OT: Math Joke



#48

This came my way and I thought that some might enjoy it ...

An infinite number of mathematicians walk into a bar. The first one orders a beer, the second orders half a beer, the third asks for a quarter of a beer. Before the next one can speak, the bartender says "You're all idiots", and pours two beers.

Reminder: 1 + 1/2 + 1/4 + 1/8 + ... + 1/inf = 2

Please post your favorites.

Regards,

John


#49

Some have probably heard this one before, but if not, it's kinda cute:

After the flood, Noah tells the animals from the Arc to "go forth and multiply."

After a few months, Noah figures he better wander around and see how the animals are doing. Everybody is happy until he comes across a couple of snakes - they are quite downcast and not very happy. Noah asks what wrong, and they say "We are Adders, so we can't multiply!"

Noah rubs his chin for a few moments, and then goes into the forest, cuts down a couple of trees, and makes a table out of them.

Then he puts the snakes up on the platform he has made, and says "Now you should be happy. Everybody knows that adders can multiply with log tables!"


#50

Quote:
After the flood, Noah tells the animals from the Arc to "go forth
Forth has indeed become my favorite programming language, so I'm glad he didn't say, "Go BASIC," or "C," "C++," "Ada,..." etc.
#51

A physicist, an engineer and a mathematician are each asked to empty a bucket of water placed on the floor in front of a sink.

The physicist picks up the bucket and empties it into the sink.

The engineer picks up the bucket and empties it into the sink.

The mathematician picks up the bucket and empties it into the sink.

The bucket is now placed on a shelf above the sink and each are asked to empty it into the sink.

The physicist picks up the bucket and empties it into the sink.

The engineer picks up the bucket and empties it into the sink.

The mathematician picks up the bucket, puts it on the floor and says "now we've reduced it to a problem that we have already solved".


#52

why do calculator people confuse the dates of Christmas and Halloween?

A: because Dec 25 is Oct 31

:-)

#53

Q: Why do you rarely find mathematicians spending time at the beach?

A: Because they have sine and cosine to get a tan and don't need the sun!

#54

Q. What do you get if you cross a pig with a dog?

A. Pig dog sine theta!

Nigel


#55

A group of mathematicians and a group of engineers were taking a train to attend a joint conference.
They all sat in the same car and after a while the engineers found out that only one of the mathematicians had a ticket. Each of the engineers of course had a ticket. Some time later a mathematician returned to the car and shouted, "Conductor's coming!"

All of the mathematicians crammed into a restroom, and when the conductor came by, he knocked on the door
and said "Ticket please." The mathematician with the ticket passed it under the door, and the conductor punched it and returned it. After the conductor left, the engineers sat there in amazement.

On the return trip the engineers had only one ticket.

This time however, none of the mathematicians had a ticket. Some time later an engineer
ran in the car and shouted "Conductor's coming." All of the engineers piled into one restroom and all
of the mathematicians into another. The last mathematician went to the restroom of the engineers, knocked on the door: "Ticket, please."

What this story exemplifies:

Engineers use the methods of the mathematicians, but they do not understand them fully.

#56

Q: What do you get if you cross a mosquito with a mountain climber?

A: Nothing - You can't cross a vector with a scalar!

#57

A group of people are asked to prove or disprove the statement "All odd numbers greater than one are prime."

The mathematician says "Three is prime, five is prime, seven is prime, nine is not prime. Thus the statement is false."

The engineer says "Three is prime, five is prime... seven is prime... (slowing down because he doesn't have his slide rule with him) nine is prime... eleven is prime. Looks like they're all prime."

The physicist says "Three is prime, five is prime, seven is prime, nine... well, that could be experimental error, eleven is prime, thirteen is prime, fifteen... oh, we have too many data points. They're all prime."

The computer scientist says nothing, but comes back a month later with a huge ream of printout showing that every even number greater than two is not prime, thus having solved the wrong problem by brute force.


