What is the formula for the volume of a thick crust pizza?

[anemone]

Why did the mathematical tree fall over?
Because it had no real roots!:pWrite the expression for the volume of a thick crust pizza with height \(\displaystyle a\) and radius \(\displaystyle z\).
View attachment 966
The formula for volume is \(\displaystyle \pi(\text{radius})^2(\text{height})\). In this case, \(\displaystyle pi.z.z.a\).

 

[Chris L T521]

A mathematician, a physicist, and a biologist are eating lunch at a café when they observe two people enter a house and three people leave.

Physicist: That measurement wasn't accurate.
Biologist: They must have reproduced!
Mathematician: If one person enters the house, it will be empty.

 

[Evgeny.Makarov]

Three logicians are walking into a bar. The barman says, "Would y'all like a beer?" The first logician says, "I am not sure". The second one also says, "I am not sure". The third logicians says, "Yes".

 

[topsquark]

Three logicians are walking into a bar. The barman says, "Would y'all like a beer?" The first logician says, "I am not sure". The second one also says, "I am not sure". The third logicians says, "Yes".

(sighs) Okay, someone is going to need to explain this one to me...

- (Doh)

 

[Evgeny.Makarov]

The logicians interpreted the barman's question "Would y'all like a beer?" as a conjunction of three statements: "The first logician would like a beer and the second one would like a beer and the third one would like a beer". The first logicican knew that he himself would like a beer, but he was not sure about the rest. Therefore, he could not say whether the complete conjunction was true. Same for the second logician. If any of the first two did not want a beer, they could answer "No" because a single false conjunct makes the whole conjunction false. Since they did not say "No", the third logician knew they they themselves wanted a drink. So did he, and now he could confirm that the whole conjunction is true.

 

[Nono713]

A mathematiciation, physicist and engineer are on a bus in Scotland. They see a black sheep through the window.

The engineer says: "All sheep in Scotland are black!"

The physicist replies: "No, some sheep in Scotland are black."

The mathematician rolls his eyes and says: "In Scotland, there exists at least one field, containing at least one sheep, at least one side of which is black."

----

A mathematician's, physicist's, and engineer's approach towards finding which numbers are prime.

Mathematician: "A prime has only two divisors, itself and 1. This definition encodes the entire sequence of prime numbers."

Physicist: "I know that 3, 5, and 7 are prime. Therefore I experimentally conclude all odd numbers are prime. 2 is evidently an incorrect measurement."

Engineer: "2 is prime, so all even numbers are prime."

:)

.

 

[Ackbach]

A mathematiciation, physicist and engineer are on a bus in Scotland. They see a black sheep through the window.

The engineer says: "All sheep in Scotland are black!"

The physicist replies: "No, some sheep in Scotland are black."

The mathematician rolls his eyes and says: "In Scotland, there exists at least one field, containing at least one sheep, at least one side of which is black."

I've heard a very similar story w.r.t. Aaron Burr, who was extremely loath to make any unqualified statements.

 

[kaliprasad]

(sighs) Okay, someone is going to need to explain this one to me...

- (Doh)

the 1st one is yes (wants beer) otherwise he should know that all do not want.
the 2nd one is yes otherwise he should know that all do not want.
so 3rd one knows that 1st and 2nd are yes and then 3rd is yes so all are yes or all want beer

 

[anemone]

Q: Why couldn't the negative pair square things away?
A: Because they had complex issues!

__________________________________________

Q: Why did the mathematician's pen run out of ink?
A: Because he was writing in recursive.

__________________________________________

Q: Why was the number zero fired?
A: Because he didn't add any value to the company.

__________________________________________

Q: Why did the two vectors start an internet-based company?
A: Because they thought they had a good dot product.

 

[Chris L T521]

An engineer, a physicist, and a mathematician are shown a pasture with a herd of sheep, and told to put them inside the smallest possible amount of fence. The engineer is first. He herds the sheep into a circle and then puts the fence around them, declaring, "A circle will use the least fence for a given area, so this is the best solution." The physicist is next. She creates a circular fence of infinite radius around the sheep, and then draws the fence tight around the herd, declaring, "This will give the smallest circular fence around the herd." The mathematician is last. After giving the problem a little thought, he puts a small fence around himself and then declares, "I define myself to be on the outside!"

