jack-of-diamonds and trust to my luck. For it's whiskey, rye whiskey, rye whiskey I cry. If I don't get rye whiskey I surely will die. The logical equivalent (the contrapositive): If I never reach bottom or sometimes come up, Then the ocean's not whiskey, or I'm not a duck. But my luck can't be trusted, or the cards I'll not buck, So the ocean is whiskey or I am a duck. For it's whiskey, rye whiskey, rye whiskey I cry. If my death is uncertain, then I get whiskey (rye).
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From: "Zozo" <nnobandl#NoSpam.csir.co.za>
CALCULUS
If only I could get to the derivative of you,
To navigate your slope just like I used to do,
Your sine curve so smooth, so well elevated,
Just waiting for me to come and make it integrated.
Remember how during our second differentiation,
I'd derivate and agitate until I'd reach acceleration?
My little pet parabola whom I so much adore,
Why can't we have a functional relationship once more?
By: Ken Feinstein (kenf1234#NoSpam.hotmail.com)
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From: chrisman#NoSpam.ucdmath.ucdavis.edu (Mark Chrisman) "Aleph-0 bottles of beer on the wall, Aleph-0 bottles of beer; Take one down, pass it around, Aleph-0 bottles of beer on the wall! Aleph-0 bottles of beer on the wall..."
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From: Steve Davis <"sdsd#NoSpam.userid"#NoSpam.west.net> Googolplex bottles of beer on the wall, Googolplex bottles of beer; Take one down, pass it around, Um...ah.......oops.
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From: fc3a501#NoSpam.math.uni-hamburg.de (Hauke Reddmann) One bottle of beer on the wall One bottle of beer on the wall if this bottle MAY fall there is a half bottle of beer on the wall (assuming equiprobability, of course)
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From: fc3a501#NoSpam.GEO.math.uni-hamburg.de (Hauke Reddmann) One bottle of beer on the wall If one bottle should fall there are zero bottles of beer on the wall Zero bottles of beer on the wall If one bottle should fall there are minus one bottles of beer on the wall Minus one bottles of beer on the wall If one bottle should fall there are i bottles of beer on the wall Whoops? Must be root beer.
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One and one make two, But if one and one should marry, Isn't it queer- Within a year There's two and one to carry.
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Geometry keeps you in shape. Decimals make a point. Einstein was ahead of his time. Lobachevski was out of line.
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"IF" (School Maths version) =========================== If you can solve a literal equation And rationalise denominator surds, Do grouping factors (with a transformation) And state the factor theorem in words; If you can plot the graph of any function And do a long division (with gaps), Or square binomials without compunction Or work cube roos with logs without mishaps. If you possess a sound and clear-cut notion Of interest sums with P and I unknown; If you can find the speed of trains in motion, Given some lengths and "passing-times" alone; If you can play with R (both big and little) And feel at home with l (or h) and Pi, And learn by cancellation how to whittle Your fractions down till they delight the eye. If you can recognise the segment angles Both at the centre and circumference; If you can spot equivalent triangles And Friend Pythagoras (his power's immmense); If you can see that equiangularity And congruence are two things and not one, You may pick up a mark or two in charity And, what is more, you may squeeze through, my son. [Times Educational Supplement 19th July 1947]
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This poem was written by Jon Saxton (an author of math textbooks). ((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0 Or for those who have trouble with the poem: A Dozen, a Gross and a Score, plus three times the square root of four, divided by seven, plus five times eleven, equals nine squared and not a bit more.
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March 14
'Tis a favorite project of mine
A new value of pi to assign.
I would fix it at 3
For it's simpler, you see,
Than 3 point 1 4 1 5 9.
("The Lure of the Limerick" by W.S. Baring-Gould, p.5. Attributed to
Harvey L. Carter).
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From: Jeff Wisnia <jwisnia#NoSpam.conversent.net>
Null vectors have zero projection,
So you ask, "What can be their direction?"
They point any which way.
"That's BS!" you say?
Not really; it's just misdirection.
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April 25 June 22 From: "Cybe R. Wizard" <Cybe_R_Wizard@WizardsTower> "Klein's bottle," said one who's Knowing, "'s a bottle with just one side showing, so what you pour in just pours out again. You can't tell if it's coming or going."
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From: "Cybe R. Wizard" <Cybe_R_Wizard@WizardsTower> November 17 September 26 If you ever find you're enshrined in a M५bius 4D-ish kind of 2D-faced space it'd be no discrace to slide on out if you're inKleined.
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March 14 If inside a circle a line Hits the center and goes spine to spine And the line's length is "d" the circumference will be d times 3.14159
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If (1+x) (real close to 1) Is raised to the power of 1 Over x, you will find Here's the value defined: 2.718281...
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Here's a limerick I picked up off the net a few years back - looks better
on paper.
3_
\/3
/
| 2 3 X pi 3_
| z dz X cos(--------) = ln (\/e )
| 9
/
1
Which, of course, translates to:
Integral z-squared dz
from 1 to the cube root of 3
times the cosine
of three pi over 9
equals log of the cube root of 'e'.
And it's correct, too.
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Not a joke, but a humorous ditty I heard from some guys in an engineering fraternity (to the best of my recollection): I'll do it phonetically: ee to the ex dee ex, ee to the why dee why, sine x, cosine x, natural log of y, derivative on the left derivative on the right integrate, integrate, fight! fight! fight!
