rafy@cairo.anu.edu.au (Rafy Marootians):
Logic is a systematic method for getting the wrong conclusion...
with confidence.
Surely _statistics_ is a systematic method for getting the wrong conclusion...
with 95% confidence.
From: phk@data.fls.dk (Poul-Henning Kamp/P-HK)
Mathematics is the systematic misuse of a nomenclature developed for that
specific purpose.
M__________________________________________________________________________
A topologist is a man who doesn't know the difference between a coffee
up and a doughnut.
M__________________________________________________________________________
From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman)
Most prime numbers are even.
Proof: pick up any math text and look
for a prime number. The first one you
find will probably be even.
M__________________________________________________________________________
Once upon a time, when I was training to be a mathematician, a group of
us bright young students taking number theory discovered the names of
the smaller prime numbers.
2: The Odd Prime --
It's the only even prime, therefore is odd. QED.
3: The True Prime --
Lewis Carroll: "If I tell you three times, it's true."
31: The Arbitrary Prime --
Determined by unanimous unvote. We needed an arbitrary prime
in case the prof asked for one, and so had an election. 91
received the most votes (well, it *looks* prime) and 3+4i the
next most. However, 31 was the only candidate to receive none
at all.
Since the composite numbers are formed from primes, their qualities are
derived from those primes. So, for instance, the number 6 is "odd but
true", while the powers of 2 are all extremely odd numbers.
M__________________________________________________________________________
From: Tpotter@voyager.cris.com (Tom_Potter)
Tom Potter: Life is complex. It has real and imaginary components.
M__________________________________________________________________________
From: Erland.Gadde@sm.luth.se (Erland Gadde)
Trigonometry for farmers: swine and cowswine.
M__________________________________________________________________________
From: mstueben@pen.k12.va.us (Michael A. Stueben)
I liked the PI-ous one best.
M__________________________________________________________________________
Q: What does an analytic number theoriest say when he is drowning?
A: Log-log, log-log, log-log, . . .
M__________________________________________________________________________
From: Alan Craig
Mathematicians have announced the existence of a new whole number which lies
between 27 and 28. "We don't know why it's there or what it does," says
Cambridge mathematician, Dr. Hilliard Haliard, "we only know that it doesn't
behave properly when put into equations, and that it is divisible by six,
though only once."
M__________________________________________________________________________
From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman)
"The number you have dialed is imaginary.
Please rotate your phone 90 degrees and try again."
M__________________________________________________________________________
From: david_gonda@qm.yale.edu
A student was doing miserably on his oral final exam in General Toplogy
(yes, this guy _really_ did give oral finals in topology). Exasperated by
the student's abysmal performance up to that point, the professor asked the
student "So, what _do_ you know about topology?" The student replied, "I
know the definition of a topologist." The professor asked him to state the
definition, expecting to get the old saw about someone who can't tell the
difference between a coffee cup and a doughnut. Instead, the student
replied: "A topologist is someone who can't tell the difference between his
ass and a hole in the ground, but who can tell the difference between his
ass and _two_ holes in the ground."
The student passed.
M__________________________________________________________________________
Definitions of Terms Commonly Used in Higher Math
The following is a guide to the weary student of mathematics who
is often confronted with terms which are commonly used but rarely
defined. In the search for proper definitions for these terms we
found no authoritative, nor even recognized, source. Thus, we
followed the advice of mathematicians handed down from time
immortal: "Wing It."
CLEARLY: I don't want to write down all the "in-
between" steps.
TRIVIAL: If I have to show you how to do this, you're
in the wrong class.
OBVIOUSLY: I hope you weren't sleeping when we discussed
this earlier, because I refuse to repeat it.
RECALL: I shouldn't have to tell you this, but for
those of you who erase your memory tapes
after every test...
WLOG (Without Loss Of Generality): I'm not about to do all the
possible cases, so I'll do one and let you
figure out the rest.
IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should
be able to prove this without me holding your
hand.
CHECK or CHECK FOR YOURSELF: This is the boring part of the
proof, so you can do it on your own time.
SKETCH OF A PROOF: I couldn't verify all the details, so I'll
break it down into the parts I couldn't
prove.
HINT: The hardest of several possible ways to do a
proof.
BRUTE FORCE (AND IGNORANCE): Four special cases, three counting
arguments, two long inductions, "and a
partridge in a pair tree."
SOFT PROOF: One third less filling (of the page) than
your regular proof, but it requires two extra
years of course work just to understand the
terms.
ELEGANT PROOF: Requires no previous knowledge of the subject
matter and is less than ten lines long.
SIMILARLY: At least one line of the proof of this case is
the same as before.
CANONICAL FORM: 4 out of 5 mathematicians surveyed
recommended this as the final form for their
students who choose to finish.
TFAE (The Following Are Equivalent): If I say this it means that,
and if I say that it means the other thing,
and if I say the other thing...
BY A PREVIOUS THEOREM: I don't remember how it goes (come to
think of it I'm not really sure we did this
at all), but if I stated it right (or at
all), then the rest of this follows.
TWO LINE PROOF: I'll leave out everything but the conclusion,
you can't question 'em if you can't see 'em.
BRIEFLY: I'm running out of time, so I'll just write
and talk faster.
LET'S TALK THROUGH IT: I don't want to write it on the board lest
I make a mistake.
PROCEED FORMALLY: Manipulate symbols by the rules without any
hint of their true meaning (popular in pure
math courses).
QUANTIFY: I can't find anything wrong with your proof
except that it won't work if x is a moon of
Jupiter (Popular in applied math courses).
PROOF OMITTED: Trust me, It's true.
M__________________________________________________________________________
From: mstueben@pen.k12.va.us (Michael A. Stueben)
WHAT'S OUT AND WHAT'S IN
FOR
MATHEMATICAL TERMS
by
Michael Stueben (November 7, 1994)
---------------------------------------------------------
Today it is considered an egregious faux pas to speak
or write in the crude antedated terms of our grandfathers.
To assist the isolated student and the less sophisticated
teacher, I have prepared the following list of currently
fashionable mathematical terms in academia. I pass this
list on to the general public as a matter of charity and
in the hope that it will lead to more refined elucidation
from young scholars.
OUT IN
thinking: hypothesizing.
proof by contradiction or indirect proof: reductio ad absurdum.
mistake: non sequitur.
starting place: handle.
with corresponding changes: mutatis mutandis.
counterexample: pathological exception.
consequently: ipso facto.
swallowing results: digesting proofs.
therefore: ergo.
has an easy-to-understand, but hard-to-find solution: obvious.
has two easy-to-understand, but hard-to-find solutions: trivial.
truth: tautology.
empty: vacuous.
drill problems: plug-and-chug work.
criteria: rubric.
example: substantive instantiation.
similar structure: homomorphic.
very similar structure: isomorphic.
same area: isometric.
arithmetic: number theory.
count: enumerate.
one: unity.
generally/specifically: globally/locally.
constant: invariant.
bonus result: corollary.
distance: metric measure.
several: a plurality.
function/argument: operator/operand.
separation/joining: bifurcation/confluence.
fourth power or quartic: biquadratic.
random: stochastic.
unique condition: a singularity.
uniqueness: unicity.
tends to zero: vanishes.
tip-top point: apex.
half-closed: half-open.
concave: non-convex.
rectangular prisms: parallelepipeds.
perpendicular (adj.): orthogonal.
perpendicular (n.): normal.
Euclid: Descartes.