#58

An engineering student is walking down the sidewalk at the university, when he sees his friend riding the other way on a new bicycle. He says, "Where did you get that great bicycle?"

The friend says, "Well, it was the strangest thing. I was walking down the sidewalk yesterday when this pretty young girl came riding by on a bicycle. She got off the bike, took off all her clothes, and said to me, "Take what you want.""

The first student thinks a moment and says, "Good choice. The clothes probably wouldn't have fit."

#59

A statistician tried to wade across a river that was one foot deep on average.


He drowned.


#60

IMO, that is actually the best one so far.

#61

What is the difference between an extroverted mathematician and an introverted one? While talking with you the extroverted will gaze at his shoes.

Ciao.....Mike

#62

A mathematician, a physicist, and an engineer, are all placed 8 feet from a beautiful woman and the stipulation that at each time interval, they may move half of the remaining distance towards her.

The mathematician concludes that after N iterations there will be 8 divided by 2N feet remaining which will never equal zero so he gives up on the spot.

The physicist opines that if each iteration requires a finite amount of energy then the energy expended in the approach will be inversely proportional to the distance remaining and gives up on the spot.

The engineer says "8 feet, 4 feet, 2 feet, 1 foot, 6 inches, good enough for practical purposes".


#63

This one is my favorite (can you guess which discipline I belong to?), and was going to be my response to the earlier, clearly outlandish one where the mathematicians steal the engineer's train ticket. Thieves.

BTW, the punch line for this joke as I learned it years ago went something along the lines of "But where are you going?!? Under the rules you can never get there!" "I can get close enough!!"

#64

University administrations and industry leaders are very concerned because so few women are going into Science and Engineering. However the reason is very simple:

Women have been slaves for the last 5,000 years. Why on earth would they now want to become Scientists or Engineers?

#65

An engineer, a practical and a theoretical mathematician are asked to catch a lion in the African desert.

The engineer runs across the desert until he manages to catch the lion.

The practical mathematician builds a long fence around the desert. Thus the lion is fenced in.

The theoretical mathematician sits down in the desert and draws a fence around himself. Then he calls this area the outside.

Edited: 30 Apr 2009, 4:50 p.m.

#66

An astronomer, a physicist and a mathematician travel on a train through Scotland.

On a field they see a black sheep. Look! says the astronomer, in Scotland all sheep are black.

No, replies the physicist, all we know is that there are black sheep in Scotland.

Thats not true, the mathematician says, all we can say is that in Scotland there is at least one sheep with at least one black side.

#67

A man is flying in a hot air balloon and realizes he is lost. He reduces height and spots a man down below. He lowers the balloon further and shouts, "Excuse me, can you tell me where I am?"
The man below said, "Yes, you're in a hot air balloon, hovering 30 feet above this field."
"You must be an engineer," said the balloonist.
"I am," replied the man. "How did you know?"
"Well," said the balloonist, "everything you have told me is technically correct, but it's of absolutely no use to anyone."
The man below said, "You must be in management."
"I am," replied the balloonist, "but how did you know?"
"Well," said the man, "you don't know where you are, or where you're going, but you expect me to be able to help. You're in the same position you were before we met, but now it's my fault."

#68

A ten year old public school boy was finding fifth grade math to be the challenge of his life. His mom and dad did everything and anything to help their son... private tutors, peer assistance, CD-ROMs, textbooks and even hypnosis. Nothing worked. However, as a last resort they enrolled him into a small Catholic school.

At the end of the first day of Catholic school the boy walked in with a stern expression on his face and walked right past the parents and went straight to his room and quietly closed the door. For nearly two hours he toiled away in his room with math books strewn about his desk and the surrounding floor. He only emerged long enough to eat and after quickly cleaning his plate he went straight back to his room, closed the door, and worked feverishly at his studies until bedtime. The parents were not sure if they should comment on the boys extra efforts for fear of him losing this new found fervor so they seemingly ignored it. This pattern continued ceaselessly.

