9) Aleph-naughty


As the name suggests, these links have mathematical humor of a more adult nature. While it is certainly not my intention to offend anyone who visits these links, some readers might find the the humor below a bit crude or embarrassing. Viewer discretion is advised.

Dirty Limericks

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 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 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 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 Dewar
Whose maths were incredibly pure,
Clamped his penile device
In an engineer’s vice,
Then in microns he measured his skewer.

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 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 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 Hyde,
Took a busload of girls for a ride.
And in preparation,
For multiplication,
Each girl forced her legs to divide.

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!”

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 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 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 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 Week,
Has geometry which is unique.
If A equals B
And B equals C,
ABC is his lower left cheek.

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.

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.

There once was a man from Rancine
Who invented a fucking machine.
Both concave and convex,
It could serve either sex,
But oh what a bastard to clean!1

There once was a mathematician
Who preferred an exotic position
‘Twas the joy of his life
To achieve with his wife
Topologically complex coition.

The was a young lady called Hatch
Who had a rectangular snatch.
So she practiced coition
With a mathematician,
Whose square root was just made to match.

Dirty riddles

Q: What’s the square root of 69?
A: 8 something…

Q: What’s the square root of -69?
A: i 8 something….

Q: What do you call a dwarf 69?
A: A 34.5.

Q: What’s this? (Run your hand horizontally over an invisible, flat surface.)
A: The Fourier Transform of this. (Give ’em the middle finger.)

Q: What does a topologist call a virgin?
A: Simply connected.

Dirty Jokes

A professor of mathematics sent an email to his wife:

Dear Wife,

You must realize that you are 54 years old, and I have certain needs which you are no longer able to satisfy. I am otherwise happy with you as a wife, and I sincerely hope you will not be hurt or offended to learn that by the time you receive this letter, I will be at the Grand Hotel with my 18-year-old teaching assistant. I’ll be home before midnight.

–Your Husband.

When he arrived at the hotel, there was an email waiting for him that read as follows:

Dear Husband,

You, too, are 54 years old, and by the time you receive this letter, I will be at the Breakwater Hotel with the 18-year-old pool boy. Since you are a mathematician, you will appreciate that 18 goes into 54 more times than 54 goes into 18. Therefore, don’t wait up.

–Your Wife.

Little Jimmy comes home from school one day with his head hanging low and a dejected expression. His father asks, “What’s the matter with you, boy?”

“My teacher gave me an F in math today,” Jimmy says.

“Why? What happened?” asks the father.

“I don’t know. First she asked me what 2 times 3 is. I told her 6.”

“But that’s correct, son!” says the father.

“Yeah, but then she asked me what 3 times 2 is.”

“Well what the fuck’s the difference?” demands the father.

“Yeah,” agrees Jimmy, “that’s just what I told her.”

Jimmy was in his arithmetic class when the teacher, Mrs. Jones, singles him out. “If I gave you $20,” she asks, “and you gave $5 to Mary and $5 to Sally and $5 to Betty, what would you have?”

Johnny smiles. “One hell of a good time!”

Mrs. Jones, the math teacher, asks little Jimmy, “If there were 5 birds sitting on a phone line and you shot and killed one, how many would be left?”

Jimmy answers “None.”

Mrs. Jones shakes her head. “No,” she explains, “if there were 5 birds and you shot one, then 5 take away 1 leaves 4 birds left.”

Jimmy shakes his head and replies, “No. If I shot and killed one of the birds, the others would fly away, ’cause they’d see how good a shot I was.”

Mrs. Jones smiles and says “Good point. I like the way you think.:

Jimmy looks up and says “Now I have a question for you. Three woman are eating ice cream, and one is licking it, one is sucking it, and one is biting it. Which one is married?”

Mrs. Jones thinks for a bit and says, “Ummmmm…, the one biting it?”

Jimmy smiles and says, “No, the one with the wedding band on. But I like the way you think.”

A mathematics major is walking across campus when his classmate rides up to him on a new bicycle. “Where did you get the bike from?” he asks.

“It’s a Thank you present from that freshman girl I’ve been tutoring,” he explains. “Yesterday she called me and told that she had passed her math final and wanted to drop by to thank me in person. She arrived at my place on her bicycle. When I had let her in, she took all her clothes off, smiled, and said to take anything I wanted!”

The classmate stares at him for a moment, and then replies, “Good choice. I doubt the clothes would’ve have fit.”