Fermat: Wiles.
path: trajectory.
shift: rectilinear translation.
similar: homologous.
very similar: congruent.
whopper-jawed: skew or oblique.
change direction: perturb.
join: concatenate.
approximate to two or more places: accurate.
high school geometry or plane geometry: geometry of the Euclidean plane
under the Pythagorean metric.
clever scheme: algorithm.
initialize to zero: zeroize.
* : splat.
{ : squiggle.
decimal: denary.
alphabetical order: lexical order.
a divide-and-conquer method: an algorithm of logarithmic order.
student ID numbers: witty passwords.
that bitch secretary in the math dept: the witch of Agnesi
numerology and number sophistry: descriptive statistics
Special thanks to Peter Braxton who got me started
writing this stuff and who contributed five of
the items above.
M__________________________________________________________________________
From: goddard@NeXTwork.Rose-Hulman.Edu (Bart E. Goddard)
& rja093@nwu.edu (Rajan Jain)
mathematician's PICK UP LINE
Hey baby, How would you like to join me in some math? We'll add you and me,
subtract our clothes, divide your legs, and multiply!
Of course, we'll be entirely discrete.
M__________________________________________________________________________
From: hammond@cs.utk.edu (James Michael Hammond)
When Mathematicians Go Bad
"Psst, c'mere," said the shifty-eyed man wearing a long black
trenchcoat, as he beckoned me off the rainy street into a damp dark
alley. I followed.
"What are you selling?" I asked.
"Geometrical algebra drugs."
"Huh!?"
"Geometry drugs. Ya got your uppers, your downers, your sidewaysers, your
inside-outers..."
"Stop right there," I interrupted. "I've never heard of inside-
outers."
"Oh, man, you'll love 'em. Makes you feel like M.C. ever-lovin'
Escher on a particularly weird day."
"Go on..."
"OK, your inside-outers, your arbitrary bilinear mappers, and here,
heh, here are the best ones," he said, pulling out a large clear
bottle of orange pills.
"What are those, then?" I asked.
"Givens transformers. They'll rotate you about more planes than you
even knew existed."
"Sounds gross. What about those bilinear mappers?"
"There's a whole variety of them. Here's one you'll love -- they call
it 'One Over Z' on the street. Take one of these little bad boys and
you'll be on speaking terms with the Point at Infinity."
M__________________________________________________________________________
From: v090nlb4@ubvms.cc.buffalo.edu (Mark J. VanDerwater)
halloween math
Q: Wadaya get when you take the circumference of your jack-o-lantern and
divide it by its diameter?
A: Pumpkin Pi
M__________________________________________________________________________
UR 2 Good
2 Me
2 Be
4 Got
==
10 "You are too good to me to be forgotten"
M__________________________________________________________________________
A lazy dog is a slow pup.
A slope up is an inclined plane.
An ink-lined plane is a sheet of writing-paper.
Therefore lazy dog is a sheet of writing-paper.
M__________________________________________________________________________
Complete the next two terms of this sequence:
O T T F F S S E .. ..
(A. N T - Nine Ten)
Likewise here:
3 3 5 4 4 3 5 5
(A. 4 3 -number of letters in the words "nine" and "ten").
M__________________________________________________________________________
The four branches of arithmetic - ambition, distraction, uglification and
derision. (Lewis Caroll: "Alice in Wonderland")
ME_________________________________________________________________________
The first law of Engineering Mathematics: All infinite series converge,
and moreover converge to the first term.
M__________________________________________________________________________
Numb, adj., devoid of sensation...
Number, comparative of numb.
[Webster's Third New international Dictionary]
M__________________________________________________________________________
Patageometry, n.:
The study of those mathematical properties that are invariant
under brain transplants.
M__________________________________________________________________________
kcarver@fox.nstn.ns.ca (Kevin Carver) writes:
I know most of you people who are "into" math have heard the pun (over and
over and over ...) about knowing the difference between your "asymptote and
a hole in the graph" but here's one you may not have heard. IT'S A TRUE
STORY!
A student at our high school a few years back, having had his fill with
drawing graph after graph in senior high math class, told his teacher:
Mrs. ___, I'll do algebra, I'll do trig, and I'll even do statistics, but
graphing is where I draw the line!
M__________________________________________________________________________
This one can better be told in a pub. First three points on the table:
a
b
c
On a lies a beermat and on c stands a glass. The mathematican has
to move the c to a. He takes the glas and puts it on the beermat.
Now the glas is put on point b and the mathematican has to move it
to a. The mathematican takes the glas and puts it on c - the problem
has been reduced to one already solved.
M__________________________________________________________________________
A bunch of Polish scientists decided to flee their repressive
government by hijacking an airliner and forcing the pilot to fly them
to a western country. They drove to the airport, forced their way on
board a large passenger jet, and found there was no pilot on board.
Terrified, they listened as the sirens got louder. Finally, one of
the scientists suggested that since he was an experimentalist, he
would try to fly the aircraft.
He sat down at the controls and tried to figure them out. The sirens
got louder and louder. Armed men surrounded the jet. The would be
pilot's friends cried out, "Please, please take off now!!!
Hurry!!!!!!"
The experimentalist calmly replied, "Have patience. I'm just a simple
pole in a complex plane."
M__________________________________________________________________________
A group of Polish tourists is flying on a small airplane through the
Grand Canyon on a sightseeing tour. The tour guide announces: "On the
right of the airplane, you can see the famous Bright Angle Falls."
The tourists leap out of their seats and crowd to the windows on the
right side. This causes a dynamic imbalance, and the plane violently
rolls to the side and crashes into the canyon wall. All aboard are
lost. The moral to this episode is: always keep your poles off the
right side of the plane.
Caveat: While this joke mentions Polish people, it is not, in my
opinion, in the category of the infamous Polish jokes. I hope no one
is offended but only humored.
M__________________________________________________________________________
Three standard Peter Lax jokes (heard in his lectures) :
1. What's the contour integral around Western Europe?
Answer: Zero, because all the Poles are in Eastern Europe!
Addendum: Actually, there ARE some Poles in Western Europe, but
they are removable!
2. An English mathematician (I forgot who) was asked by his very religious
colleague:
Do you believe in one God?
Answer: Yes, up to isomorphism!
3. What is a compact city?
It's a city that can be guarded by finitely many near-sighted
policemen!
M__________________________________________________________________________
"Algebraic symbols are used when you do not know what you are talking about."
M__________________________________________________________________________
Q: What quantity is represented by this ?
/\ /\ /\
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
/______\ /______\ /______\
|| || ||
|| || ||
A: 9, tree + tree + tree
Q: A dust storm blows through, now how much do you have ?
A: 99, dirty tree + dirty tree + dirty tree
Q: Some birds go flying by and leave their droppings,
one per tree, how many is that ?
A: 100, dirty tree and a turd + dirty tree and a turd
+ dirty tree and a turd
M__________________________________________________________________________
Asked how his pet parrot died, the mathematician answered
"Polynomial. Polygon."
M__________________________________________________________________________
Lumberjacks make good musicians because of their natural logarithms.
M__________________________________________________________________________
From: Dr. David Batchelor batchelor@nssdca.gsfc.nasa.gov:
Theorem: Consider the set of all sets that have never been considered.
Hey! They're all gone!! Oh, well, never mind...
M__________________________________________________________________________
Pie are not square. Pie are round. Cornbread are square.
M__________________________________________________________________________
This was made by Mike Bender and Sarah Herr:
MATHEMATICS PURITY TEST
Count the number of yes's, subtract from 60, and divide by 0.6.
