See if you can figure out the optimal strategy in this neat game. The rules are simple, whoever eats the poisoned apple (red one) loses. It was created by Philip Brocoum.

Click below to go to the game:

http://www.philipbrocoum.com/munch/

Posted by mathfail
on March 16, 2011
6 comments

See if you can figure out the optimal strategy in this neat game. The rules are simple, whoever eats the poisoned apple (red one) loses. It was created by Philip Brocoum.

Click below to go to the game:

http://www.philipbrocoum.com/munch/

Posted by mathfail
on March 14, 2011
5 comments

Using pi calculated out to only 39 decimal places would allow one to compute the circumference of the entire universe to the accuracy of less than the diameter of a hydrogen atom.

3.14 backwards is PIE.

The letter π is the first letter of the Greek word “periphery” and “perimeter.” The symbol π in mathematics represents the ratio of a circle’s circumference to its diameter. In other words, π is the number of times a circle’s diameter will fit around its circumference.

The first 144 digits of pi add up to 666 (which many scholars say is “the mark of the Beast”). And 144 = (6+6) x (6+6).

William Shanks (1812-1882) worked for years by hand to find the first 707 digits of pi. Unfortunately, he made a mistake after the 527th place and, consequently, the following digits were all wrong.

The first million decimal places of pi consist of 99,959 zeros, 99,758 1s, 100,026 2s, 100,229 3s, 100,230 4s, 100,359 5s, 99,548 6s, 99,800 7s, 99,985 8s, and 100,106 9s.

Posted by mathfail
on March 13, 2011
1 comment

Memorize some pi for pi day!

Here are some Mnemonics to help you remember the digits of pi,

which begin 3.1415926535897932384626433832795…

- Yes, I know a digit.
- May I draw a circle?
- Wow, I made a great discovery!
- Now I need a verse recalling pi.
- How I wish I could enumerate pi easily today.
- May I have a large container of coffee right now?
- May I have a large container of coffee — sugar and cream?
- Sir, I need a large microwave to simmer, broil, and roast.
- Hey, I need a large motorboat to rescue women and girls.

And some longer ones:

How I wish I could recollect pi

Eureka! cried the great inventor.

Christmas pudding, Christmas Pie

Is the problem’s very center.

God! I need a drink –

Alcoholic of course –

After all those lectures

Involving radical equations.

See, I have a rhyme assisting

My feeble brain, its tasks ofttimes resisting.

See, I have a rhyme assisting

My feeble brain, its tasks ofttimes resisting.

Posted by mathfail
on March 4, 2011
No comments

I haven’t seen this joke before but it was posted over on the xkcd forums by user ++$_. Enjoy:

Three investment bankers met for a power lunch.

“Guys,” said the first banker, “I just had a billion-dollar idea.”

“You’d better tell us,” said the other two bankers simultaneously. They could smell the scent of their impending bonus checks, even over the delicious aroma ascending from the filet mignon.

“It’s a simple matter of probabilities,” said the first banker, adjusting his tie. “You know the lottery, right? Suppose I go out to the store and buy a ticket. What are the two possibilities?”

“Well,” said the second banker, furrowing his brow, “I can think of one. There are really two?”

“I’m stumped too,” said the third banker. “You’d better tell us.”

“Well,” said the first banker, feeling very proud of his insight, “either I win, or I lose.”

“Oh, of course,” said the second banker. “I had thought of both of those. I just counted them wrong.”

“Anyway,” said the first banker, “there are two possibilities. As everyone knows, that means the probability of each is 1/2! So if I play the lottery, the probability that I win is 1/2!” He pounded his fist on the table.

“Gentlemen,” he said, “I think I’m going to open a new fund. I’ll call it ‘Modern Probabilistic Investment Fund.’ I can offer you the opportunity to contribute some capital for a minority stake…”

“Wait a moment,” said the second banker, interrupting the negotiations. “Suppose I were to tell you how you could make twice as much money. Could I be an equal partner in the fund if I did that?”

“I suppose so,” said the first banker. “What’s your idea?”

“Well,” said the second banker, “we’ve just seen that if you buy one lottery ticket, the probability that you win is 1/2. So if you buy a second lottery ticket, the probability that you’ll win with that one is also 1/2, right?”

“Of course,” said the first banker. “Go on.”

“Now, what is 1/2 plus 1/2?” asked the second banker.

“Seven!” said the third banker. “Wow! A probability of seven! Who ever heard of such a thing?”

“I don’t think that’s right,” said the first banker, who had taken a calculator from his briefcase. “My calculator says that the answer is 1.”