There are two nuns. One of them is known as Sister Mathematical (SM) and the other one is known as Sister Logical (SL). It is getting dark and they are still far away from the convent.

SM: Have you noticed that a man has been following us for the past thirty-eight and a half minutes? I wonder what he wants.

SL: It’s logical. He wants to ravage us.

SM: Oh, no! At this rate he will reach us in 15 minutes at the most. What can we do?

SL: The only logical thing to do of course is to walk faster.

SM: It’s not working.

SL: Of course it’s not working. But the man did the only logical thing. He started to walk faster too.

SM: So, what shall we do? At this rate he will reach us in one minute.

SL: The only logical thing we can do is split up. You go that way and I’ll go this way. He cannot follow us both.

So the pair split up, with Sister Mathematical heading towards the convent and Sister Logical running away from it. Making a quick decision, the man decided to follow Sister Logical. Sister Mathematical arrives at the convent and is worried about what has happened to Sister Logical. But a few short minutes later, Sister Logical arrives.

SM: Sister Logical! Thank God you are here! Tell me what happened!

SL: The only logical thing happened. The man couldn’t follow us both, so he followed me.

SM: Yes, yes! But what happened then?

SL: The only logical thing happened. I started to run as fast as I could and he started to run as fast as he could.

SM: And?

SL: The only logical thing happened. He reached me.

SM: Oh, dear! What did you do?

SL: The only logical thing to do. I lifted my dress up.

SM: Oh, Sister! What did the man do?

SL: The only logical thing to do. He pulled down his pants.

SM: Oh, no! What happened then?

SL: Isn’t it logical, Sister? A nun with her dress up can run faster than a man with his pants down…..

The sad story of little Polly Nomial

Wherein it is related how that Polygon of Womanly Virtue, your Polly Nomial (our heroine) is accosted by that Notorious Villain Curly Pi, and factored (oh, horror)

Once upon a time (1/t) pretty little Polly Nomial was strolling across a field of vectors when she came to the boundary of a singularly large matrix. Now Polly was convergent, and her mother had made it an absolute condition that she must never, ever enter such an array without her brackets on. Polly, however, who had changed her variables that morning and was feeling particularly badly behaved, ignored this condition on the basis that it was insufficient, and made her way in amongst the complex elements.

Rows and columns closed in on her from all sides. Tangents approached her surface, and she became tensor and tensor. Quite suddenly, two branches of a hyperbola touched her at a single point. She oscillated violently, became unstable, lost all sense of directrix, tripped over a square root that was protruding from the erf, and plunged headlong down a steep gradient. She was completely divergent by the time she reached the turning point. When she rounded off once more, she found herself inverted, apparently alone in a non-euclidean space.

She was being watched, however. That smooth operator, Curly Pi, was lurking inner product. As his eyes devoured her curvilinear coordinates, a singular expression crossed his face. He wondered, was she convergent? He decided to integrate improperly at once.

Hearing a common fraction behind her, Polly rotated and saw Curly Pi approaching with his lower series extended. She could see at once his degenerate conic and his dissipative terms, and knew he was irrational.

“Arcsinh!” she gasped.

“Hey, what’s your sine?” he asked. “What a symmetric set of asymptotes you have!”

“Stay away from me!” she protested. “I haven’t got any brackets on!”

“Calm yourself, my dear!” said the smooth operator. “Your fears are purely imaginary.”

“i, i, …” she thought, “Prehaps he’s not normal, but homologous.”

“What order are you?” the brute suddenly demanded.

“Seventeen,” replied Polly.

Curly leered, “I suppose you’ve never been operated upon?”

“Of course not. I’m absolutely convergent!” Polly replied quite properly.

“Come on,” said Curly: “Let’s go to decimal place I know of, and I’ll take you to the limit.”

“Never!” gasped Polly.

“Abscissa!” he swore a violent oath. Coshing her over the coefficient with a log until she was powerless, Curly removed her discontinuities. He stared at her significant places, and began smoothing her points of inflection. Poor Polly Nomial! The algorithm method was now her only hope. She felt him approaching her asymptotic limit. Her convergence would soon be gone forever.

There was no mercy; Curly was a heavy side operator. His radius squared itself and Polly’s loci quivered. He integrated by parts. He integrated by partial fractions. After he cofactored, he performed Runge-Kutta on her. The complex beast even went all the way around and did a contour integration. Curly went on operating until he satisfied her hypotheses, then he exponentiated and became completely orthogonal.