The Basics
1) Have you ever been excited about math?
2) Had an exciting dream about math?
3) Made a mathematical calculation?
4) Manipulated the numerator of an equation?
5) Manipulated the denominator of an equation?
6) On your first problem set?
7) Worked on a problem set past 3:00 a.m.?
8) Worked on a problem set all night?
9) Had a hard problem?
10) Worked on a problem continuously for more than 30 minutes?
11) Worked on a problem continuously for more than four hours?
12) Done more than one problem set on the same night (i.e. both
started and finished them)?
13) Done more than three problem sets on the same night?
14) Taken a math course for a full year?
15) Taken two different math courses at the same time?
16) Done at least one problem set a week for more than four months?
17) Done at least one problem set a night for more than one month
(weekends excluded)?
18) Done a problem set alone?
19) Done a problem set in a group of three or more?
20) Done a problem set in a group of 15 or more?
21) Was it mixed company?
22) Have you ever inadvertently walked in upon people doing a problem set?
23) And joined in afterwards?
24) Have you ever used food doing a problem set?
25) Did you eat it all?
26) Have you ever had a domesticated pet or animal walk over you while you
were doing a problem set?
27) Done a problem set in a public place where you might be discovered?
28) Been discovered while doing a problem set?
Kinky Stuff
29) Have you ever applied your math to a hard science?
30) Applied your math to a soft science?
31) Done an integration by parts?
32) Done two integration by parts in a single problem?
33) Bounded the domain and range of your function?
34) Used the domination test for improper integrals?
35) Done Newton's Method?
36) Done the Method of Frobenius?
37) Used the Sandwich Theorem?
38) Used the Mean Value Theorem?
39) Used a Gaussian surface?
40) Used a foreign object on a math problem (eg: calculator)?
41) Used a program to improve your mathematical technique (eg: MACSYMA)?
42) Not used brackets when you should have?
43) Integrated a function over its full period?
44) Done a calculation in three-dimensional space?
45) Done a calculation in n-dimensional space?
46) Done a change of bases?
47) Done a change of bases specifically in order to magnify your vector?
48) Worked through four complete bases in a single night (eg: using the
Graham-Schmidt method)?
49) Inserted a number into an equation?
50) Calculated the residue of a pole?
51) Scored perfectly on a math test?
52) Swallowed everything your professor gave you?
53) Used explicit notation in your problem set?
54) Purposefully omitted important steps in your problem set?
55) Padded your own problem set?
56) Been blown away on a test?
57) Blown away your professor on a test?
58) Have you ever multiplied 23 by 3?
59) Have you ever bounded your Bessel function so that the membrane
did not shoot to infinity?
69) Have you ever understood the following quote:
"The relationship between Z^0 to C_0, B_0, and H_0
is an example of a general principle which we have
encountered: the kernel of the adjoint of a linear
transformation is both the annihilator space of the
image of the transformation and also the dual space
of the quotient of the space of which the image is
a subspace by the image subspace."
(Shlomo & Bamberg's _A "Course" in Mathematics for
Students of Physics_)
M__________________________________________________________________________
From: RVFT60@email.sps.mot.com (Mike Scott)
A Cherokee indian chief had three wives, each of whom was pregnant.
The first squaw gave birth to a boy, and the chief was so elated he
built her a teepee made of buffalo hide. A few days later, the second
squaw gave birth, and also had a boy. The chief was extremely happy;
he built her a teepee made of antelope hide.
The third squaw gave birth a few days later, but the chief kept the
birth details a secret. He built the woman a teepee out of
hippopotamus hide, and challenged the people in the tribe to guess the
most recent birth details, the correct guesser receiving a fine prize.
Several of his people tried, but were unsuccessful in their guesses.
Finally, a young brave came forth and declared that the third wife had
delivered twin boys. "Correct"!, cried the chief. "How did you know"?
"It's simple", replied the warrior. "The value of the squaw of the
hippopotamus is equal to the sons of the squaws of the other two hides."
M__________________________________________________________________________
A tribe of Native Americans generally referred to their woman by the
animal hide with which they made their blanket. Thus, one woman might
be known as Squaw of Buffalo Hide, while another might be known as
Squaw of Deer Hide. This tribe had a particularly large and strong
woman, with a very unique (for North America anyway) animal hide for
her blanket. This woman was known as Squaw of Hippopotamus hide, and
she was as large and powerful as the animal from which her blanket was
made.
Year after year, this woman entered the tribal wrestling tournament,
and easily defeated all challengers; male or female. As the men of
the tribe admired her strength and power, this made many of the other
woman of the tribe extremely jealous. One year, two of the squaws
petitioned the Chief to allow them to enter their sons together as a
wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as
a team. In this way, they hoped to see that she would no longer be
champion wrestler of the tribe.
As the luck of the draw would have it, the two sons who were wrestling
as a tandem met the squaw in the final and championship round of the
wrestling contest. As the match began, it became clear that the squaw
had finally met an opponent that was her equal. The two sons wrestled
and struggled vigorously and were clearly on an equal footing with the
powerful squaw. Their match lasted for hours without a clear victor.
Finally the chief intervened and declared that, in the interests of
the health and safety of the wrestlers, the match was to be terminated
and that he would declare a winner.
The chief retired to his teepee and contemplated the great struggle he
had witnessed, and found it extremely difficult to decide a winner.
While the two young men had clearly outmatched the squaw, he found it
difficult to force the squaw to relinquish her tribal championship.
After all, it had taken two young men to finally provide her with a
decent match. Finally, after much deliberation, the chief came out
from his teepee, and announced his decision. He said...
"The Squaw of the Hippopotamus hide is equal to the sons of the squaws
of the other two hides"
M__________________________________________________________________________
A guy decided to go to the brain transplant clinic to refreshen his
supply of brains. The secretary informed him that they had three
kinds of brains available at that time. Doctors' brains were going
for $20 per ounce and lawyers' brains were getting $30 per ounce. And
then there were mathematicians' brains which were currently fetching
$1000 per ounce.
"A 1000 dollars an ounce!" he cried. "Why are they so expensive?"
"It takes more mathematicians to get an ounce of brains," she explained.
M__________________________________________________________________________
A topologist walks into a bar and orders a drink. The bartender,
being a number theorist, says, "I'm sorry, but we don't serve
topologists here."
The disgruntled topologist walks outside, but then gets an idea and
performs Dahn surgery upon herself. She walks into the bar, and the
bartender, who does not recognize her since she is now a different
manifold, serves her a drink. However, the bartender thinks she looks
familiar, or at least locally similar, and asks, "Aren't you that
topologist that just came in here?"
To which she responds, "No, I'm a frayed knot."
M__________________________________________________________________________
There are three kinds of people in the world;
those who can count and those who can't.
And the related:
There are two groups of people in the world;
those who believe that the world can be
divided into two groups of people,
and those who don't.
M__________________________________________________________________________
The world is divided into two classes:
people who say "The world is divided into two classes",
and people who say
The world is divided into two classes:
people who say: "The world is divided into two classes",
and people who say:
The world is divided into two classes:
people who say ...
M__________________________________________________________________________
What follows is a "quiz" a student of mine once showed me (which she'd
gotten from a previous teacher, etc...). It's multiple choice, and if
you sort the letters (with upper and lower case disjoint) questions
and answers will come out next to each other. Enjoy...