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Other cheers: E to the x dx dy radical transcendental pi secant cosine tangent sine 3.14159 2.71828 come on folks let's integrate!!
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E to the i dx dy E to y dy cosine secant log of pi disintegrate em RPI !!!
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square root, tangent hyperbolic sine, 3.14159 e to the x, dy, dx, sliderule, slipstick, TECH TECH TECH!
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e to the u, du/dx e to the x dx cosine, secant, tangent, sine, 3.14159 integral, radical, u dv, slipstick, slide rule, MIT!
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E to the X D-Y, D-X E to the X D-X. Cosine, Secant, Tangent, Sine 3.14159 E-I, Radical, Pi Fight'em, Fight'em, WPI! Go Worcester Polytechnic Institute!!!!!!
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Hiawatha Designs an Experiment Hiawatha, mighty hunter, He could shoot ten arrows upward, Shoot them with such strength and swiftness That the last had left the bow-string Ere the first to earth descended. This was commonly regarded As a feat of skill and cunning. Several sarcastic spirits Pointed out to him, however, That it might be much more useful If he sometimes hit the target. "Why not shoot a little straighter And employ a smaller sample?" Hiawatha, who at college Majored in applied statistics, Consequently felt entitled To instruct his fellow man In any subject whatsoever, Waxed exceedingly indignant, Talked about the law of errors, Talked about truncated normals, Talked of loss of information, Talked about his lack of bias, Pointed out that (in the long run) Independent observations, Even though they missed the target, Had an average point of impact Very near the spot he aimed at, With the possible exception of a set of measure zero. "This," they said, "was rather doubtful; Anyway it didn't matter. What resulted in the long run: Either he must hit the target Much more often than at present, Or himself would have to pay for All the arrows he had wasted." Hiawatha, in a temper, Quoted parts of R. A. Fisher, Quoted Yates and quoted Finney, Quoted reams of Oscar Kempthorne, Quoted Anderson and Bancroft (practically in extenso) Trying to impress upon them That what actually mattered Was to estimate the error. Several of them admitted: "Such a thing might have its uses; Still," they said, "he would do better If he shot a little straighter." Hiawatha, to convince them, Organized a shooting contest. Laid out in the proper manner Of designs experimental Recommended in the textbooks, Mainly used for tasting tea (but sometimes used in other cases) Used factorial arrangements And the theory of Galois, Got a nicely balanced layout And successfully confounded Second order interactions. All the other tribal marksmen, Ignorant benighted creatures Of experimental setups, Used their time of preparation Putting in a lot of practice Merely shooting at the target. Thus it happened in the contest That their scores were most impressive With one solitary exception. This, I hate to have to say it, Was the score of Hiawatha, Who as usual shot his arrows, Shot them with great strength and swiftness, Managing to be unbiased, Not however with a salvo Managing to hit the target. "There!" they said to Hiawatha, "That is what we all expected." Hiawatha, nothing daunted, Called for pen and called for paper. But analysis of variance Finally produced the figures Showing beyond all peradventure, Everybody else was biased. And the variance components Did not differ from each other's, Or from Hiawatha's. (This last point it might be mentioned, Would have been much more convincing If he hadn't been compelled to Estimate his own components From experimental plots on Which the values all were missing.) Still they couldn't understand it, So they couldn't raise objections. (Which is what so often happens with analysis of variance.) All the same his fellow tribesmen, Ignorant benighted heathens, Took away his bow and arrows, Said that though my Hiawatha Was a brilliant statistician, He was useless as a bowman. As for variance components Several of the more outspoken Make primeval observations Hurtful of the finer feelings Even of the statistician. In a corner of the forest Sits alone my Hiawatha Permanently cogitating On the normal law of errors. Wondering in idle moments If perhaps increased precision Might perhaps be sometimes better Even at the cost of bias, If one could thereby now and then Register upon a target. W. E. Mientka, "Professor Leo Moser -- Reflections of a Visit" American Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972)
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April 25 June 22 A mathematician named Klein Thought the Mobius Band was divine. Said he, "If you glue The edges of two You get a weird bottle like mine."
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April 25
June 22
From: "David Miller" <davidianmiller#NoSpam.optushome.com.au>
One Klein bottle left on the wall,
I'm hoping the mongrel don't fall;
'Coz it's not a fake
And if it should break,
I don't know what'd happen at all.
David Miller
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Special Category: Pierre de Fermat
Januari 12
August 17
A challenge for many long ages
Had baffled the savants and sages.
Yet at last came the light:
Seems old Fermat was right--
To the margin add 200 pages.
-- Paul Chernoff
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December 28
November 22
Special Category: Arthur Eddington
_There Once Was a Breathy Baboon_ by Sir Arthur Eddington
There once was a breathy baboon
Who always breathed down a bassoon,
For he said, "It appears
That in billions of years
I shall certainly hit on a tune."
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From: blc#NoSpam.solomon.technet.sg (Brian Cohen) A mathematician named Hall had a hexahedronical ball. The cube of its weight, times his pecker plus eight is his phonenumber. Give him a call!
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From: Melanie Aultman <afn10453#NoSpam.afn.org> A mathematician named Bath Let X equal half that he hath. He gave away y Then sat down to pi And choked. What a sad aftermath.
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From: The Professor (franbo#NoSpam.globalnet.co.uk)
One or two from the archives, but I've included them because they inspired the others.