When Polly got home that night, her mother noticed that she was no longer piecewise continuous, but had been truncated in several places. But it was too late to differentiate now. As the months went by, Polly’s denominator increased monotonically. Finally, they took her to L’Hopital and generated a small but pathological function which left surds all over the place and drove Polly to deviation.

The moral of this tale: If you want to keep your expressions convergent, never allow them a single degree of freedom.

— (c) Richard A Gibbs,
The Best of The Journal of Irreproducible Results,
Workman Publishing, 1983.

e x = f (u n )

Have you done it?

  • Manipulated the denominator of an equation?
  • On your first problem set?
  • Worked on a problem set past 3:00 a.m.?
  • Worked on a problem set all night?
  • Had a hard problem?
  • Worked on a problem continuously for more than 30 minutes?
  • Worked on a problem continuously for more than four hours?
  • Done more than one problem set on the same night (i.e. both started and finished them)?
  • Done more than three problem sets on the same night?
  • Taken a math course for a full year?
  • Taken two different math courses at the same time?
  • Done at least one problem set a week for more than four months?
  • Done at least one problem set a night for more than one month (weekends excluded)?
  • Done a problem set alone?
  • Done a problem set in a group of three or more?
  • Done a problem set in a group of 15 or more?
  • Was it mixed company?
  • Have you ever inadvertently walked in upon people doing a problem set?
  • And joined in afterwards?
  • Have you ever used food doing a problem set?
  • Did you eat it all?
  • Have you ever had a domesticated pet or animal walk over you while you were doing a problem set?
  • Done a problem set in a public place where you might be discovered?
  • Been discovered while doing a problem set?
  • Have you ever applied your math to a hard science?
  • Applied your math to a soft science?
  • Done an integration by parts?
  • Done two integration by parts in a single problem?Bounded the domain and range of your function?
  • Used the domination test for improper integrals?
  • Done Newton’s Method?
  • Done the Method of Frobenius?
  • Used the Sandwich Theorem?
  • Used the Mean Value Theorem?
  • Used the Dominated Convergence Theorem?
  • Used the Hairy Ball Theorem?
  • Used a Gaussian surface?
  • Used a Lipschitz condition?
  • Used a foreign object on a math problem (eg: calculator)?
  • Used a program to improve your mathematical technique (eg: MACSYMA)?
  • Not used brackets when you should have?
  • Integrated a function over its full period?
  • Factored a polynomial under the order of 17?
  • Done a calculation in three-dimensional space?
  • Done a calculation in n-dimensional space?
  • Done a change of bases?
  • Done a change of bases specifically in order to magnify your vector?
  • Worked through four complete bases in a single night (eg: using the Graham-Schmidt method)?
  • Inserted a number into an equation?
  • Calculated the residue of a pole?
  • Scored perfectly on a test?
  • Swallowed everything your professor gave you?
  • Used explicit notation in your problem set?
  • Purposefully omitted important steps in your problem set?
  • Padded your own problem set?
  • Been blown away on a test?
  • Blown away your professor on a test?
  • Have you ever multiplied 23 by 3?
  • Have you ever used a unit?
  • …But were disappointed to find your unit was idempotent?
  • …But relieved to find your unit wasn’t nilpotent?
  • Have you ever calculated the size of your unit ball using a Weiner measure?
  • Have you ever bounded your Bessel function so that the membrane did not shoot to infinity?

Wanna do it?