One day the first quarter report card came out. Unopened, he dropped the envelope on the family dinner table and went straight to his room. His parents were petrified. What lay inside the envelope? Cautiously the mother opened the letter, and to her amazement she saw a bright red "A" under the subject, MATH.

Overjoyed, she and her husband rushed into their son's room, thrilled at the remarkable progress of their young son! "Was it the nuns that did it?", the father asked. The boy only shook his head and said, "No." "Was it the one-on-one tutoring? The peer-mentoring?", asked the mother. Again, the boy shrugged, "No." "The textbooks? The teacher? The curriculum?", asked the father. "Nope," said the son. "It was all very clear to me from the very first day of Catholic school."

"How so?", asked his mom. "When I walked into the lobby, and I saw that guy they'd nailed to the plus sign I knew those people meant business!"

#69

Quote:
Please post your favorites.

There are three types of mathematician: those who can count and those who can't.


#70

I know it this way:

There are 10 types of mathematicians: those who can count and those who can't.


#71

or, "There are 10 types of people in the world - those who understand binary and those who don't."


#72

And another version:

There are actually 11 types of people: the ones that know binary, the ones that don't and the rest of 20% who don't have a clue about percentages.

And then the fourth kind who think the other three types must be weird geeks to even find this stuff funny.

;-)

#73

I can't choose only one.

Why did the maths book commit suicide?

It had too many problems.



A mathematician, a biologist and a physicist are outside a bar enjoying a beer.
They look to the house at the other side of the street.
Two people get in the house. Sometime later three people get out.

The physicist: “The measurement was not accurate.”

The biologist: “They have reproduced.”

The mathematician: “Now, if one, and only one, person gets in, the house will be empty again.”


#74

A jet airliner flying over the south Pacific loses power and is forced to make an emergency landing near a deserted island. The landing goes well, but the plane quickly sinks. All the passengers get out without major injury, and all make it to shore. They assemble on the beach, and procede to introduce themselves and discuss what to do.

One woman speaks up. "I'm a Vice-President at Amalgamated Assets, and here's what we should do. We need to form up teams, appoint team leaders, and divide up responsibilities for finding shelter, food, water and other necessities among the teams. Everybody should fan out over the island and exercise their assigned core competency. Team leaders, report back to me at sunset.

Another man is fiddling with an oversized cell phone, obviously frustrated. "Does anyone have a signal?" he asks. "No? All right then, I'm an engineer with Connectroid Telecomm, and here's what we should do. You folks over there, go inland a bit and bring back any dry wood or palm fronds you can find. You people over there, scour the shoreline and bring back some damp seaweed. Anybody got a lighter or dry matches? Yes? Good. We're going to build a signal fire."

A third man has been busily scratching equations in the sand. "Ah-hah!" he shouts. "I'm an economist at Leveraged Derivatives Bank, and it's all so simple! First, assume a raft..."

#75

A mathematician, a theoretical an an experimental physicist are sitting in jail for a few days. They are getting hungry.

Each of them is offered a sealed tin can with food.

The experimental physicist throws the can against wall. Picks it up. Throws again. Eventually the lid goes off and he can eat.

The theoretical physicist examins the can thoroughly, then scratches some formulas in the dust on the floor. A single throw against the wall opens the can and he can eat.

The mathematician sits in front of the can an makes an assumption: Let's suppose this can is open...

#76

Quote:
An infinite number of mathematicians walk into a bar. The first one orders a beer, the second orders half a beer, the third asks for a quarter of a beer. Before the next one can speak, the bartender says "You're all idiots", and pours two beers.

Not a joke anymore but how many beers would the bartender have poured them if the second mathematician had ordered three-halves of a beer, the third one had asked for five-fourths of a beer, the fourth had asked for seven-eighths of a beer... and so on?
Notice the bartender has neither calculator nor computer to figure this out, only the knowledge and skills he had used before.

Regards,

Gerson.


#77

The way you're asking the question, the bartender has to pour an infinite number of beers because you're adding an infinite number of values >= 1.