A mathematician called Bird, Had students who thought him absurd. There were cries of derision When he said long division, Meant one into one made a third.
A mathematician called Rumbold, One day, quite by accident, stumbled On the Meaning of Life, Then went on, for his wife, To find out why all her apple pies crumbled.
A mathematician called Strong, Got all his conclusions quite wrong. His value for pi Was put much too high, As the average length of his dong.
A mathematician called Babbit Put some quite simple sums to a rabbit. The rabbit replied "I must learn to divide, With me multiplication's a habit."
A mathematician called called Dick Tried to measure the size of his prick. But he was enraged When he found that he gauged It, not quite the short side of a brick.
A mathematician called Week, Has geometry which is unique. If A equals B And B equals C ABC is his lower left cheek.
A mathematician called Day, Who was anxious to have it away, Said the value of X Turned his thinking to sex, X times Y was the price he would pay.
A mathematician called Power, Calculated his lust in the shower, But he was nonplussed When the force of his thrust, Stopped the water for over an hour.
A mathematician called Hall, Had a hexahedronical ball, And the cube of its weight, Times his pecker, plus eight, Was four fifths of five eighths of sod all.
A mathematician called Rubik, Has a very strange area pubic. His balls are both conical, They look very comical, With a penis described best as cubic.
A mathematician called Able, Made love to a young girl called Mabel, They hadn't a bed, So made use instead, Of an old mathematical table.
A mathematician called Cross, Fell in love with the wife of his boss. The boss's reaction, Suggested subtraction, He said, "Take her away, she's no loss."
A mathematician called Hill, Had a wife who was not on the Pill. Though he missed no occasion, To try multiplication, The product produced was just nil.
A mathematician called Plumb, Was engrossed in a difficult sum, And even in bed, It stayed in his head Till his wife said, "For God's sake, Plumb, come."
A mathematician called Hyde, Took a busload of girls for a ride. And in preparation, For multiplication, Each girl forced her legs to divide.
A mathematician called Dewar Whose maths were incredibly pure, Clamped his penile device In an engineer's vice, Then in microns he measured his skewer.
The was a young lady called Hatch Who had a rectangular snatch. So she practised coition With a mathematician, Whose square root was just made to match. From: Marlene (mlewis#NoSpam.missionx.com)
Mathematics: of sciences, queen Has more rules than I've ever seen. There are no exceptions, Just number deceptions. On calculators, I am quite keen. --ML {Toastpoint first line -- with help from Croc}
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FOUNDATIONS OF ARITHMETIC
By J.A. Lindon
One day when Mugg the Missing Link was prowling through the woods,
In search of wives and mammoth-meat and other usefull goods,
Whom should he see, on pushing out from deep arboreal shade,
But Ogg, the Paleolithic Man, cross-legged in a glade.
This Ogg had made a neat array of pebbles on the ground,
In number they were twenty-one, the most that could be found,
And Ogg, with one red-hairy hand pressed to his bony brow,
Was staring at hese pebbles like a ruminating cow.
o o o o o o o
o o o o o o o
o o o o o o o
Thought Mugg - for he was Primitive - I should be very dull
To lose this opportunity of busting in his skull;
My club weighs half a hundredweigh, he doesn't wear a hat
(And here he wondered) Yes, but what the devil is he at?
For Ogg was touching pebbles and then prodding at his digits,
Until the weirdness of it all afflicted Mugg with fidgets:
"Invented any goodish wheels just recently?" he hollered,
And doubled up in merriments, his face raw-beefy coloured.
Ogg looked at him in pity, then he drummed upon his chest:
"I've don a Think!" he bellowed "Monkey Mugg. I've done a think!
And I would write it down, but no one's yet invented ink."
Mugg moved a little closer, and his eyes and mouth were round,
And stared in trepidation at those pebbles on the ground.
Ogg pointed with a nailed red-hairy sausage at the rows
And said, "Three people's hand-plus-two is hand-plus-feet-plus-nose."
oooo oooo oooo oooo oooo
o + o + o = o o + ooooO Oooo + A
o o o
o o o
"And this is hand-plus-two of people's three-for-each-by-name,
So three times hand-plus-two and hand-plus-to time three's the same!"
Mugg scratched his matted hairy head, not knowing what to say.
Said Ogg, "It's all made clear by this rectangular array."
o o o
o o o
o o o o o o o o o o
o o o o o o o = o o o
o o o o o o o o o o
o o o
o o o
"Three rows of hand-plus-two and hand-plus-two short rows of three
are just the same according to which way you look, you see?
In brief, a tripe heptad is the same as seven trebles,
And may quite possibly be true of other things than pebbles."
Mugg viewed it from all angles, then he gave a raucous belch
And trod on a Batrachian that perished with a sqelch.
He growled, "I do not understand these arithmetic quirks,
But maybe we should try to discover if it works."
So home they went to get their wives and drag them by the hair,
For Mugg had feet-plus-hand-plus-four, while Ogg had just a pair;
But what with all their screeching and their running every way,
At first they would not form a neat rectangular array.
So Ogg he then positioned each by holding of her down
While Mugg with mighty club in hand, just dinted in her crown;
And when they had them all in place, like pebbles, they could see
That three times hand-plus-two in wives was hand-plus-two times three!
o<= o<= =>o =>o o<= o<= =>o
=>o o<= o<= =>o o<= o<= =>o
o<= =>o =>o o<= =>o o<= =>o
Then Ogg he roared in high delight, cartwheeling to and fro
(Carts had not been invented, but he did it just to show!),
And Mugg he grinned a shaggy grin and slapped a hairy thigh
And said, "It's true, as sure as Pterodactyls learned to fly!"
