There once was a mathematician named "x"

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.

A mathematician confided
That the Moebius band is one-sided
And you'll get quite a laugh
If you cut one in half
'Cause it stays in one piece when divided.

A mathematician named Klein
Thought the Moebius band was divine
Said he: "If you glue
The edges of two
You'll get a weird bottle like mine."

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 Moebius strip.

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!

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!

There was a young fellow named Fisk,
A swordsman, exceedingly brisk.
So fast was his action,
The Lorentz contraction
Reduced his rapier to a disc.

A conjecture both deep and profound
Is whether the circle is round;
In a paper by Erdos,
written in Kurdish,
A counterexample is found.

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.

A calc student upset as could be
That his antiderivative didn't agree
With the one in the book
E'en aft one more look.
Oh! Seems he forgot to write the "+ C".

A graduate student from Trinity
Computed the cube of infinity;
But it gave him the fidgets
To write down all those digits,
So he dropped math and took up divinity.

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.

To a tightrope walker named Zekund
The a due to gravity beckoned.
His performance was great
At about 9.8
Meters per second per second.

Consider the pitiful plight
Of a runner who wasn't too bright.
For 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!

There's a leather-clad separatrix,
a vector-valued dominatrix
who divides a phase plane
into pleasure and pain
when she gets hold of more than one matrix. [CG]

Jack the mathematician
Had a very strange mission.
The problems he wrote,
He often would gloate,
Sen many a student a-wishin.' [DG]

There once was a prof, Dr. K.,
Who taught calculus everyday.
From dawn until noon,
Integrating to the moon.
To him, derivatives were okay.

There was a prof named Kowalski
Who taught all this calculus to me.
On the final -- no pass;
I must retake the class.
Why, we should all be so lucky. [ES]

Despite all the might fine teachin,'
I can't help but find myself thinkin'
That Calculus I
Will be much more fun
The second time o'takin'. [MB]

Along cam Sir Isaac Newton
Doin' mathematical computin'.
One day he contrived
To anti-derive
When findin' signed areas is suitin'.

Number crunching

'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 3.14159...

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...

If (1+ x) (real close to 1)
Is raised to the power of 1
Over x, you will find
Here's the value defined:

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.

If n in a Taylor series
Goes 2 to 11 by threes
For n = 1
Convergence is done
'Twixt 0 and 2, I believe.

Note: Here's a famous bad proof that 2=1 put into limerick form. The proof appears on the right-hand side.

If a=b (so I say)
And we multiply both sides by a
Then we'll see that a2
When with ab compared
Are the same. Remove b2. Okay?

Both sides we will factorize. See?
Now each side contains a-b.
We'll divide through by a
Minus b and olé
a+b=b. Oh whoopee!

But since I said a=b
b+b=b you'll agree?
So if b = 1
Then this sum I have done
Proves that 2 = 1.

[a = b]

[a2 = ab]

[a2-b2 = ab-b2]

[(a+b)(a-b) = b(a-b)]

[a+b = b]

[b+b = b]

[1+1 = 1]
[2 = 1]

Equations that lend themselves to rhyme

Euler's Equation:

Here are a few limericks about this one.

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.

e raised to the pi times i,
And plus 1 leaves you nought but a sigh.
This fact amazed Euler
That genius toiler,
And still gives us pause, bye the bye.

The Pythagorean Theorem:

A triangle's sides a, b, c,
With a vertex of 90 degrees,
If that vertext be
'Tween sides a and b,
The root a-squared plus b-squared is c.[AA1]

There are a number of lesser known equations that lend themselves to limerick form:

Equation 1:

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.[JS]

Equation 2:

Integral v-squared dv
from 1 to the cube root of 3
times the cosine
of three pi over 9
equals log of the cube root of e.

Equation 3:

One over point one-oh-two-three,
When raised to the second degree,
Divided by seven
Then minus eleven
Is approximately equal to e.[AFC]

Equation 4:

Th'integral from e-squared to e
Of 1 over v dot dv,
When raised to the prime
Between five and nine,
Is e to the i pi by 3.[MMB1]

Equation 5:

The integral from naught to pi
Of sine-squared of 2 phi d-phi,
When doubled and then
Not altered again,
Is log (minus 1) over i.[MMB1]

Equation 6:

To find Euler's Gamma of three,
Integrate to infinity
from zero, dx
x-squared on exp(x),
Or three bang divided by three.[MMB2]

Equation 7:

'Cause phi-squared less phi, minus 1,
Is exactly equal to none,
The golden mean phi,
Which so pleases the eye,
Is half of root 5 add on one.[also MMB2]

Equation 8:

The square root of minus 2 pi
On th'square root of inverse sine phi;
All that need be done
Is let phi equal one:
It's twice exp of i pi on i.[AA2]

In addition, there are a few figures that lend themselves to limericks:

Figure 1:

If a circle through B, like so,
Has arc AD with center O,
The angle at B,
Wherever B be,
Is half of the angle at O.[MMB3]

Figure 2:

A body with mass m kg
Feels a force of magnitude T.
When its weight t'wards the ground
Is added it's found
To speed up at T on m, less g.[AA3]

Computer science limericks

There once was a user named fred,
Who one day used grep, awk, and sed.
He parsed a huge text stream,
Used regexps to the extreme,
Now his file's tail is its head.

function createLimmerick(){

var scanning=terriblySlick;
do(laugh(); performNewTrick();)}

Not quite limericks...

pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?

Chebychev said it and I'll say it again:
There's always a prime between n and 2n.

Man has pondered
Since time immemorial
Why 1 is the value
Of zero-factorial.

Three jolly sailors from Blaydon-on-Tyne
They went to sea in a bottle by Klein.
Since the sea was entirely inside the hull
The scenery seen was exceedingly dull. [FW]

Little Willie was a Chem-E,
Little Willie is no more.
What Willie thought was H2O
Was really H2SO4. [CR]

When calculating polynomial degree,
The minimum value it can be
Is "1" plus the number of bends.
And remember this too my friends:
The polynomial's degree is only even
If its graph enters the same side its leavin'.