---

A physicist, an engineer, and a statistician were out game hunting. The engineer spied a bear in the distance, so they got a little closer. "Let me take the first shot!" said the engineer, who missed the bear by three meters to the left. "You're incompetent! Let me try" insisted the physicist, who then proceeded to miss by three meters to the right. "Ooh, we got him!" said the statistician.

 

[Evgeny.Makarov]

One professor decided to give an open-ended question for a final exam. Instead of coming up with a concrete problem, he handed out pieces of paper to each student on which the following was written. "You are to invent a problem that you feel is suitable for a final exam, write it down and then write a solution to this problem".

One of the students received the paper. After some thinking, she copied its content twice and handed it in.

 

[Nono713]

One professor decided to give an open-ended question for a final exam. Instead of coming up with a concrete problem, he handed out pieces of paper to each student on which the following was written. "You are to invent a problem that you feel is suitable for a final exam, write it down and then write a solution to this problem".

One of the students received the paper. After some thinking, she copied its content twice and handed it in.

That is genius!

 

[Evgeny.Makarov]

During an oral exam, a student received a question and spent half an hour preparing his answer. He comes to the professor's desk holding a small piece of paper with one sentence. The professor asks, "Where is your answer?" "In my head", replies the student. "And what about this?", the professor points to the piece of paper. "This did not fit", says the student.

During older days, students in Russia received a small stipend that was not sufficient to survive for a month. So, on the day of the stipend, a student used the right-hand rule in the cafeteria: he closed the prices in the paper menu with his right hand and selected the dishes based on their names. During the following few days, he used the left-hand rule: he closed the names with his left hand and selected the dished based on their prices. Finally, for the rest of the month, he used the rule of the right-handed screw: he would turn around a few times and go home.

A student was reading "Field Theory" by Landau and Lif****z on the subway and fell asleep covering his face with the book. At the last station, a worker who was making sure everybody left the train read the title and said, "Hey, agronomist, wake up! Final station!"

 

[soroban]

Q: Why was the identity $$\sin2r \,=\,2\sin r$$ refused a loan?

A: Because he needed a $$\cos r.$$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~What is the difference between a psychotic and a neurotic?

The psychotic thinks $$2 + 2 \,=\,5.$$

The neurotic knows that $$2 + 2 \,=\,4$$, but it worries him!~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~What is the difference between data and information?

. . . . . . $$\begin{array}{c}\text{Data} \\ 362436 \\ \\ \text{Information}\\ 36\text{-}24\text{-}36 \end{array}$$

 

[soroban]

. . . . $$\boxed{\begin{array}{c}\Large\text{National Sarcasm Society} \\ \text{Like we need your support} \end{array}}$$

 

[soroban]

The bee is such a busy soul.

He has no time for birth control.

That's why in troubled times like these

There are so many sons of bees.

​

 

[Prove It]

What do you get when you divide a pumpkin's circumference by its diameter?

Pumpkin Pi :D

 

[soroban]

What do you get when you divide an igloo's circumference
. . by its diameter?

Eskimo $$\pi$$

 

[Fantini]

I just saw this on Quora:

Why do all Republicans have straight hair?

Because the curl of all conservative fields is zero.

 

[Chris L T521]

I just saw this on Quora:

Why do all Republicans have straight hair?

Because the curl of all conservative fields is zero.

(Rofl)

I needed a good laugh.

Ahem...anyways...

---

How they knew it was a deer:

The physicist observed that it behaved in a deer-like manner, so it must be a deer.
The mathematician asked the physicist what it was, thereby reducing it to a previously solved problem.
The engineer was in the woods to hunt deer, therefore it was a deer.