And then they feasted on their wives in unuxorious zest,
Exept for one whose skull was rather thicker than the rest,
And she was sent to dig a pit and bury every bone,
While Mugg and Ogg went off to find a flat unsullied stone.
Then Ogg he sharpened up a flint and scratched upon the rock:
First Arithmetic Theorem - by Ogg the son of Mok.
He drew his little diagram, and proved, with QED,
That three times hand-plus-two of x is hand-plus-two times three.
But Mugg the Missing Link grew bored, and left him there alone,
Still scratching with his silly flint upon his silly stone;
And belching, plunged back in the woods on feet toe's simple fives,
In search of wives and mammoth-meat, particularly wives!
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Each wive of Fibonacci, Eating nothing that wasn't starchy, Weighted as much as the two before her. His fifth was some signora! - J.A. Lindon
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Hues Are what mathematicians use (While hungry patches gobble 'em) For the 4-colour problem. - J.A. Lindon 'A Clerihew'
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Januari 12 August 17 The method of Diophantus May cease to enchant us After a life spent trying to gear 'em To Fermat's Last theorem. - J.A. Lindon 'A Clerihew'
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Points Have no parts or joints How then can they combine To form a line? - J.A. Lindon
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From: rjmnapa#NoSpam.aol.com (Renee ) Practical Application: He's teaching her arithmetic, He said it was his mission, He kissed her once, he kissed her twice and said, "Now that's addition." As he added smack by smack In silent satisfaction, She sweetly gave the kisses back and said, "Now that's subtraction." Then he kissed her, she kissed him, Without an explanation, And both together smiled and said, "That's multiplication." Then Dad appeared upon the scene and Made a quick decision. He kicked that kid three blocks away And said, "That's long division!"
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THE KISS PRECISE
For pairs of lips to kiss maybe
Involves no trigonometry.
'T is not so when for circles kiss
Each one the other three.
To bring this off the four must be:
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance form the center.
Though their intrigue left Euclid dumb
There's now no need for rule of thumb.
Since zero's bend's a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.
To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
And now besides the pair of pairs
A fifth spere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four
The quare of the sum of all five bends
Is thrice the sum of their squares.
- Frederick Soddy
And let us not confine our cares
To simple circles, planes and spheres,
But rise to hyper flats and bends
Where kissing multiple appears.
In n-ic space the kissing pairs
Are hyperspheres, and Truth declares-
As n + 2 such osculate
Each with an n + 1-fold mate.
The square of the sum of all the bends
Is n times the sum of their squares.
- Thorold Gosset
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A graduate student at Trinity Computed the square of infinity. But it gave him the fidgets To put down the digits, So he dropped math and took up divinity.
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March 14
Pi vs e
Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?
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A rose-red city half as old as Time. One billion years ago the city's age Was just two-fifths of what Time's age will be A billion years from now. Can you compute How old the crimson city is today?
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November 17 September 26 July 23 September 26 A burleycue dancer, a pip Named Virginia, could peel in a zip; But she read science fiction and died of constriction Attempting a Moebius strip. - Cyril Kornbluth
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November 17 September 26 A mathematician confided That a Moebius strip is one-sided. You' get quite a laugh If you cut it in half, For it stay in one piece when divided.
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From: chollanamdo#NoSpam.mindspring.com (The Sanity Inspector) There once was a mathematician Who preferred an exotic position 'Twas the joy of his life To achieve with his wife Topologically complex coition. From Betsy Devine and Joel E. Cohen, _Absolute Zero Gravity_
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From: mini-AIR 1995-07-04 Inevitably, Limericks We hesitantly announce a new research project: The AIRhead Science Limerick Compendium. The first entry is from reader Peter Olsen. Olsen used as it the entire answer to a final examination question: "Describe what you have learned in this course." In Arctic and Tropical Climes, The Integers, addition, and times, Taken (mod p) will yield, A full finite field, As p ranges over the primes.
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From: 'PIGDOG' Eric Struckhoff <ericcs#NoSpam.u.washington.edu> August 18 December 29 If n in a Taylor series goes 2 to 11 by threes for x = 1 convergence is done 'twixt zero and two, I believe.
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From: mcripps#NoSpam.computan.on.ca (Mervyn Cripps) From: Gordon Weir <gordonweir#NoSpam.shaw.ca> I used to think math was no fun, 'Cause I couldn't see how it was done. Now Euler's my hero, for I now see why 0 Equals e^(pi * i) + 1.
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From: SteveMR200#NoSpam.aol.com (Steve)
Don't know much about geography,
Don't know much trigonometry.
Don't know much about algebra,
don't know what a slide rule is for.
But I know that one and one is two,
And if this one could be with you,
What a wonderful world this world this would be.
--Sam Cooke (1931-1964)
_Wonderful World_
(Lyrics by Sam Cooke, Herb Alpert and Lou Adler)
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Special Category: Paul Erd५s September 20 March 26 A conjecture both deep and profound Is whether the circle is round. In a paper of Erd५s Written in Kurdish A counterexample is found Limerick from Leo Moser about Paul Erd५s tendency to publish important proofs in obscure journals. Note: On hearing this limerick, Erd५s tried to publish in a Kurdish mathematical journal, but he could not find any.