S. What the acorn said when he grew up
N. bisects
u. A dead parrot
g. center
F. What you should do when it rains
R. hypotenuse
m. A geometer who has been to the beach
H. coincide
h. The set of cards is missing
y. polygon
A. The boy has a speech defect
t. secant
K. How they schedule gym class
p. tangent
b. What he did when his mother-in-law wanted to go home
D. ellipse
O. The tall kettle boiling on the stove
W. geometry
r. Why the girl doesn't run a 4-minute mile
j. decagon
M__________________________________________________________________________
___ 1. That which Noah built.
___ 2. An article for serving ice cream.
___ 3. What a bloodhound does in chasing a woman.
___ 4. An expression to represent the loss of a parrot.
___ 5. An appropriate title for a knight named Koal.
___ 6. A sunburned man.
___ 7. A tall coffee pot perking.
___ 8. What one does when it rains.
___ 9. A dog sitting in a refrigerator.
___ 10. What a boy does on the lake when his motor won't run.
___ 11. What you call a person who writes for an inn.
___ 12. What the captain said when the boat was bombed.
___ 13. What a little acorn says when he grows up.
___ 14. What one does to trees that are in the way.
___ 15. What you do if you have yarn and needles.
___ 16. Can George Washington turn into a country?
A. hypotenuse I. circle
B. polygon J. axiom
C. inscribe K. cone
D. geometry L. coincide
E. unit M. cosecant
F. center N. tangent
G. decagone O. hero
H. arc P. perpendicular
M__________________________________________________________________________
A team of engineers were required to measure the height of a flag
pole. They only had a measuring tape, and were getting quite
frustrated trying to keep the tape along the pole. It kept falling
down, etc.
A mathematician comes along, finds out their problem, and proceeds to
remove the pole from the ground and measure it easily.
When he leaves, one engineer says to the other: "Just like a
mathematician! We need to know the height, and he gives us the
length!"
M__________________________________________________________________________
There was once a very smart horse. Anything that was shown it, it
mastered easily, until one day, its teachers tried to teach it about
rectangular coordinates and it couldn't understand them. All the
horse's acquaintances and friends tried to figure out what was the
matter and couldn't. Then a new guy (what the heck, a computer
engineer) looked at the problem and said,
"Of course he can't do it. Why, you're putting Descartes before the
horse!"
M__________________________________________________________________________
"The integral of e to the x is equal to f of the quantity
u to the n."
/ x n
| e = f(u )
/
M__________________________________________________________________________
TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
1. I accidentally divided by zero and my paper burst into flames.
2. Isaac Newton's birthday.
3. I could only get arbitrarily close to my textbook. I couldn't
actually reach it.
4. I have the proof, but there isn't room to write it in this margin.
5. I was watching the World Series and got tied up trying to prove
that it converged.
6. I have a solar powered calculator and it was cloudy.
7. I locked the paper in my trunk but a four-dimensional dog got in
and ate it.
8. I couldn't figure out whether i am the square of negative one or
i is the square root of negative one.
9. I took time out to snack on a doughnut and a cup of coffee.
I spent the rest of the night trying to figure which one to dunk.
10. I could have sworn I put the homework inside a Klein bottle, but
this morning I couldn't find it.
M__________________________________________________________________________
The guy gets on a bus and starts threatening everybody: "I'll
integrate you! I'll differentiate you!!!" So everybody gets scared and
runs away. Only one person stays. The guy comes up to him and
says: "Aren't you scared, I'll integrate you, I'll differentiate
you!!!" And the other guy says; "No, I am not scared, I am e^x."
M__________________________________________________________________________
A mathematician went insane and believed that he was the
differentiation operator. His friends had him placed in a mental
hospital until he got better. All day he would go around frightening
the other patients by staring at them and saying "I differentiate
you!"
One day he met a new patient; and true to form he stared at him and
said "I differentiate you!", but for once, his victim's expression
didn't change. Surprised, the mathematician marshalled his energies,
stared fiercely at the new patient and said loudly "I differentiate
you!", but still the other man had no reaction. Finally, in
frustration, the mathematician screamed out "I DIFFERENTIATE YOU!" --
at which point the new patient calmly looked up and said, "You can
differentiate me all you like: I'm e to the x."
M__________________________________________________________________________
A function and a differentiation operator meet somewhere in
Hilbert space.
The differentation operator: Make place or I differentiate you.
Function: Forget it buster, I am e^x.
The differentation operator: Well, I am d/dy.
M__________________________________________________________________________
Boy's Life, May 1973:
Ralph: Dad, will you do my math for me tonight?
Dad: No, son, it wouldn't be right.
Ralph: Well, you could try.
M__________________________________________________________________________
Mrs. Johnson the elementary school math teacher was having children do
problems on the blackboard that day.
``Who would like to do the first problem, addition?''
No one raised their hand. She called on Tommy, and with some help he
finally got it right.
``Who would like to do the second problem, subtraction?''
Students hid their faces. She called on Mark, who got the problem but
there was some suspicion his girlfriend Lisa whispered it to him.
``Who would like to do the third problem, division?''
Now a low collective groan could be heard as everyone looked at
nothing in particular. The teacher called on Suzy, who got it right
(she has been known to hold back sometimes in front of her friends).
``Who would like to do the last problem, multiplication?''
Tim's hand shot up, surprising everyone in the room. Mrs. Johnson
finally gained her composure in the stunned silence. ``Why the
enthusiasm, Tim?''
``God said to go fourth and multiply!''
M__________________________________________________________________________
In the bayous of Louisiana, there is a small river called the Dirac.
Many wealthy people have their mansions near its mouth. One of the
social leaders decided to have a grand ball. Being a cousin of the
Governor, she arranged for a detachment of the state militia to serve
as guards and traffic directors for the big doings. A captain was
sent over with a small company; naturally he asked if there was enough
room for him and his unit. The social leader replied, "But of course,
Captain! It is well known that the Dirac delta function has unit
area."
M__________________________________________________________________________
When I was a Math/Chem grad student at Princeton in 1973-74, there was
a story going around about a grad student. This guy was always late.
One day he stumbled into class late, saw seven problems written on the
board, and wrote them down. As the week went on he began to panic:
the math department at Princeton is fiercely competitive, and here he
was unable to do most of a simple homework assignment! When the next
class rolled around he only had solved two of the problems, although
he had a pretty good idea of how to solve a third but not enough time
to complete it.
When he dejectedly flung his partial assignment on the prof's desk,
the prof asked him "What's that?" "The homework." "What homework?"
Eventually it came out that what the prof had written on the board
were the seven most important unsolved problems in the field.
This is largely an academic legend, at least according to Jan Harold
Brunvand, the author of a series of books on so-called Urban Legends.
He talks about it in his latest book _Curses! Broiled Again!_ in the
chapter entitled "The Unsolvable Math Problem." It is, however, based
in some fact. The Stanford mathematician, George B. Danzig,
apparently managed to solve two statistics problems previously
unsolved under similar circumstances.
M__________________________________________________________________________
Russell to Whitehead: "My Godel is killing me!"
M__________________________________________________________________________
"The reason that every major university maintains a department of
mathematics is that it is cheaper to do this than to institutionalize
all those people."
M__________________________________________________________________________
One attractive young businesswoman to another, over lunch:
``My life is all math. I am trying to add to my
income, subtract from my weight, divide my time,
and avoid multiplying.''
M__________________________________________________________________________
We use epsilons and deltas in mathematics because mathematicians
tend to make errors.