 

[Chris L T521]

And one more...it's quite a long one...in theorem/lemma format with "proofs." XD

---

Lemma 1. All horses are the same color.
(Proof by induction)
Proof. It is obvious that one horse is the same color. Let us assume the proposition $P(k)$ that $k$ horses are the same color and use this to imply that $k+1$ horses are the same color. Given the set of $k+1$ horses, we remove one horse; then the remaining $k$ horses are the same color, by hypothesis. We remove another horse and replace the first; the $k$ horses, by hypothesis, are again the same color. We repeat this until by exhaustion the $k+1$ sets of $k$ horses have been shown to be the same color. It follows that since every horse is the same color as every other horse, $P(k)$ entails $P(k+1)$. But since we have shown $P(1)$ to be true, $P$ is true for all succeeding values of $k$, that is, all horses are the same color.$\hspace{.25in}\blacksquare$Theorem 1. Every horse has an infinite number of legs.
(Proof by intimidation.)
Proof. Horses have an even number of legs. Behind they have two legs and in front they have fore legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite number of legs. Now to show that this is general, suppose that somewhere there is a horse with a finite number of legs. But that is a horse of another color, and by the lemma that does not exist.$\hspace{.25in}\blacksquare$Corollary 1. Everything is the same color.
Proof. The proof of lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the universally-quantified conditional 'For all $x$, if $x$ is a horse, then $x$ is the same color,' namely 'is a horse' may be generalized to 'is anything' without affecting the validity of the proof; hence, 'for all $x$, if $x$ is anything, $x$ is the same color.'$\hspace{.25in}\blacksquare$Corollary 2. Everything is white.
Proof. If a sentential formula in $x$ is logically true, then any particular substitution instance of it is a true sentence. In particular then: 'for all $x$, if $x$ is an elephant, then $x$ is the same color' is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain 'The Stolen White Elephant'). Therefore all elephants are white. By corollary 1 everything is white.$\hspace{.25in}\blacksquare$Theorem 2. Alexander the Great did not exist and he had an infinite number of limbs.
Proof. We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, 'If Alexander the Great existed, then he rode a black horse Bucephalus.' But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the consequent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist.

We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and 'forewarned is four-armed.' This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs.$\hspace{.25in}\blacksquare$

 

[Fantini]

After getting done with a meal, a mathematician announced: "$(\sqrt{-1/64})$".

 

[Chris L T521]

Claim: If you study, you fail.

Proof: It's common knowledge that if you study for an exam, you typically don't fail it; on the other hand, if you don't study, then you typically fail. Hence we have the equations
\[\begin{aligned} \text{study} &= \text{no fail}\\ \text{no study} &= \phantom{no }\,\text{fail}\end{aligned}\]
If we add these two expressions together, we see that
\[\text{study}+\text{no study} = \text{no fail}+\text{fail}\]
This implies that
\[(1+\text{no})\text{study} = (1+\text{no})\text{fail}\]
Cancelling out the common term now leaves us with
\[\text{study} = \text{fail}\]
Therefore, if you study, you fail.$\hspace{.25in}\blacksquare$

 

[Deveno]

Claim: If you study, you fail.

Proof: It's common knowledge that if you study for an exam, you typically don't fail it; on the other hand, if you don't study, then you typically fail. Hence we have the equations
\[\begin{aligned} \text{study} &= \text{no fail}\\ \text{no study} &= \phantom{no }\,\text{fail}\end{aligned}\]
If we add these two expressions together, we see that
\[\text{study}+\text{no study} = \text{no fail}+\text{fail}\]
This implies that
\[(1+\text{no})\text{study} = (1+\text{no})\text{fail}\]
Cancelling out the common term now leaves us with
\[\text{study} = \text{fail}\]
Therefore, if you study, you fail.$\hspace{.25in}\blacksquare$

I have discovered a small error in your proof: since it leads to a contradiction, you must have divided by zero. The correct conclusion should be:

no = -1.

 

[Deveno]

(Rofl)

I needed a good laugh.

Ahem...anyways...