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From: Afetrmath2#NoSpam.aol.com (author) To a tightrope walker named Zekund The 'a' due to gravity beckoned. His performance was great At about 9.8 m/sec/sec. April 25 June 22 A mathematician named Crottle Poured water into a Klein bottle. When asked, "Do you doubt That some will run out?" He replied, "No, I don't. Quite a lot'll." There was young maiden named List Whose mouth had a funny half-twist. She'd turned both her lips Into Moebius strips... 'Til she's kissed you, you haven't been kissed! Man has pondered Since time immemorial Why 1 is the value Of 0!.
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From: Mathwoman199436#NoSpam.aol.com
MATH 101 LIMERICKS
(meaning, precalc and finance math, required math course for all students
at some universities)
(Quadratics)
A fair maid from North Minneapolis
was an expert at drawing parabolas.
She extended their arms
and showed off their charms
and they looked positively fabulous.
(Cost Analysis)
The cost of producing is mixed.
Part of that cost will be fixed
and the rest, never-ending
on level depending
(or maybe on politics).
(Rational Functions)
Said your favorite Zada or Tante
"for an assymptote horizonta
"you need to both both
"of the leading coeff's
"whether or not you wanta."
(Exponential Functions)
The bottom is perfectly noble
but x is now upwardly mobile
so that constant, poor dear
must downsize its carweer
and it's feeling a bit claustrophob-al.
These guys are as busy as beavers.
They've got Monday morning fever.
They just grow, grow, and grow.
They're NEVER zero
and they don't remain one for long, either.
(Logarithms)
Do logs give you logarrhea?
Is a logjam drawing near?
Just use your cerdentials
and take exponentials
to make those ol' logs disappear.
(Matrix multiplication)
Just pair off each row with each column.
Take the sums of those products so solemn.
Then beat the odds
with those scalar prods
or whatever the devil you call 'em.
(Compound interest)
"Nothing succeeds like success,"
as these formulas show with finesses.
Thus again and again
A gets bigger with n
though not quite as big as you'd guess.
(Annuities)
And now here's another fine source
(to tickle your brains in this course)
of mo' and mo' dough.
It's dough a go-go.
Oh, don't you just wish it was yours?
CALC
(Product Rule)
Diff-ing x to the x is fun.
change the n to n-l
then go back to n
and use it again
in front of it all, and you're done.
There's a general rule for all this
(in case we have a pop quiz):
n steps down two ways
for the rest of its days
and x remains right where it is.
(Calc applications)
"Than receive, 'tis better to give."
Also, "live, live, and let live."
These are words to clutch
but not as much
as "velocity equals deriv."
(General Power Rule)
Are you bored with powers of x?
What would you like to do next?
Some powers of g
will do quite nicely
but watch out for the special effects.
(Product Rule)
Don't forget, f appears twice.
g will behave likewise.
If you make like a dunce
and write them just once. . .
well, you'll get what you get for half-price?
Said a wiseguy named Georgie O-Porgie
"Let's have a Quotient Rule orgy.
"On top, to be nice
"g appears twice
"and then on the bottom one more g."
(Chair Rule)
Rinky, dinky, dinky.
g provies the link-y.
But the x and the f
are not to be left
unless you run out of ink-y.
(Curve Sketching)
There was a young man named Kareem
who explained, "For a point rel-extreme
"the tangent at a
"to rest must lay
"and I wish it the pleasantest dream."
(integrating Powers of x)
There's general rule for all this
(and it's something you don't want to miss):
n moves up and down
without making a sound
and x stays right where it is.
(Integrating Exponentials)
And now here's a grave admonition
delivered with proper precision:
It's about that ol' k.
k steps down ONE way
and the x doesn't go where it isn't.
Minus one is a special case
delicious and dainty as lace.
So don't play the hero.
Don't divide by zero.
If you do, be sure to erase.
(Curve sketching)
We can plot and plot til we plotz.
But we've got to plot the right spots.
Or those lows and highs
could elude us like flies.
Likewise the flips and the flops.
A fair maid from North Minnesota
was drawing a steep assymptot-a.
when it got 'way too high
she murmured bye-bye
and mourned not a single iota.
("Parts")
"We need f and g-prime," said Mitch
"and it matters which is which."
"But not to worry,"
said his cousin Jerry.
"It doesn't work out, we'll switch."
Root-a-toot toot-a-falutin'.
It's time for some substitutin'.
Take the stuff on display
and collapse it away
right along with Leibnitz and Newton.
(Area between curves)
don't forget, those curves might cross
in which case you should take time to pause
so you don't subtract
when add's where it's at.
"twould be a lamentable loss.
(Solids of revolution)
a strappin' young woman named Evvie
was handed a solid of rev-vy
and asked for the volume.
She answered, quite solemn
"It's not very big but it's heavy."
(Integrations tecnniques, "sine-saving")
Said a technique freak named Zeek
"if you think sine-saving is chic
"and you want to save
"yourself into the grave
"try cos and tang and sec."
(Derivatives of trig functions)
A darling named Clementine
said "First sine, then cos, then sine
"and the minus and plus
"make things even wuss.
"Can't it make up its mind?"
(A non-limerick)
Can we integrate tan?
Yes, we can.
Can we integrate secant?
No, we can't.
(Trig-triggers -- that is, trigonometric substitutions)
A trig-trigging trickster from Beacon
is stuck on an odd-powered secant.