M__________________________________________________________________________
A mathematician decides he wants to learn more about practical
problems. He sees a seminar with a nice title: "The Theory
of Gears." So he goes. The speaker stands up and begins,
"The theory of gears with a real number of teeth is well known ..."
M__________________________________________________________________________
What keeps a square from moving ? why, square roots of course.
How many square roots does it have ? why, 2 obviously.
M__________________________________________________________________________
How can you tell that Harvard was layed out by a mathematician?
The div school [divinity school] is right next to the grad school...
M__________________________________________________________________________
First of all let me make it clear that I have nothing against
contravariant functors. Some of my best friends are cohomology
theories! But now you aren't supposed to call them contravariant
anymore. It's Algebraically Correct to call them 'differently
arrowed'!!
In the same way that transcendental numbers are polynomially
challenged?
Manifolds are personifolds (humanifolds).
Neighborhoods are neighbor victims of society.
It's the Asian Remainder Theorem.
It isn't PC to use "singularity" - the function is "convergently
challenged" there.
M__________________________________________________________________________
Godel can't prove he was here.
Descartes though he was here.
M__________________________________________________________________________
Mathematical Sex
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 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 never
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 amongst the
complex elements. Rows and columns closed in from all sides. Tangents approached
her surface. She became tensor and tensor. Quite suddenly, two branches of a
hyperbola touched her at a single point. She oscillated violently, lost all
sense of directrix, and went completely divergent. As she reached a turning
point, she tripped over a square root that was protruding from the erf and
plunged headlong down a steep gradient. When she rounded off once more, she
found herself inverted, apparently alone, in a non-Euclidian space.
She was being watched, however. That smooth operator, Curly Pi, was lurking
innerproduct. As his eyes devoured her curvilinear coordinates, a singular
expression crossed his face. He wondered, was she still convergent? He decided
to integrate improperly at once.
Hearing a common fraction behind her, Polly rotated and saw Curly Pi
approaching with his power series extrapolated. She could see at once by his
degenerate conic and dissipative terms that he was bent on no good.
"Arcsinh," she gasped.
"Ho, ho," he said. "What a symmetric little asymptote you have. I can see
your angles have a lot of secs."
"Oh, sir," she protested, "keep away from me. I haven't got my brackets on."
"Calm yourself, My Dear," said our Suave Operator. "Your fears are purely
imaginary."
"I, I," she thought, "perhaps he's not normal but homologous."
"What order are you?" the Brute demanded.
"Seventeen," replied Polly.
Curly leered. "I suppose you've never been operated on."
"Of course not," Polly replied quite properly. "I'm absolutely convergent."
"Come, come," said Curly, "Let's off to a decimal place I know and I'll take
you to the limit."
"Never," gasped Polly.
"Abscissa," he swore, using the vilest oath he knew. His patience was gone.
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 out her points of inflection. Poor Polly. The algorithmic method was
now her only hope. She felt his hand tending to her asymptotic limit. Her
convergence would soon be gone forever.
There was no mercy, for Curly was a heavyside operator. Curly's radius
squared itself; Polly's loci quivered. He integrated by parts. He integrated by
partial fractions. After he cofactored, he performed rungecutta on her. The
complex beast even went all the way around and did a contour integration. Curly
went on operating until he had satisfied her hypothesis, 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 is was too
late to differentiate now. As the months went by, Polly's denominator increased
monotonically. Finally, she went to the L'Hopital and generated a small but
pathological function which left surds all over the place and drove Polly to
deviation.
The moral of our sad story is this:
'If you want to keep your expressions convergent, never allow them a single
degree of freedom...'
M__________________________________________________________________________
He thinks he's really smooth, but he's only C^1.
He's always going off on a tangent.
M__________________________________________________________________________
From: Jim Slepicka
After the earth dries out, Noah tells all the animals to 'go forth
and multiply'. However, two snakes, adders to be specific, complain to
Noah that this is one thing they have never been able to do, hard as
they have tried. Undaunted, Noah instructs the snakes to go into the
woods, make tables from the trunks of fallen trees and give it a try
on the tabletops.
The snakes respond that they don't understand how this will help them
to procreate whereupon Noah explains: "Well, even adders can multiply
using log tables!"
M__________________________________________________________________________
A man camped in a national park, and noticed Mr. Snake and Mrs. Snake
slithering by. "Where are all the little snakes?" he asked. Mr.
Snake replied, "We are adders, so we cannot multiply."
The following year, the man returned to the same camping spot. This
time there were a whole batch of little snakes. "I thought you said
you could not multiply," he said to Mr. Snake. "Well, the park ranger
came by and built a log table, so now we can multiply by adding!"
FORMULA'S:
M__________________________________________________________________________
/
| 1
| ----- = log cabin
| cabin
/
M__________________________________________________________________________
/
| 1
| ----- = log cabin + C = houseboat
| cabin
/
M__________________________________________________________________________
8 5
If lim - = oo (infinity), then what does lim - = ?
x->0 x x->0 x
answer: (write 5 on it's side)
M__________________________________________________________________________
I saw the following scrawled on a math office blackboard in college:
1 + 1 = 3, for large values of 1
M__________________________________________________________________________
lim ----
8-->9 \/ 8 = 3
M__________________________________________________________________________
"The integral of e to the x is equal to f of the quantity
u to the n."
/ x n
| e = f(u )
/
M__________________________________________________________________________
Fuller's Law of Cosmic Irreversability:
1 pot T --> 1 pot P
but
1 pot P -/-> 1 pot T
M__________________________________________________________________________
lim sin(x)
n --> oo ------ = 6
n
Proof: cancel the n in the numerator and denominator.
M__________________________________________________________________________
From: surd@apollo.hanyang.ac.kr (ps park (Seoul Univ.))
From: chrisman@ucdmath.ucdavis.edu (Mark Chrisman) (many additions)
HOW TO PUT AN ELEPHANT INTO A REFRIGERATOR:
Analysis:
1) Differentiate it and put into the refrig.
Then integrate it in the refrig.
2) Redefine the measure on the referigerator (or the elephant).
3) Apply the Banach-Tarsky theorem.
Number theory:
1) First factorize, second multiply.
2) Use induction. You can always squeeze a bit more in.
Algebra:
1) Step 1. Show that the parts of it can be put into the refrig.
Step 2. Show that the refrig. is closed under the addition.
2) Take the appropriate universal refrigerator and get
a surjection from refrigerator to elephant.
Topology:
1) Have it swallow the refrig. and turn inside out.
2) Make a refrig. with the Klein bottle.
3) The elephant is homeomorphic to a smaller elephant.
4) The elephant is compact, so it can be put into a finite collection
of refrigerators. That's usually good enough.
5) The property of being inside the referigerator
is hereditary. So, take the elephant's mother,
cremate it, and show that the ashes fit inside the refrigerator.
6) For those who object to method 3 because it's cruel to animals.
Put the elephant's BABY in the refrigerator.
Algebraic topology:
Replace the interior of the refrigerator by its
universal cover, R^3.
Linear algebra:
1) Put just its basis and span it in the refrig.
2) Show that 1% of the elephant will fit inside the refrigerator.
By linearity, x% will fit for any x.
Affine geometry:
There is an affine transformation putting the
elephant into the refrigerator.
Set theory:
1) It's very easy!
refrigerator = { elephant }
2) The elephant and the interior of the refrigerator both have cardinality c.
Geometry:
Declare the following:
Axiom 1. An elephant can be put into a refrigerator.