---

How they knew it was a deer:

The physicist observed that it behaved in a deer-like manner, so it must be a deer.
The mathematician asked the physicist what it was, thereby reducing it to a previously solved problem.
The engineer was in the woods to hunt deer, therefore it was a deer.

This reminds me of a similar joke:

A mathematician was sleeping in a hotel when a fire broke out in the hallway. Alarmed, he arose, and stumbled into the hallway whereupon he spied a fire extinguisher.

"Ah," he said, "I see how the problem could be solved", and went back to bed.

 

[paulmdrdo1]

I have discovered a small error in your proof: since it leads to a contradiction, you must have divided by zero. The correct conclusion should be:

no = -1.

it's a joke anyway. :p

 

[Deveno]

it's a joke anyway. :p

Indeed, I realize that. And, see, my reply is a joke, too, because I am responding as if a "joke" were "serious math" which is sheer lunacy. :P

 

[Evgeny.Makarov]

it's a joke anyway. :p

Be it as it may, a large portion of the "proof" actually makes sense.

\[\begin{aligned} \text{study} &= \text{no fail}\\ \text{no study} &= \phantom{no }\,\text{fail}\end{aligned}\]
If we add these two expressions together, we see that
\[\text{study}+\text{no study} = \text{no fail}+\text{fail}\]
This implies that
\[(1+\text{no})\text{study} = (1+\text{no})\text{fail}\]
Cancelling out the common term now leaves us with
\[\text{study} = \text{fail}\]

Here is a code for the Coq proof assistant.

Variables study fail : Prop.

Hypothesis h1 : study <-> ~fail.
Hypothesis h2 : ~study <-> fail.

Lemma l1 : study \/ ~study <-> fail \/ ~fail.
Proof. rewrite h2, h1; tauto. Qed.

Definition prop2_plus (f1 f2 : Prop -> Prop) (P : Prop) :=
  f1 P \/ f2 P.

Infix "+" := prop2_plus.

Lemma l2 : (id + not) study <-> (id + not) fail.
Proof. apply l1. Qed.

Here Prop is the type of propositions, i.e., the type of Boolean formulas. Disjunction is denoted by \/ and the negation not is denoted by ~.

The formulas (study \/ ~study) and (fail \/ ~fail) have the same shape, so the idea is to factor out this shape. A similar thing can be done with numbers. The expressions $2+3\cdot2^2$ and $5+8\cdot5^2$ look similar. We can define a function $f(x,y)=x+yx^2$ and represent the two expressions as $f(2,3)$ and $f(5,8)$, respectively. In the same way, we define a function that takes and returns propositions: $f(P)=P\lor{\sim}P$, and say that $f(\text{study})\leftrightarrow f(\text{fail})$.

To make it even more similar to (1 + no)study = (1 + no) = fail from the original proof, we define a higher-order function prop2_plus that takes two functions of type (Prop -> Prop) and returns a similar function. It is basically a pointwise disjunction. It is needed because we cannot apply regular disjunction, which has type Prop -> Prop -> Prop, to the identity function id and the negation not : Prop -> Prop. And voilà,

(id + not) study <-> (id + not) fail.

The only thing is that this is not multiplication, but function application. And since (id + not) is not injective, unlike multiplication by a nonnegative number, we cannot conclude that study <-> fail.

This ability to define functions not only on datatypes like numbers and strings, but also on propositions, as well as the ability to define higher-order functions (those that take functions as arguments) are characteristics of the so called type theory, on which Coq is based.

OK, I'll crawl back into my nerdy hovel now...

 

[topsquark]

Be it as it may, a large portion of the "proof" actually makes sense.

Here is a code for the Coq proof assistant.

Variables study fail : Prop.

Hypothesis h1 : study <-> ~fail.
Hypothesis h2 : ~study <-> fail.

Lemma l1 : study \/ ~study <-> fail \/ ~fail.
Proof. rewrite h2, h1; tauto. Qed.

Definition prop2_plus (f1 f2 : Prop -> Prop) (P : Prop) :=
  f1 P \/ f2 P.

Infix "+" := prop2_plus.