An integral table
would render him able
but his conscience is prodding "no peekin'."
(Improper integrals)
Said a ship-shape chap from the congo
"Since our area's infinitely long-o
"it's likely that you'd
"be inclined to conclude
"that it's infinitebig, but you're wrong-o."
(Separable Eff Eq -- Duh; what, me worry?)
A ditzo from hither or thither
refused to get all in a tither.
"'Tis true," said he, "I
"can't tell x from y
"but can't tell left from right-y, either."
COMPLEX ANALYSIS
A reality complex had Fred.
He felt kind of bad in the head.
So he took Complex Far
with Cohen Mar
got a complex complex instead.
Oh, pity the poor lonely guy.
He ex ran away with his y.
then z came along
but done him wrong.
Then his one-and-only turned i.
There was a young lady named suzie
who couldn't add 2z and 2z.
She said, "Can't it be
"without that ol' z?"
She's being a little too choosy.
(nth roots of unity)
There are n of them sprawled on a wheel.
Among them at most two are real.
The others must go
half above, half below.
But they get paired off in the dea.
e to the z is exotic
and it changes a sum to a product.
It has no root
but it's kind of cute
and it's vertically periodic.
A young man named Kenny macKenzie
had trouble computing ln z.
He breezed through the r-part
with the slickness of pop-art
but the theta-part gave him a frenzy.
Here's the key to z to the c:
It's just e to the c ln z.
But watch for ln y.
Its values are many
thought sometimes e makes them agree.
(sin and cos, revisited)
In trig and calc all through
one was the limit we knew.
But now we're set free.
Now we can be
anything we desire such as two.
How smart the conditions of C-R.
They're almost as brilliant as we are.
But they're known for their sly-ness.
Watch out for that minus
or we'll spend half the night in the E.R.
(more about the C-R conditions)
Here they come, hot off the griddle
spiffy and spicy and little.
One sports a plus
the other mi-nus
and none of them sports the middle.
The research team Cauchy and Goursat
was busting its brain and its torso..
They went huffin' and puffin
but came up with nothin'.
Now they're living on noodles and orzo.
The pretty professor from Jersey
just stood there and pleaded for mercy.
She said "in complex
"v-y equals u-x --
"or maybe it's vice-vers-y."
i after e after u
after pi after n after 2
after p'renthesis ln
and then no more spellin'
unless we cah find something new.
(Thaks to student Bob Blackard for getting me started on this one.)
The pretty professor's a rarity
her lectures the height of clarity.
Except that when
she does minus-1- to the n
n turns out to be the wrong parity.
Yes, the pretty professor, our rarity
was engulfed in hyper-hilarity
'cause again she had spun
a spare minus-one.
She said, "Well, we can give it to charity."
(About the integral of f(z) over (z - z-nought) to the n, over a closed
contour con-
taining z-nought)
When C's end is at its beginnin'
ask "Is z-nouight out'n or in'n?"
Draw the point, draw the curve.
Then stand back and observe.
If in doubt, get a second opin'on.
Computing it's easy as pie
(especially if you try).
There's a derivation
and an exclamation
and don't forget two pi i.
An industrious lad from the near East
was summing a long Taylor series.
By the twentieth head
he just shrugged and said
"That's as far as I go, my dearies."
Geometric ser's are a gem.
But let's add that little m --
OUTSIDE, if you please
the parentheses.
Did you hope I'd forget about them?
The Last of those spunky Mohicans
was at work on a long Cauchy sequence.
It was i pi y
from Mon to Fri
and he took it back home on the weekends.
Can you count? Then here's one for you:
One less z to the minus-two.
Write 1, 2, 3
then blank, z, z
and the powers and the plus signs, too.
a fair-maid from North Miami
was at work on the triple-whammy.
She tried subtraction
and partial fractions
then she called for her pappy and mammy.
A lazy young lad named Laurent-o
used his series to integrate pronto.
Just b-one will do
and as for b-two
you need only find that if you want to.
O what will the fair maid named Tessa do?
She's been after a simple-pole residue.
She says, "Oh, NOW I see.
"It's q-prime UNDER p.
"Then I plug in z-nough -- or I guess I do."
(non-limerick -- TEACh-TONE PHONE (Remember, I gave out my phone number?
Well,
no one ever called, but if you had, here's what my recording said -- See
what you
missed?)
For Cauchy-Goursat
press 0.
For some integral fun
press 1.
For a residue
press 2.
For l / (l - z)
press 3.
For contours galore
press 4.
But to find out the fate of a minus sign
be patient, please, and stay on the line.
You might want to check out my SERIOUS math poems on my website:
http://mathwoman.com.