Complex analysis:
Put the refrig. at the origin
and the elephant outside the unit circle.
Then get the image under the inversion.
Numerical analysis:
1) Put just its trunk and refer the rest to the error term.
2) Work it out using the Pentium.
Statistics:
1) bright statistician.
Put its tail as a sample and say "Done."
2) dull statistician.
Repeat the experiment pushing the elephant to the refrig.
3) Our NEW study shows that you CAN'T put the elephant
in the refrigerator.
M__________________________________________________________________________
Math and Alcohol don't mix, so...
PLEASE DON'T DRINK AND DERIVE
Then there's every parent's scream when their child walks into the
room dazed and staggering:
OH NO...YOU'VE BEEN TAKING DERIVATIVES!!
*M_________________________________________________________________________
Q: What's purple and commutes?
A: An abelian grape.
Q: What's purple, commutes, and is worshiped by a limited number
of people?
A: A finitely venerated abelian grape.
Q: Why did the mathematician name his dog "Cauchy"?
A: Because he left a residue at every pole.
Q: Why is it that the more accuracy you demand from an interpolation
function, the more expensive it becomes to compute?
A: That's the Law of Spline Demand.
Q: What do a mathematician and a physicist [or engineer, or musician,
or whatever the profession of the person addressed] have in common?
A: They are both stupid, with the exception of the mathematician.
Q: What do you call a teapot of boiling water on top of mount everest?
A: A high-pot-in-use
Q: What do you call a broken record?
A: A Decca-gone
Q: What do you get when you cross 50 female pigs and 50 male deer?
A: One hundred sows-and-bucks
Q: Why did the chicken cross the Moebius strip?
A: To get to the other ... er, um ...
Q: What is the world's longest song?
A: "Aleph-nought Bottles of Beer on the Wall."
Q: What does a mathematician do when he's constipated?
A: He works it out with a pencil.
Q: What's yellow and equivalent to the Axiom of Choice.
A: Zorn's Lemon.
Q: What do you get if you cross an elephant with a zebra.
A: Elephant zebra sin theta.
Q: What do you get when you cross an elephant and a grape?
A: Elephant-grape-sin(theta)
Q: What do you get if you cross an elephant with a mountain climber.
A: You can't do that. A mountain climber is a scalar.
Q: What do you get when you cross an elephant with a banana?
A: Elephant banana sine theta in a direction mutually perpendicular to
the two as determined by the right hand rule.
Q: What do you get when you cross a tsetse with a mountain climber?
A: Nothing, you can't cross a vector with a scalar.
Q: To what question is the answer "9W."
A: "Dr. Wiener, do you spell your name with a V?"
Q: What's non-orientable and lives in the sea?
A: Mobius Dick.
Q: What do you get when you put a spinning flywheel in a casket and
turn a corner?
A: A funeral precession
Q: What's big, grey, and proves the uncountability of the reals?
A: Cantor's Diagonal Elephant!
Q: What do you call a young eigensheep?
A: A lamb, duh!!!
Q: What goes "Pieces of seven! Pieces of seven!"?
A: A parroty error!!
Q: What did the circle say to the tangent line?
A: "Stop touching me!"
From: Jos van Kan
Q: What's yellow, linear, normed and complete?
A: A Bananach space.
From: dmc@sjfc.edu (Dan Cass)
Q: What's polite and works for the phone company?
A: A deferential operator.
M__________________________________________________________________________
Q: What's the title of this picture ?
.. .. ____ .. ..
\\===/======\\==
|| | | ||
|| |____| ||
|| ( ) ||
|| \____/ ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| ||
|| (\ ||
|| ) ) ||
|| //||\\ ||
A: Hypotenuse
M__________________________________________________________________________
Los Angeles High School Math Exam
1. Johnny has an AK47 with a 40 round clip. If he misses 6 out of 10 shots
and shoots 15 times each drive by, how many drive by shootings must he
conduct before he shoots 50 people?
2. Paul has 2 ounces of cocaine and he sells 10 grams to Jackson for $820, and
2 grams to Billy for $85 per gram. What is the street value of the balance of
the cocaine if he doesn't cut it?
3. Willie gets $200 for stealing a BMW, $50 for a Chevy and $100 for a 4x4. If
he has stolen two BMWs and three 4x4s, how many Chevys will he have to steal to
make $800?
4. If the contents of an average can of spray paint covers 22 square feet and
the average letter is eight square feet, how many letters can a teenager spray
with eight cans of paint?
5. Hector got six girls in his gang pregnant. There are 27 girls in the gang.
What percentage of girls in the gang has Hector knocked up?
6. Kathy gets $125 for sneaking an illegal alien across the border from
Mexico. She sneaked three illegals over the border every night for six days but
then one of them ripped her off for $500. How much money does she have left?
7. Byron can trade $150 worth of food stamps for two tickets to a Lakers
regular season game. If a play-off game costs 20 percent more, how many
play-off tickets can he get for $500 in food stamps?
From: jdmcmine@coop2.b11.ingr.com (Jeff)
Answers to City of Los Angeles
High School Math Proficiency Exam
1. Johnny has an AK47 with a 40 round clip. If he misses 6 out of 10 shots
and shoots 15 times each drive by, how many drive by shootings must he
conduct before he shoots 50 people?
Johnny hits 15*(4/10) people per drive by, which means that he
will have to participate in 9 drive bys to shoot 50 people.
However, he will have completed two drive-by shootings and be
just starting the third when he has to reload. Since he only
stole a single clip, he'll only have shot 16 people when the
homeboys with the UZIs' make Swiss cheese out of him.
2. Pony has 2 ounces of cocaine and he sells an 8 ball to Jackson for
$320 and 2 grams to Billy for $85 per gram. What is the street value
of the balance of the cocaine if he doesn't cut it?
At 454 grams per pound, 2oz of the rock = 56.75 grams. An "8
ball" is 8 grams, so pony has sold 10 grams total and has 46.75
grams left. If he keeps selling 8-balls, he can sell 5 more (for
a total of 5*$320=$1,600) and have 6.75 grams for his own nose.
If he sells 2 gram packs, he can sell (46/2-23) packs at $85
apiece = (23*$85)=$1,955. However, he could divide it into small
parts, bake it up into crack and sell the rocks for an even
larger profit. This problem is really more suited for the Gang
Multi-Variable Economics Test.
3. Ron is pimping for 3 girls. If the price is $65 for each trick,
how many tricks will each have to turn so Ron can pay for his $800
per day crack habit.
800/$64=12 tricks plus a dance. Also, Ron should consider making
a deal with Pony from Question #2.
4. Susan wants to cut her 1/2 pound of heroin to make 20% more profit.
How many ounces of cut will she need?
If she sells the cut heroin at the same price per unit volume,
she will need 20% more volume. 20% of 1/2 pound (=8oz) is 1.6oz.
So, Susan will need 1.6oz of cut to add to the 8 oz of heroin to
get 20% more volume. She will want a cut which looks similar to
raw heroin and has approximately the same melting point. Plain
sugar or laundry detergent are suggested. Laundry detergent has
the added benefit of removing the possibility of customer
complaints, but will sharply limit repeat business.
5. Blade gets $200 for stealing a BMW, $50 for a Chevy, and $100 for
a 4x4. If he has already stolen 2BMW's and 3 4x4's, how many Chevy's
will he have to steal to make $800?