Lemma l2 : (id + not) study <-> (id + not) fail.
Proof. apply l1. Qed.

Here Prop is the type of propositions, i.e., the type of Boolean formulas. Disjunction is denoted by \/ and the negation not is denoted by ~.

The formulas (study \/ ~study) and (fail \/ ~fail) have the same shape, so the idea is to factor out this shape. A similar thing can be done with numbers. The expressions $2+3\cdot2^2$ and $5+8\cdot5^2$ look similar. We can define a function $f(x,y)=x+yx^2$ and represent the two expressions as $f(2,3)$ and $f(5,8)$, respectively. In the same way, we define a function that takes and returns propositions: $f(P)=P\lor{\sim}P$, and say that $f(\text{study})\leftrightarrow f(\text{fail})$.

To make it even more similar to (1 + no)study = (1 + no) = fail from the original proof, we define a higher-order function prop2_plus that takes two functions of type (Prop -> Prop) and returns a similar function. It is basically a pointwise disjunction. It is needed because we cannot apply regular disjunction, which has type Prop -> Prop -> Prop, to the identity function id and the negation not : Prop -> Prop. And voilà,

(id + not) study <-> (id + not) fail.

The only thing is that this is not multiplication, but function application. And since (id + not) is not injective, unlike multiplication by a nonnegative number, we cannot conclude that study <-> fail.

This ability to define functions not only on datatypes like numbers and strings, but also on propositions, as well as the ability to define higher-order functions (those that take functions as arguments) are characteristics of the so called type theory, on which Coq is based.

OK, I'll crawl back into my nerdy hovel now...

I think I watched a Dr. Who episode based on this.

-Dan

 

[anemone]

1. Where was the Declaration of Independence signed?
Answer: On the bottom of the page.

2. River Ravi, flows in which state?
Answer: Liquid State.

3. What can you never eat for breakfast?
Answer: Lunch and Dinner

4. What looks like half an apple?
Answer: The other half.

5. What is the main reason for divorce?
Answer: Marriage

6. In which battle did Napoleon die?
Answer: His last one.

 

[eddybob123]

An infinite crowd of mathematicians enters a bar.
The first one orders a pint, the second one a half pint, the third one a quarter pint...
"I understand", says the bartender - and pours two pints.

 

[anemone]

View attachment 1218

 

[anemone]

View attachment 1251

 

[agentredlum]

An infinite crowd of mathematicians enters a bar.
The first one orders a pint, the second one a half pint, the third one a quarter pint...
"I understand", says the bartender - and pours two pints.

So the Hilbert Hotel also has a Hilbert Bar and Hilbert himself is tending bar with Cantor as the 'BOUNCER'

:D

 

[Chris L T521]

Here are a couple jokes I came across recently! XD

---

A Statistician, Engineer and Physicist go to the horse track. Each have their system for betting on the winner and they're sure of it.

After the race is over, the Statistician wanders into the nearby bar, defeated. He notices the Engineer, sits down next to him, and begins lamenting: "I don't understand it. I tabulated the recent performance of all these horses, cross-referenced them with trends for others of their breed, considered seasonal variability, everything. I couldn't have lost."

"Yeah," says the Engineer, "well, forget that. I ran simulations based on their weight, mechanical ratios, performance models, everything, and I'm no better off."

Suddenly, they notice a commotion in the corner. The Physicist is sitting there, buying rounds and counting his winnings. The Engineer and Statistician decide they've got to know, so they shuffle over and ask him, "what's your secret, how'd you do it?"

The Physicist leans back, takes a deep breath, and begins, "Well, first I assumed all the horses were spherical and identical..."

---

A mathematician, a physicist, and an engineer are given the task of finding how high a particular red rubber ball will bounce when dropped from a given height onto a given surface.

The mathematician derives the elasticity of the ball from its chemical makeup, derives the equations to determine how high it will bounce and calculates it.

The physicist takes the ball into the lab, measures its elasticity, and plugs the variables into a formula.

The engineer looks it up in his red rubber ball book.