Marion Cohen
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From: Mathwoman199436#NoSpam.aol.com Here are the others. (I guess you can tell -- every time I teach a course, about which I haven't already written limericks, I start in. I'm currently writing Linear Algebra limericks; they're not perfected yet; when they are, I'll send them.) DIFF EQ A starry-eyed lad from Wisconsin was hoping those coeff's would be constant. But his hopes turned to hexes when he saw all those x's so he shrugged and remarked "Stuff and nonsense." There was a young woman named Sally. Legendre was right up her alley. "Minus x square plus one "is what starts the fun "and n-square plus n's the finale." Her cousin named Mary Magee said "Bessel's much besser to me. "x-square WITHOUT one "seems much more fun "and nu's cooler than n," said she. Their cousin from Doodle=Skadiddle said, "Yes, but what's in the middle?" Answered they, "We suspects "it's x or 2x. "We're feeling a bit non-commital." An attractive young ms. named Cassandra was solving equations Legendre. a-nought was do-able a-one construable but x-(n+2) was beyond 'er. There was a fine fellow named ian who was ready to give up on P-n. He said "Too much mess 'with the n and the x." And sometimes I can't help agreein'. There are 5 n's, 5 2's, and 6 m's (and be careful not to mix 'ems) minus and factorals in the plurals and all those parentheses betwix 'ems. PDE A lad thought he'd service society by studying math and psychiatry. but his plans went a-ragin' with the first wave equation 'cause he got Separation Anxiety. March 21 May 16 (Fourier series, exponential form) Those functions e to the in x can be treated like cos x and sin x. And if they can't call me Bell Atlant- or try MCI or Nynex. March 21 May 16 (Fourier integral) Are we feeling morbid and mopey just 'cause f(x) has n p? Don't be so limid. Go to the limit. When there's life, there's always hope-y. It's Jan. 14 and our prof by a factor of two is off. Is she going to cry? Says she, "Not I. "In fact, I'm more likely to laugh." Do you think this is getting hum-drum? It's time to consider a drum-drum. We'll get double series and double theories and B's and B*'s under 'em. Next we make our rod very lengthy thus increasing its impact and strenth-y. So we've shed the L but acquired integrell: For thy patience I humbly thank thee. There was a spry guy from Saigon who was searching for values eigen-. but the boundary conditions surpassed all his wishin's and wouldn't let bygones by bygone. VECTOR ANALYSIS Here's something to contemplate: A vector's an arrow so straight. For forces, its length expresses its strength and direction expresses its fate. Two vectors, whatever the size can be added, component-wize so make so this rhymes by adding three times then put in the k, j, and i's. (Scalar multiplication) a spunky young woman named Ralpha would multiply vectors by alpha. She thought it quite nice to multiply thrice in this city of Philadal-pha. (Scalar product) Here's the most fun you ever had: Take products three times and then add. And do mind your mommas and DON'T put in commas (or momma will tell your Dad). (Vector product) In this glossy and glorious firmament nothing's more perfect and permanent or more fancy-free for u criss-cross v than our ever-lovin' determinant. i, j, and k are cute and they're specially fixed to compute. E.g., i cross j is lower-case k. But as arrows, they're too short to shoot. (curve parametrization) Straight lines are quite matter-of-fact if you know how to add and subtract. True, there's multiplication in this situation but nothing on which you need act. Although all of us are mere amateurs in this business of making parameters when it's circles in question I have a suggestion: Try not to forget the diameters. (formular for curvature) r-dot dot r-dot-dot. Yes, sometimes we dot a lot. But dot-dot-dot? Or r-quad-dot? . . . well, sometimes we do not. For that curvature fer t' compute that formula's really a beaut. But when figuring kappa do mind your Pappa and don't you forget that square root. (Div, grad, and curl) It's easy and fun to do grad. It makes us feel gleesome and glad. Don't you feel so alive when you partial-deriv? But put commas, now -- don't you dare add. Here's something no one will object to: When doing the div please expect to take partials, three of components of v and be careful which with respect to. Aloha, tres bien, and shalom? May I mention a vital syndrome? Towards the end of the div you should get additive (or just wait 'til your father gets home). Now, the hardest is curl, we agree. But let's have a determinant spree. First, three vectors little next, del in the middle and then on the bottom goes v. All told (and telling it true) there's more in the curl to do. We've got partials six and note how they mix and the answer's a vector, too. (Directional derivative) If we're out in the wide blue yon rates of change depend, which directi-on. So divide b by mag then dot it with grad and we'll find out how quickly we've gone. (unit normals to surfaces given in the formf(x, y, z) = C ) Said a dashing young man named Aeneas "I have a few dandy ideas. "Just take our f's grad "divide by the mag "and it doesn't much matter what C is." (Note to smart-alecks) When these poems you so dutif-ly edit keep one thing in mind (to my credit): I realize that mag does not rhyme with grad but the point is: YOU won't forget it. (surface parametrization) (plane) If you want to be this term's winner remember, the keyword is linear. So let us let z be ua + vb (for integrals outer and inner). (cylinder) First, think of the x-y plane. (That's not such a drain on the brain.) Next, move once around and then up and down. If tired out, go hop on the train. (sphere) Said a student from South Singapore "We use cosines and sines galore "or the sum of three squares "would give us nightmares -- "Yep, that's what the trig stuff is for." (Line integrals) And now we've got functions three. What could the integral be? The answer, essential: Component, tangential. It gets things in terms of small-t. (surface integrals) Next, functions (three) with a surface (And Murphy's Law gets much more Murfish). But the answer, informal: Component, normal to get u's and v's at our service. (triple integrals) Triple int's are very chic so of them we now shall speak. One thing to make clear: No vectors here (or you're grounded for a week). (Divergence theorem) Next, the surface int. above that we've all come to know and love will be giving way on this fabulous day to a triple int. of the div. of. (Stokes) And now it is late, not early. 