  • Hey baby, what’s your sine?
  • I wish I was your derivative so I could lie tangent to your curves.
  • My love for you is like a concave up function because it is always increasing.
  • How can I know so many hundreds of digits of pi and not the 7 digits of your phone number?
  • I wish I was your second derivative so I could investigate your concavities.
  • You and I would add up better than a Riemann sum.
  • You must be a protractor, because you look good from any angle.
  • I need a little help with my Calculus, can you integrate my natural log?
  • By looking at you I can tell you’re 36-25-36, which by the way are all perfect squares.
  • Are you a 90 degree angle? ‘Cause you are looking all right!
  • My love for you is like pi… never ending.
  • I’d like to plug my solution into your equation.
  • Since distance equals velocity times time, let’s let velocity and time approach infinity, because I want to go all the way with you.
  • I am equivalent to the Empty Set when you are not with me.
  • I’m trying to get over my x. Mind if I do a u-substitution?
  • I can figure out the square root of any number in less than 10 seconds. What? You don’t believe me? Well, then, let’s try it with your phone number.
  • Hey, baby want to Squeeze my Theorem while I poly your nomial?
  • Hey…nice ass…ymptote.
  • I’m not being obtuse, but you’re acute girl.
  • I don’t know if you’re in my range, but I’d sure like to take you back to my domain.
  • Are you a 45 degree angle? Because you’re acute-y.
  • My love for you is like y=2^x… exponentially growing.
  • I’ll take you to your limit if you show me your end behavior.
  • Can I explore your mean value?
  • The derivative of my love for you is 0, because my love for you is constant.
  • I’m good at math… let’s add a bed, subtract our clothes, divide your legs, and multiply!
  • Our love is like dividing by zero… you cannot define it.
  • If you were a graphics calculator, I’d look at your curves all day long!
  • I’ve been secant you for a long time.
  • If I’m sine and you’re cosine, wanna make like a tangent?
  • I heard you’re good at algebra – Could you replace my X without asking Y?
  • Are you a math teacher? Because you got me harder than calculus.
  • I’ll take you to the limit as X approaches infinity.
  • Let’s take each other to the limit to see if we converge
  • You must be the square root of two because I feel irrational around you.
  • Let me integrate our curves so that I can increase our volume
  • If I were a function you would be my asymptote – I always tend towards you.
  • I wish i was your problem set, because then I’d be really hard, and you’d be doing me on the desk.
  • My love is like an exponential curve – it’s unbounded
  • My love for you is like a fractal – it goes on forever.
  • I hope you know set theory because I want to intersect and union you
  • You’ve got more curves than a triple integral.
  • Honey, you’re sweeter than pi.
  • If you were sin^2 x and I was cos^2 x, then together we’d make one.
  • Baby, you’re like a student and I’m like a math book… you solve all my
  • My friends told me that I should ask you out because you can’t differentiate. Do you need math help?
  • Wanna expand my polynomial?
  • Voulez vous Cauchy avec moi?
  • Is your name Google? Because you have everything I’ve been searching for.
  • You make my software turn into hardware!Are you sitting on the F5 key?
  • Cause your ass is refreshing.
  • Want to see my hard disk? I promise it isn’t 3.5 inches and it ain’t floppy.
  • You can put a Trojan on my Hard Drive anytime.
  • You still use Internet Explorer? You must like it nice and slow.
  • I hope you’re an ISO file, because I’d like to mount you.
  • My servers never go down… but I do!
  • My ‘up-time’ is better than BSD.You’ve stolen the ASCII to my heart.
  • Are you a computer keyboard? Because you’re my type.
  • You got me stuck on Caps Lock, if you know what I mean.
  • If you were a web browser, you’d be called a Fire-foxy lady
  • Mind if I run a sniffer to see if your ports are open?
  • You must be Windows 95 because you’ve got me feeling so unstable.
  • I was hoping you wouldn’t block my pop-up.
  • If you have an empty slot, I have the card to fill it.
  • Hey, how ’bout I take off your cover and insert a bigger CPU.
  • Roses are #ff0000, violets are #0000ff, all my base are belong to you.
  • Are your pants a compressed file? Because I’d love to unzip them!
  • Girl, you are hotter than the bottom of my laptop.
  • Computer techs have skilled fingers if you know what I mean.

How do they do it?