IIRC, the infinite sum of 1/n is unbound, too. So even if the 2nd would have ordered 1/2, the 3rd 1/3 and so on, the beer will never be enough.


#78

Quote:
you're adding an infinite number of values >= 1.

1, 3/2 and 5/4 >=1, but 7/8, 9/16, 11/32,... <1

Regards,

Gerson.


#79

O.K. I didn't read the post thoroughly enough.

#80

Hi Gerson. I'm not as smart as our fictitious bartender so I had to write a program to get an answer of 6 beers.

Regards,

John

Edited: 2 May 2009, 12:12 a.m.


#81

Hi John,

Yes, the answer is really six beers. Anyway I think the bartender would need at least pencil and paper to solve this.

The solution to this problem is interesting so I'll wait some time before posting it just in case someone wants to find it by himself/herself.

Regards,

Gerson


#82

Sequence: (2n+1)/2^n

n=0: 1
n=1: 3/2
n=2: 5/4
n=3: 7/8
n=4: 9/16
...

We are looking for

   oo
Sum (2k+1)/2^k
k=0

oo oo
= Sum 1/2^k + Sum 2k/2^k
k=0 k=0

oo
= 2 + Sum k/2^(k-1)
k=0

oo
= 2 + Sum k/2^(k-1) since the first element is 0.
k=1

oo
= 2 + Sum (k+1)/2^k
k=0

oo oo
= 2 + Sum 1/2^k + Sum k/2^k
k=0 k=0

oo
= 4 + Sum k/2^k
k=0

The last term is definitely greater then 2 so I doubt the solution which has been posted so far.

Did I make an obvious mistake? I don't know.


#83

Quote:
The last term is definitely greater then 2 so I doubt the solution which has been posted so far.

2 is the solution of the original problem solved by the bartender in first math joke, which was summing up 1 + 1/2 + 1/4 + ...

Quote:
       oo
= 4 + Sum k/2^k
k=0


This indeed equals 6, which is the solution to the second problem, but the summation should be resolved. That is, the problem has now been reduced to finding the sum 1/2 + 2/4 + 3/8 + 4/16 + ...

Regards,

Gerson.


#84

Gerson, you're right, it's not obviously greater than 2 (mathematicians can't compute ;))


1/2
1/4 1/4
1/8 1/8 1/8
... ... ... ...
--- --- --- ---
1 1/2 1/4 1/8 ...

I was quick enough to see your solution, so this is not my idea. :)

A more formal approach:

 oo
Sum k/2^k
k=1

oo oo
= Sum Sum 1/2^j as can be seen from the schema above
k=0 j=k+1

oo oo k
= Sum ( Sum 1/2^j - Sum 1/2^j )
k=0 j=0 j=0

oo k
= Sum ( 2 - Sum 1/2^j )
k=0 j=0

oo
= Sum 1/2^k
k=0

= 2


#85

Quote:
I was quick enough to see your solution, so this is not my idea. :)

I guessed you would be, but I knew you would work out your own idea :-)

Congratulations for your solution and thanks for your nice analytical approach.

Here is mine again, more like the one the bartender would have come up with:

     1 + 3/2 + 5/4 + 7/8 + ...

= 1 +

1/2 + 1/2 + 1/2 +

1/4 + 1/4 + 1/4 + 1/4 + 1/4 +

1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 +

. . . . . . .
. . . . . . .
... . . . . . . . ...

------------------------------------------------------

= ... + 1/4 + 1/2 + 1 + 2 + 1 + 1/2 + 1/4 + ...

= 2 + 2 + 2

= 6

Best regards,

Gerson.

Edited: 2 May 2009, 6:17 p.m.