Blade has made 2*$200 + 3*$100=$700 dollars from his theft so
far. He needs $100 more, so he needs to steal $100/$50=2 more
Chevy's. However, he will probably want to steal 4 Chevy's so he
can take the extra two and make a really def low-rider.
6. Little Willy is in prison for 6 years for murder. He got $25,000
for the hit. If his common law wife is spending $250 per month, how
much money will be left when he gets out of prison and how many
years will he get for killing the bitch that spent his money?
6 years*12 months/year*$250/month=$18,000. Little Willy will
have $25,000 - $18,000 = $7,000 left when he gets out of prison.
If Little Willy kills her in the USA, he should expect to get 6
years. However, if he takes her down to Mexico and buries her
scrawny, track-marked butt in the desert, he can get off scott
free.
7. If the average can of spray paint covers 22 square feet, and
the average letter is 4 square feet, how many letters can a tagger
spray with 3 cans of paint?
3 cans of paint will cover 3*22=66 square feet. 66/4=16 letters
with a little paint left over to spray in the eyes of the cop
who's comin' after you. Or the tagger could do 15 letters and a
bitchin' skull.
8. Hector knocked up 6 girls in his gang. There are 27 girls in the
gang. What percentage of the girls in the gang has Hector knocked up?
6/27=22% of the girls. However, 2 of them are lying because
they've been sleeping with Pedro, Hector's lieutenant. So, in
actuality, Hector only knocked up 4/27 or 14.8%.
9. Rosie's sole source of income is shoplifting. If she gets 10 cents on
the dollar from her fence, how much merchandise must she shoplift each
week to make $250.
Solve X/10=250 for X, X=$2,500.
10. Mike carjacked a Chevy Camaro for his date Saturday night with his
young 14 year old girlfriend. He was arrested that night while making his
girlfriend in the backseat. How much prison time is he looking for for the
carjacking and for statutory rape, even though the girl looked legal?
Assume no prior convictions in arriving at your answer.
Mike is only 12 so he will serve no time and will be making
his girlfriend in the lot in someone else's car next Saturday.
M__________________________________________________________________________
Why did the calculus student have so much trouble making Kool-Aid?
Because he couldn't figure out how to get a quart of water into the
little package.
M__________________________________________________________________________
A somewhat advanced society has figured how to package basic knowledge
in pill form.
A student, needing some learning, goes to the pharmacy and asks what
kind of knowledge pills are available. The pharmacist says "Here's a
pill for English literature." The student takes the pill and swallows
it and has new knowledge about English literature!
"What else do you have?" asks the student.
"Well, I have pills for art history, biology, and world history,"
replies the pharmacist.
The student asks for these, and swallows them and has new knowledge
about those subjects.
Then the student asks, "Do you have a pill for math?"
The pharmacist says "Wait just a moment", and goes back into the
storeroom and brings back a whopper of a pill and plunks it on the
counter.
"I have to take that huge pill for math?" inquires the student.
The pharmacist replied "Well, you know math always was a little hard
to swallow."
M__________________________________________________________________________
From: a94petbe@ida.his.se (Peter Bengtsson)
In modern mathematics, algebra has become so important that
numbers will soon only have symbolic meaning.
M__________________________________________________________________________
From: sm@wf-hh.sh.sub.de (Stefan Mohr)
The shortest mathematic joke:
BEGIN -->"Epsilon less than zero"<-- END
M__________________________________________________________________________
The law of the excluded middle either rules or does not rule, O.K.?
M__________________________________________________________________________
Is the square root of ab absurd?
M__________________________________________________________________________
Algebra is x-sighting.
Vectors can be 'arrowing.
I'm partial to fractions.
I like angles ... to a degree.
I could go on and on about sequences.
Translations are shifty.
Complex numbers are unreal.
I feel positive about integers.
On average, people are mean.
M__________________________________________________________________________
From: c1prasad@watson.ibm.com (prasad)
Klein bottle for rent -- inquire within.
M__________________________________________________________________________
From: jusinkko@mail.freenet.hut.fi (jukka sinkko)
In the topologic hell the beer is packed in Klein's bottles.
M__________________________________________________________________________
Why did the chicken cross the road?
Pierre de Fermat: I just don't have room here to give the full explanation.
M__________________________________________________________________________
From:mstueben@pen.k12.va.us (Michael A. Stueben)
Puns on Theorems
The Royal Chain Mail Factory had received a large order for battle
uniforms. Each uniform consisted of a toga and a pair of short pants. Their
only problem was how long to make the pants: too short and a soldier could
be exposed; too long and a uniform would be excessively heavy. So they
called in a mathematician. He had a uniform made and tested. The hem on the
pants proved to be too short, so he increased it a little bit, then a little
more, and then a little bit more, and so on until finally he was able to
derive an exact trousers-length depending on the leg-length of the soldier.
The chief tailor was curious. "How did you determine this ratio?" he asked?
"Easy," said the mathematician. "I just used the Wire-trousers Hem Test of
Uniform Convergence."
This is a pun on the "Weierstrauss M-test of uniform convergence," where M[k]
is a convergent series of positive real numbers. (It was sent to me by
Andrius Tamulis.) I wonder why M and not, say, N (numeric) or S (sum).
M stands for . . .?
From: bdillon@admin.aurora.edu (Bob Dillon)
The following is from the January 23, 1995 issue of Chemical and
Engineering News.
Story Problems Portray Gains in Teaching Math
M__________________________________________________________________________
A commentary on the teaching of mathematics, sent in by James
Jackson of Carlisle, Ind., appeared in "Echoes" (winter 1994),
published by Rose-Hulman Institute of Technology, Terre Haute, Ind.
"Echoes" took it from the 1993-94 issue of "21st Century" (not
otherwide identified). The commentary takes the form of a series
of story problems:
In 1960: A logger sells a truckload of lumber for $100. His cost
of production is four-fifths of this price. What is his profit?
In 1970: A logger sells a truckload of lumber for $100. His cost
of production is four-fifths of this price, or $80. What is his
profit?
In 1970 (new math): A logger exchanges a set L of lumber for a set
M of money. The cardinalitiy of set M is 100, and each element is
worth $1.00. Make 100 dots representing the elements of the set M.
The set C of the costs of production contains 20 fewer points than
set M. Represent the set C as a subset of M, and answer the
following question: What is the cardinality of the set P of points?
In 1980: A logger sells a truckload of wood for $100. His cost of
production is $80, and his profit is $20. Your assignment:
underline the number 20.
In 1990 (outcome-based education): By cutting down beautiful forest
trees, a logger makes $20. What do you think of this way of making
a living? (Topic for class participation: How did the forest birds
and squirrels feel?)
M__________________________________________________________________________
From: joeshmoe@world.std.com (Jascha Franklin-Hodge) (List of Taglines)
Math is the language God used to write the universe.
M__________________________________________________________________________
If God is perfect, why did He create discontinuous functions?
M__________________________________________________________________________
From: mstueben@pen.k12.va.us (Michael A. Stueben)
THIRTEEN MISUNDERSTANDINGS
IN THE
HISTORY OF MATHEMATICS
In the interest of historical accuracy let it be known that
...
1) Fibonacci's daughter was not named "Bunny."
2) Michael Rolle was not Danish, and did not call his
daughter "Tootsie."
3) William Horner was not called "Little-Jack" by his
friends.
4) The "G" in G. Peano does not stand for "grand."
5) Rene Descartes' middle name is not "push."
6) Isaac Barrow's middle name is not "wheel."
7) There is no such place as the University of Wis-cosine,
and if there was, the motto of their mathematics
department would not be "Secant ye shall find."