  • Mathematicians do it by the numbers.
  • Mathematicians do it in numbers.
  • Mathematicians do it constantly.
  • Mathematicians do it in theory.
  • Mathematicians do it to prove themselves.
  • Mathematicians do it with a Minkowski sausage.
  • Mathematicians do it with relations.
  • Mathematicians do it with Nobel’s wife.
  • Mathematicians do it without limit.
  • Mathematicians do it ad infinitum.
  • Mathematicians have to prove they did it.
  • Mathematicians do not do it. They leave it as an exercise to the reader.
  • Aerodynamicists do it in drag.
  • Algebraic geometers do it for variety.
  • Algebraic geometers do it three-fold.
  • Algebraists do it by symbolic manipulation.
  • Algebraists do it in a ring.
  • Algebraists do it in fields.
  • Algebraists do it in groups.
  • Algebraists do it with rings.
  • Analysts do it continuously.
  • Analysts do it smoothly.
  • Analysts do it almost everywhere.
  • Analysts do it to the limit.
  • Analysts do it with their real parts.
  • Analytic number theorists do it in the critical strip.
  • Applied mathematicians do it by computer simulation.
  • Applied mathematicians do it with a real model.
  • AI researchers have tried to do it since the 60’s but haven’t yet succeeded.
  • AI researchers do it heuristically when principled techniques fail.
  • Astrophysicists do it in the dark.
  • Astrophysicists do it with telescopes.
  • Astrophysicists do it with large objects.
  • Banach spacers do it completely.
  • Bayesians do it with improper priors.
  • Catastrophe theorists do it falling off part of a sheet.
  • Chaoticians do it with sensitive dependence.
  • Class field theorists do it by capitulation.
  • Classical geometers do it with a straight edge.
  • Classical geometers do it from the right angle.
  • Classical geometers do it on the nine-point circle.
  • Combinatorists do it discretely.
  • Combinatorists do it as many ways as they can.
  • Commutative algebraists do it regularly.
  • Complex analysts do it between the sheets.
  • Complex analysts do it under a universal cover.
  • Complex analysts do it with imaginary parts.
  • Computer scientists do it depth-first.
  • Constructivists do it without excluding the middle.
  • Cosmologists do it in the first three minutes.
  • Decision theorists do it optimally.
  • Differential analysts do it in a degenerate case.
  • Differential geometers do it on smooth contours.
  • Differential geometers do it over and under the curves.
  • Functional analysts do it with compact support.
  • Functional analysts do it with degenerate colonels.
  • Game theorists do it by dominance.
  • Game theorists do it with saddle points.
  • Game theorists score most often.
  • General relativists do it with curvature.
  • General relativists do it with rubber sheets and canteloupes.
  • Geometers do it with involutions.
  • Geometers do it symmetrically.
  • Graph theorists do it in four colors.
  • Group theorists do it simply.
  • Group theorists do it with the Monster.
  • Hilbert spacers do it orthogonally.
  • Inductionists do it forever if they can do one and can do one more.
  • Large cardinals do it inaccessibly.
  • Linear programmers do it with nearest neighbors.
  • Logicians do it by choice.
  • Logicians do it consistently and completely.
  • Logicians do it incompletely or inconsistently.
  • Logicians do it necessarily and sufficiently.
  • Logicians do it with Jensen’s device.
  • (Logicians do it) or [not (logicians do it)].
  • Mathematical physicists understand the theory of how to do it, but have difficulty obtaining practical results.
  • Matrix computationalists do it by pivoting.
  • Matrix computationalists do it on a mesh.
  • Number theorists do it perfectly.
  • Number theorists do it prime number of times.
  • Physicists do it on the event horizon.
  • Physicists do it in waves.
  • Physicists do it with ropes and pulleys.
  • Physicists do it with vectors.
  • Physicists do it at the right moments.
  • Physicists do it with force.
  • Physicists do it on the spur of the moment.
  • Pure mathematicians do it rigorously.
  • Probabilists do it on random walks.
  • Probabilists do it stochastically.
  • Quantum physicists can either know how fast they do it, or where they do it, but not both.
  • Representation theorists do it for Schur.
  • Ring theorists do it ideally.
  • Set theorists do it with cardinals.
  • Set theorists do it with morass.
  • Statisticians do it.  Probably.
  • Statisticians do it continuously but discretely.
  • Statisticians do it when it counts.
  • Statisticians do it with 95% confidence.
  • Statisticians do it with large numbers.
  • Statisticians do it with only a 5% chance of being rejected.
  • Statisticians do it with two-tail T tests.
  • Statisticians do it. After all, it’s only normal.
  • Statisticians do all the standard deviations.
  • Statisticians would like to do it with the population, but only get a small sample.
  • Topologists do it on rubber sheets.
  • Topologists do it openly.
  • Togologists do it in multiply connected domains.
  • Topologists don’t do it. They would rather knot.
  • Topos theorists do it pointlessly.
  • Variationists do it locally and globally.
  • Cantor did it diagonally.
  • Cantor did it ’till he was crazy.
  • Fermat tried to do it in the margin, but couldn’t fit it in.
  • Galois did it the night before.
  • Heisenberg might have done it here.
  • Moebius always did it on the same side.
  • Markov does it with chains.
  • Newton did it standing on the shoulders of giants.
  • Turing did it but couldn’t decide if he’d finished.