#86

To evaluate sum( k*r^k, k=0..infinity ), one can also use the fact that (k+1)*r^k is the derivative of r^(k+1) with respect to r (and trust that the derivative of a sum is the sum of the derivatives, even when the sum is infinite, provided it converges absolutely). Then,

sum(k*r^k, k=0..infinity )

= sum( (k+1)*r^k, k=0..infinity ) - sum( r^k, k=0..infinity )
= sum( diff(r^(k+1),r), k=0..infinity ) - 1/(1-r)

= diff( sum( r^(k+1), k=0..infinity ), r ) - 1/(1-r)

= diff( sum( r^k, k=1..infinity ), r ) - 1/(1-r)

= diff( r/(1-r), r ) - 1/(1-r)

= 1/(1-r)^2 - 1/(1-r)
= r/(1-r)^2

provided abs(r) < 1.

Putting r=1/2, we obtain 2 for the sum, so

sum( (2*k+1)/2^k, k=0..infinity )

= 2*sum(k/2^k, k=0..infinity) + sum(1/2^k, k=0..infinity)

= 2*2 + 2

= 6

[Edited to correct an obvious mistake]


Edited: 3 May 2009, 1:30 a.m.


#87

Thanks for providing yet another analytical solution. Geometrical arrangements are nice but clearly have their limitations, that is, the 3-D space...

An example inspired in the second problem:

Let's say we'd like to compute the infinite sum 1 + 9/2 + 25/4 + 49/8 + ...

By arranging the terms as the infinite square-base pyramid below, seen from above,

. .
. .
. .

. . . 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + . . .

1/4 + 1/2 + 1/2 + 1/2 + 1/4 +

1/4 + 1/2 + 1 + 1/2 + 1/4 + (3-D)

1/4 + 1/2 + 1/2 + 1/2 + 1/4 +

. . . 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + . . .

. .
. .
. .


and summing up all the terms, from top to base, we'd get square pattern below,


. .
. .
. .

. . . 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + . . .

1/2 + 1 + 1 + 1 + 1/2 +

1/2 + 1 + 2 + 1 + 1/2 + (2-D)

1/2 + 1 + 1 + 1 + 1/2 +

. . . 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + . . .

. .
. .
. .

and eventually find the exact sum, 34.


In this case, yours and von Cube's approaches would be better. I would just integrate (2*(x-1/2)+1)^2/2^(x-1/2) from 0 to infinity and get 8*sqrt(2)/(ln 2)^3 = 33.97 ...good enough for practical purposes :-)
(Just kidding, I always prefer exact solutions.)

Regards,

Gerson.


#88

These are interesting but are just particular cases of

SUM(k=0,n,(2*k+1)^p/2^k)
where p is an integer greater than or equal to zero
I have discovered expressions, but not proven them, which allow us to find not only the infinite sum for any power (this is just a matter of finding the limit when n tends to infinity, which is evident in the expression), but the exact sums of the first n terms of these series (the formulas include p-order polynomials but they appear to follow a pattern).

For instance, for p=0, the infinite sum is 2; for p=4, the infinite sum is 3394. For p=2, the sum of the first 20 terms is exactly 1190182/35009.

I will post the formulas later if someone is interested.

Gerson.

#89

Here's my quick and dirty program for a 33s:

A0001 LBL A

A0002 0

A0003 STO S

A0004 1

A0005 STO Y

A0006 STO X

B0001 LBL B

B0002 RCL Y

B0003 RCL X

B0004 /

B0005 STO+ S

B0006 2

B0007 STO+ Y

B0008 STOx X

B0009 GTO B

Executing A will result in the number 6 being stored in register S. I just let it run for a few seconds not worrying about counters or using relative error to test for convergence.

John


#90

Hi John,

Thanks for your interest and starting this thread with a really funny joke.
Now if any number of mathematicians get into the bar and make their weird orders our bartender will be able to mock them :-) (See my posting above).

Regards,

Gerson.


#91

It's nice to see how a joke can evolve in a determinated environment.


#92

The first half of this thread had me laughing out loud, but the second half really had me rolling on the floor. Only a bunch of engineers/mathematicians/scientists etc. could turn a jokes thread into a problem solving thread!!


#93

Eventually, every joke deteriorates to a problem. ;)

#94

Why did the chicken cross the Moebius strip?

To get to the other... um...


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