8) Although Euler is pronounced oil-er, it does not follow
that Euclid is pronounced oi-clid.
9) Franklin D. Roosevelt never said "The only thing we have
to sphere is sphere itself."
10) Fibonacci is not a shortened form of the Italian name that
is actually spelled: F i bb ooo nnnnn aaaaaaaa
ccccccccccccccccccccccccccccccccccc
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii.
11) It is true that August Mobius was a difficult and
opinionated man. But he was not so rigid that he could
only see one side to every question.
12) It is true that Johannes Kepler had an uphill struggle
in explaining his theory of elliptical orbits to the
other astronomers of his time. And it is also true that
his first attempt was a failure. But it is not true that
after his lecture the first three questions he was asked
were "What is elliptical?" What is an orbit?" and "What
is a planet?
13) It is true that primitive societies use only rough
approximations for the known constants of mathematics.
For example, the northern tribes of Alaska consider the
ratio of the circumference to the diameter of a circle to
be 3. But it is not true that the value of 3 is called
Eskimo pi. Incidentally, the survival of these tribes is
dependent upon government assistance, which is not always
forthcoming. For example, the Canadian firm of Tait and
Sons sold a stock of defective compasses to the government
at half-price, and the government passed them onto the
northern natives. Hence the saying among these peoples:
"He who has a Tait's is lost."
M__________________________________________________________________________
The History of 2 + 2 = 5
by Houston Euler
"First and above all he was a logician. At
least thirty-five years of the half-century
or so of his existence had been devoted
exclusively to proving that two and two always
equal four, except in unusual cases, where
they equal three or five, as the case may be."
-- Jacques Futrelle, "The Problem of Cell 13"
Most mathematicians are familiar with -- or have at least seen references in
the literature to -- the equation 2 + 2 = 4. However, the less well known
equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other
complex quantitiy, this history has a real part and an imaginary part; we shall
deal exclusively with the latter here.
Many cultures, in their early mathematical development, discovered the equation
2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of
South America. The Bolbs counted by tying knots in ropes. They quickly
realized that when a 2-knot rope is put together with another 2-knot rope, a
5-knot rope results.
Recent findings indicate that the Pythagorean Brotherhood discovered a proof
that 2 + 2 = 5, but the proof never got written up. Contrary to what one might
expect, the proof's nonappearance was not caused by a cover-up such as the
Pythagoreans attempted with the irrationality of the square root of two.
Rather, they simply could not pay for the necessary scribe service. They had
lost their grant money due to the protests of an oxen-rights activist who
objected to the Brotherhood's method of celebrating the discovery of theorems.
Thus it was that only the equation 2 + 2 = 4 was used in Euclid's "Elements,"
and nothing more was heard of 2 + 2 = 5 for several centuries.
Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after
putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with
considerably more than 4 rabbits. Fearing that too strong a challenge to the
value 4 given in Euclid would meet with opposition, Leonardo conservatively
stated, "2 + 2 is more like 5 than 4." Even this cautious rendition of his
data was roundly condemned and earned Leonardo the nickname "Blockhead." By
the way, his practice of underestimating the number of rabbits persisted; his
celebrated model of rabbit populations had each birth consisting of only two
babies, a gross underestimate if ever there was one.
Some 400 years later, the thread was picked up once more, this time by the
French mathematicians. Descartes announced, "I think 2 + 2 = 5; therefore it
does." However, others objected that his argument was somewhat less than
totally rigorous. Apparently, Fermat had a more rigorous proof which was to
appear as part of a book, but it and other material were cut by the editor so
that the book could be printed with wider margins.
Between the fact that no definitive proof of 2 + 2 = 5 was available and the
excitement of the development of calculus, by 1700 mathematicians had again
lost interest in the equation. In fact, the only known 18th-century reference
to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it
in an old manuscript, wryly commented, "Well, now I know where all the departed
quantities went to -- the right-hand side of this equation." That witticism so
impressed California intellectuals that they named a university town after him.
But in the early to middle 1800's, 2 + 2 began to take on great significance.
Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean
2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an
arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great
confusion as to the actual value of 2 + 2. Because of changing opinions on
this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years
later to yield, instead, the 5-color theorem. Dedekind entered the debate with
an article entitled "Was ist und was soll 2 + 2?"
Frege thought he had settled the question while preparing a condensed version
of his "Begriffsschrift." This condensation, entitled "Die Kleine
Begriffsschrift (The Short Schrift)," contained what he considered to be a
definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand
Russell, reminding him that in "Grundbeefen der Mathematik" Frege had proved
that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned
mathematics altogether and went into university administration.
Faced with this profound and bewildering foundational question of the value of
2 + 2, mathematicians followed the reasonable course of action: they just
ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing
being done with its rival equation during the 20th century. There had been
rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first
forty pages taken up by the symbolic expression for the number five), but those
rumor remained unconfirmed. Recently, though, there have been reported
computer-assisted proofs that 2 + 2 = 5, typically involving computers
belonging to utility companies. Perhaps the 21st century will see yet another
revival of this historic equation.
M__________________________________________________________________________
THE STORY OF BABEL:
In the beginning there was only one kind of Mathematician, created by
the Great Mathematical Spirit form the Book: the Topologist. And they
grew to large numbers and prospered.
One day they looked up in the heavens and desired to reach up as far
as the eye could see. So they set out in building a Mathematical
edifice that was to reach up as far as "up" went. Further and further
up they went ... until one night the edifice collapsed under the
weight of paradox.
The following morning saw only rubble where there once was a huge
structure reaching to the heavens. One by one, the Mathematicians
climbed out from under the rubble. It was a miracle that nobody was
killed; but when they began to speak to one another, SUPRISE of all
surprises! they could not understand each other. They all spoke
different languages. They all fought amongst themselves and each went
about their own way. To this day the Topologists remain the original
Mathematicians.
- adapted from an American Indian legend
of the Mound Of Babel
*M_________________________________________________________________________
From: kfoster@rainbow.rmii.com (Kurt Foster)
First mathemetician: I know this is a group, but it's hard to study.
Second mathematician: Well, I can prove it's commutative.
First mathematician: Thanks abelian!
*M_________________________________________________________________________
From: rrcraig@eos.ncsu.edu (Ralph Ray Craig)
Q: How many numerical analysts does it take to screw in a light bulb?
A: 0.9973 after the first three iterations.
*M_________________________________________________________________________
From: immortal@wam.umd.edu (Immortal = Justin Wyss-Gallifent)
Q: Why can't you grow wheat in Z/6Z ?
A: Because it's not a field.
*M_________________________________________________________________________
From: kovarik@mcmail.cis.mcmaster.ca (Zdislav V. Kovarik)
A retired mathematician took up gardening, and is now growing carrots
with square roots.
*M_________________________________________________________________________
From: kovarik@mcmail.cis.mcmaster.ca (Zdislav V. Kovarik)
(From a cartoon by J. Effel): In the Garden of Eden, God is giving Adam a
geometry lesson: "Two parallel lines intersect at infinity. It can't be
proved but I've been there."
*M_________________________________________________________________________
From: wft@math.canterbury.ac.nz (Bill Taylor)
Some say the pope is the greatest cardinal.
But others insist this cannot be so, as every pope has a successor.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
--
Joachim Verhagen Email:J.C.D.Verhagen@fys.ruu.nl
Department of molecular biofysics, University of Utrecht
Utrecht, The Netherlands.