How to do it?

  • Look for her tan line.
  • Subtract her pants.
  • Stack her on the bed.
  • Divide her legs.
  • Calculate the distance.
  • Arc her back.
  • Add your length.
  • Function properly.
  • Provide constant movement.
  • Give her a square root.
  • Turn her over for a reverse Polish notion.
  • Gradiently increase the integer.
  • Round the remainder.
  • Fill her pi.
  • Hope she doesn’t multiply.
  • Log the event.
  • Sine on the dotted line.
  • Get her to cosine.
  • Profit from the experience.
  • Base the result on an exponent.

How to do it quickly?

  • Add two people,
  • Subtract their clothes,
  • Divide the legs,
  • And multiply!

Functional relationship

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?

Stress analysis of a strapless evening gown

Effective as the strapless evening gown is in attracting attention, it presents tremendous engineering problems to the structual engineer. He is faced with the problem of designing a dress which appears as if it will fall at any moment and yet actyuall stays up some small factor of safety. Some of the problems faced by the engineer readily appear from the following structual analysis of strapless evening gowns.

If a small elemental strip of cloth from a strapless evening gown is isolated as a free body in the area of plane A in figure 1, it can be seen that the tangential force F is balanced by the equal and opposite tangential force F. The downward vertical force W (weight of the dress) is balanced by the force V acting vertically upward due to the stress in the cloth above plane A. Since the algebraic summation of vertical and horizontal forces is zero and no moments are acting, the elemental strip is in equilibrium.

Consider now an elemental strip of cloth isolated as a free body in the area of plane B of figure 1. The two tangible forces F1 and F2 are equal and opposite as before, but the force W (weight of the dress) is not balanced by an upward force V because there is no cloth above plane B to supply the force. Thus, the algebraic summation of horizontal forces is zero, but the sum of the vertical forces is not zero. Therefore, this elemental strip is not in equilibrium; but it is imperative, for social reasons, that this elemental strip be in equilibrium. If the female is naturally blessed with sufficient pectoral development, she can supply this very vital force and maintain the elemental strip at equilibrium. If she is not, the engineer has to supply this force by artificial methods.

In some instances, the engineer has made use of friction to supply this force. The friction force is expressed by F = f N, where F is the frictional force, f is the coefficient of friction, and N is the normal force acting perpendicularly to F. Since, for a given female and a given dress, f is constant, then to increase F, the normal force N must be increased. One obvious method of increasing the normal force is to make the diameter of the dress at c in figure 2 smaller than the diameter of the female at this point. This has, however, the disadvantage of causing the fibres along the line c to collapse, and, if too much force is applied, the wearer will experience discomfort.

As if the problem were not complex enough, some females require that the back of the gown be lowered to increase the exposure and correspondingly attract more attention. In this case, the horizontal forces F1 and F2 (figure 1) are no longer acting horizontally, but are replaced by forces T1 and T2 acting downward at an angle a. Therefore, there is a total downward force equal to the weight of the dress below B plus the vector summation of T1 and T2. This vector sum increases in magnitude as the back is lowered because R = 2 T sin(a), and the angle a increases as the back is lowered. Therefore, the vertical uplifting force which has to be supplied for equilibrium is increased for low-back gowns.

Since these evening gowns are worn to dances, an occasional horizontal force, shown in figure 2 as i, is accidentally delivered to the beam at the point c, causing impact loading, which compresses all the fibres of the beam. This compression tends to cancel the tension in the fibres between e and b, but it increases the compression between c and d. The critical area is a point d, as the fibres here are subject not only to compression due to moment and impact, but also to shear due to the force s; a combination of low, heavy dress with impact loading may bring the fibres at point d to the “danger point.”

There are several reasons why the properties discussed in this paper have never been determined. For one, there is a scarcity of these beams for experimental investigation. Many females have been asked to volunteer for experiments along these lines in the interest of science, but unfortunately, no cooperation was encountered. There is also the difficulty of the investigator having the strength of mind to ascertain purely scientific facts. Meanwhile, trial and error and shrewd guesses will have to be used by the engineer in the design of strapless evening gowns until thorough investigations can be made.

— Robert A Baker
A stress analysis of a strapless evening gown, and other essays
(c) (c) Prentice Hall, 1963