“Good,” said the second banker. “That’s what I got too. So if you buy two tickets, the probability of winning is 1. That’s twice as much as if you had bought only one ticket!”

“Brilliant!” said the first banker. “I knew you guys wouldn’t let me down. So, about that fund. I’ll be the chairman, and you can be the president.”

“No,” said the second banker. “I want to be the chairman. You can be the president.”

“No,” said the first banker. “I’m definitely going to be the chairman.”

After this had been going on for some time, the third banker at last broke in.

“Wait a minute,” he said. “I just thought of a problem with your idea.”

“Hey, enough of your negative thinking,” said the first banker. “That’s the kind of thing that brings down companies, you know.”

“It couldn’t hurt to hear it, though,” said the second banker. “Let’s see what he says before we dismiss it. It’s good to keep an open mind.”

“Thank you,” said the third banker. “Now, when you buy two lottery tickets, would you buy two with the same numbers selected, or with different numbers?”

“Well, obviously with different numbers,” said the first banker scornfully. “If they had the same numbers, then you’d split the pot with yourself if you win, so it would just be the same as buying one ticket. We’re not as stupid as you think.”

“That’s not the problem,” said the third banker. “But now consider the possibilities. Since the tickets have different numbers, only one of them can win, right?”

“Of course,” said the second banker.

“OK,” said the third banker. “So there are three possibilities. Either the first ticket wins, or the second ticket wins, or neither ticket does. That’s three possibilities, and you win in two of them. So the probability of winning is actually 2/3!”

“So what?” said the second banker. “2/3 is still better than 1/2. And even with a probability of 1/2 we’ll still make enough money.”

“There’s no such thing as enough money,” said the first banker. “But whatever. I don’t see the problem.”

“Well,” said the third banker, “Let’s say the jackpot is one million dollars. If you leverage the one-ticket method, you get an average of 500,000 dollars, but you have to pay one dollar to do it. So your return on investment is 50,000,000%. If you leverage the two-ticket method, you get an average of 666,667 dollars, but you have to pay two dollars to do it, so your return on investment is only 33,333,333%. So the best method is the one-ticket method, and not the two-ticket method!”

“Whatever,” said the second banker. “I still get to be chairman.”

“No, I do,” said the first banker.

“Wait a moment,” said the second banker. “If the one-ticket method is better than the two-ticket method, then wouldn’t the best method be the ZERO-ticket method? After all, one is less than two, and zero is even less than one! You could make even more money that way!”

“I don’t know,” said the third banker. “You just went way beyond my mathematical abilities. But I’ll call my quant. He’s got a PhD in math, so I’m sure he’ll know the answer.”

So the third banker got out his Blackberry and dialed a number. “Vitaly,” he said into the phone, “we’ve been having a power lunch and we need to know the answer to a question.”

There was something said on the other end of the phone that neither of the other bankers could hear.

“Here’s the question,” said the third banker. “Is it true that the best number of lottery tickets one can buy is zero?” There was a tense pause. Even the waiters froze in their tracks, waiting. The fate of the city, the planet, and even the entire known universe seemed to hang in the balance.

“Vitaly says yes,” said the third banker. “The best number of lottery tickets to buy is zero.”

“But,” said the first banker, “if we don’t buy any lottery tickets, then we won’t make any money at all!”

“That’s too bad,” said the second banker.

“A shame,” said the third banker.

They turned sadly back to their filet mignon.

Posted by mathfail
on February 28, 2011
No comments

“If you don’t like your analyst, see your local algebraist!”

*Gert Almkvist*

“logloglog n has been proved to go to infinity, but has never been observed to do so.”

“Anyone can count the seeds in an apple, but no one can count the apples in a seed.”

“It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.”

“Spending time with math people is a lot of fun. As a result of the play, I’ve had semi-drunken dinners with mathematicians all over the country. I recommend the experience.”

“Mathematics is a collection of cheap tricks and dirty jokes.”

“We all agree that your theory is crazy, but is it crazy enough?”

“I hate algebra.”

“A mathematician is a blind man in a dark room looking for a black cat which isn’t there.”

“I wrote a few papers on Koszul algebras, but I really don’t understand the definition of Koszul algebras.”

Posted by mathfail
on February 27, 2011
No comments

Posted by mathfail
on February 27, 2011
No comments

This is a pretty genius post by Ξ over at the 360 blog. Ξ talks about different kinds of “mathematical diets”, such as the Harmonic diet, Zeno diet, Banach-Tarski diet and Fibonacci diet. Go check it out!

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