'Tis time for Stokes' Theorem, surely. Any int. (closed line) can be redesigned as an int. involving the curl-y. (for those smart-alecks again) Again, as these lim'ricks you edit remember one thing (to my credit): I know that designed does not rhyme with line but it rhymes more than how Stokes said it. ABSTRACT ALGEBRA We're a bunch of nincompoops. We can't get a grip on our groups. We ask, in a frenzy "Z-n or nZ?" Guess wrong, so grin and go "Ooops." This quarter we're all pretty group-y. It can get pretty meaty and soup-y. Z-3 order 3 Z-p order p and D-sub-p order 2p. Special Category: Leopold Kronecker December 7 December 29 (You know how that religious mathematician Kronecker said, "God created the integers; the rest is the work of man." Well -- ) "Integers are neat," said God, "both the even and the odd. "So I'll give you some, Kronecker "for Christmas or Chanukah. "(Do you mind if I package them mod?") Said a group theory pro named McClellan "We've got too many isom and elem "and homom and autom "but already bought 'em. "Perhaps we can try to re-sell 'em." (Automorphisms) Some're outer, some're inner. All're autom's (though it's winter). Some turn out to be the mere identity. But that's good when you're a beginner. Rub-a-dub, rub-a-dub bub-bub. What, O pray tell, is this hub-hub? It's subgroups so cool. They obey the strict rule: Order-wise, they divide what they're sub-ub. In the kitchen you'll hear lots of slubbering. In the bathroom you might see a tubring. But the classroom, I claim is quite tidy and tame. All it's got is a subgroup or subring. Special Category: Leopold Kronecker December 7 December 29 (More dialog between God and Kronecker) "Integers are great," said God "and it's fun doing sum and prod. "But I've now got some notions "to tackle the quotients" and all except K. oo'd and ah'd. "It was nice dividing by bd "but now I'm getting more greedy." Thus spake our Lord standing straight at the board writing Q bracket x and Q.E.D. "One was good for a laugh "and two was a treat for my staff. 'but I've now got a hankerin' "to do some tankerin'. "Aw c'mon, not even a half? "For seven long days labored I "with integers low, then high. "But now 'tis day eight. "'Tis time to create "quotients and roots and pi." Deep in waters hot, not tepid feeling rueful but intrepid our two creators and integer-traitors shrugged "Sorry, we just can't he'p it." Special Category: Leopold Kronecker December 7 December 29 "Please forgive me," said Kronecker L. "I hope you won't send me to hell. "But x caught my attention "and x led to extension" and the rest we know only too well. Yes, pity our genius and hero who fiddled, but not like Nero. He started with F. Now he's got nothing left for he sold his soul for a zero. (Primitive element theorem) A fair maid from Alabam-y was given a double whammy. But she knew how to mingle so's to make it a single and ace the final exam-y. (When is F(a) isomorphic to F(x)?) If about a we have no spec's then a might as well be x. And e and pi are good a's to try though it's not quite clear how it checks. We might grow up to be tax-collectors or city or country inspectors. But Chap. 23 ensures that we will never be angle-trisectors. Special Category: Leopold Kronecker December 7 December 29 (God confesses to Kronecker) First I couldn't stop at 10. Then I couldn't stop at n. Then Z and then Q and the square root of 2. But I've now come to C. Amen. (Epilogue -- by God and Kronecker) We work together like brothers. One creates, the other discovers. And Galleon writes and Cohen recites and we welcome any others.
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From: chergarj#NoSpam.cs.com (Chergarj) Old McDonald had a farm 2.7182818... (-1)^(0.5) 2.7182818... (-1)^(0.5) O
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From: William Elliot <marsh#NoSpam.privacy.net> An analytic geometric says: rho rho rho your slope gently down the angle, verily, verily, verily math is but a wrangle.
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From: Tiddy Ogg <tiddyogg#NoSpam.madasasheep.com> Of rabbits, I can't figure why They add not, but sure multiply. They have the potential To be exponential, But don't give a toss about pi.
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March 14 From: danube <root#NoSpam.danube.cwcom.net> Quite agree, I say with a sigh rabbits don't think, heaven knows why! But when they circle a bend, they must feel that they'll end up in something one calls Rabbit Pi.
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From: Katherine Wagner <dancingkatbunny#NoSpam.yahoo.com>
The Aftermath of Algebra
My wit has died
my brain is fried
Algebra is neurocide
I worked so hard
Oh how I tried!
but fruit of efforts
been denied
I'm back to where I started
My wheels have turned
until they burned
and nothing more is really learned
love of knowledge
Has been spurned
All suspicion’s
been confirmed
My head and sense have parted
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From: saffron#NoSpam.rochester.rr.com
Pythagoras thought of a theorem.
Figures, he no longer did fear them.
For every triangle
One had to untangle
He had the right angle to clear 'em.
-- P. E. Murphy
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From: Stephen Nesbitt <sci-smn#NoSpam.jcu.edu.au> I was wondering what would happen if a group of uni mathematics dropouts formed a death metal band. I came up with a list of possible song tracks for their debut CD. (remember to read the titles in a typical DEATH vocal). Band Name: REGRESSION CD Title: Linearly Separable 1. Derivatives of Death 2. Transcendental Terrors 3. Sin 4. Normalisation of Murder 5. Exponential Tendencies 6. Square Bloody Roots 7. Sequence of Destruction 8. The Corpse of Gaussian's Elimination 9. Disarray 10. Praying Mantissa 11. Binomial Blood 12. Human Division 13. The Raising of the Beast to the Infinite Power 14. Angle Of Death
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