Monday, January 23, 2012

More interesting than 22/7

This post is based on this posting from Futility Closet.

You set up an infinite series

1*x + 1*(x^2) + 2*(x^3) + 3*(x^4) + 5*(x^5) + 8*(x^6) + 13*(x^7) + ...

Call that expression A. Multiply A by x to get A*x =

1*(x^2) + 1*(x^3) + 2*(x^4) + 3*(x^5) + 5*(x^6) + 8*(x^7) + 13*(x^8) + ...

Then subtract these two expressions by subtracting each term of the second expression from the term of the first expression with the same power of x -- the resulting expression

A - A*x = 1*x + 1*(x^3) + 1*(x^4) + 2*(x^5) + 3*(x^6) + 5*(x^7) + ...

which except for the first term is exactly A*(x^2)

In other words

A - A*x = x + A*(x^2)

If you solve this for A by bringing all terms involving A to one side and then factoring out A, you end up with

A = x / (1 - x - x^2)

By now you're wondering what is the point of all of this. Well if you go back to the original series

1*x + 1*(x^2) + 2*(x^3) + 3*(x^4) + 5*(x^5) + 8*(x^6) + 13*(x^7) + ...

and substitute .001 for x, the terms become

.001 + .000001 + .000000002 + .000000000003 + .000000000000005 + .000000000000000008 + .000000000000000000013 + ...

which equals

.001001002003005008013 ...

so the same should be true if you substitute .001 for x in

A = x / (1 - x - x^2)

and if you do you get the fraction

1000 / 998,999

The decimal equal to this fraction begins with all the Fibonacci numbers with 1, 2 or 3 digits. If you want a fraction that has all the Fibonacci numbers with 1, 2, 3, or 4 digits, then you substitute .0001 for x into A (instead of .001).

Joseph G. Rosenstein
Professor of Mathematics
Rutgers University

Sistine Chapel panorama

Incredible work.

Fun with graphing equations

Link to NPR article

Fracking explained

Sunday, January 22, 2012

Churchill on Italian Cruise Lines

A friend reminded me of a comment made by Winston Churchill.

After his retirement he was cruising the Mediterranean on an Italian cruise liner and some Italian journalists asked why an ex British Prime Minister should choose an Italian ship.

“There are three things I like about being on an Italian cruise ship” - said Churchill.

“First their cuisine is unsurpassed. Second their service is superb. And then, in case of an emergency, there is none of this nonsense about women and children first."

Lost in Translation

Ted Koppel of ABC and Rick Kaplan, his executive producer, are laughing at a misunderstanding which has just occurred with a friendly Kremlin functionary. The official approached the Americans and wished them a Happy Christmas. With a straight face Kaplan, who is Jewish, replied, "To me you will have to say "Happy Hanukkah". "Why would I have to say 'Happy Honecker'? asked the official, puzzled. The Americans bust out laughing at the official's assumption the Kaplan is referring to Erich Honecker, who fled to Moscow after the fall of the Berlin Wall two years earlier.

The Last Day of the Soviet Union
Moscow December 25, 1991
Conor O'Clery
Public Affairs

Wednesday, January 4, 2012

Student who obtained 0% on an exam

I would have given him 100%. -L

Q1. In which battle did Hannibal die? * his last battle
Q2. Where was the Declaration of Independence signed? * at the bottom of the page
Q3. River Ravi flows in which state? * liquid
Q4. What is the main reason for divorce? * marriage
Q5. What is the main reason for failure? * exams
Q6. What can you never eat for breakfast? * Lunch & dinner
Q7. What looks like half an apple? * The other half
Q8. If you throw a red stone into the blue sea what it will become * It will simply become wet
Q9. How can a man go eight days without sleeping? * No problem, he sleeps at night.
Q10. How can you lift an elephant with one hand? * You will never find an elephant that has only one hand.
Q11. If you had three apples and four oranges in one hand and four apples and three oranges in other hand, what would you have? * Very large hands
Q12. If it took eight men ten hours to build a wall, how long would it take four men to build it? * No time at all, the wall is already built.
Q13. How can you drop a raw egg onto a concrete floor without cracking it? * Any way you want, concrete floors are very hard to crack.

Everything has its consequences

Always think about what you do...

Monday, January 2, 2012

Japan says thank you

Our current President thinks we have gotten "soft" and "lazy". Someone needs to remind him of the incredible humanitarian missions we do on a daily basis...not only in Japan but all over the world.

Sunday, January 1, 2012

Flight 109 Hudson River

Let this load awhile before you press the play button. This is full of suspense – even though I knew what was going to happen!

Public Service Announcement

Please, take care of yourself out on the roads this holiday season.

A recent joint study conducted by the Department of Health and the Department of Motor Vehicles indicates that 23% of traffic accidents are alcohol related.

This means that the remaining 77% are caused by a$$h*les who drink bottled water, Starbucks, soda, juice, energy drinks, and sh*t like that.

Therefore, beware of those who do not drink alcohol. They cause three times as many accidents.

This message is sent to you by someone who worries about your safety.

Problem magnification

On a television show, Eddie Fisher complained to George S. Kaufman that women refused to date him because he looked so young. Kaufman considered this and replied:

“Mr. Fisher, on Mount Wilson there is a telescope that can magnify the most distant stars up to 24 times the magnification of any previous telescope. This remarkable instrument was unsurpassed until the construction of the Mount Palomar telescope, an even more remarkable instrument of magnification. Owing to advances and improvements in optical technology, it is capable of magnifying the stars to four times the magnification and resolution of the Mount Wilson telescope. Mr. Fisher, if you could somehow put the Mount Wilson telescope inside the Mount Palomar telescope, you still wouldn’t be able to detect my interest in your problem.”

"Quite, er, dainty, Mr. Bond."

The Beretta 418 was an unmitigated piece of shit. A .22 is a far better killer than a .25 ACP. The most worthless cartridge out of any in production. The Walther in .32 isn't much better. Fleming knew absolutely nothing about firearms, you can tell it from reading the Bond novels.

Rule#1: If you must get in a gunfight with only a pistol, make sure the caliber starts with the number "4".

From Wikipedia

The Beretta 418 is also known as the favorite pistol of James Bond. In the James Bond novels his pistol is described as having a skeleton grip (i.e. grips removed - frame only), and either a threaded barrel to support a silencer or completely sawed off barrel. It was his weapon of choice up until the novel and theatric adaption of Dr. No when a Major Boothroyd, introduced as "the greatest small-arms expert in the world", insists it be replaced by the Walther PPK. In reality Ian Flemming received a fan letter in 1957 from Geoffrey Boothroyd, a Bond enthusiast and gun expert, criticizing the choice of firearm for Bond calling it "a lady's gun" and suggesting several alternatives, among which were the PPK.


Dear Internet, you've been trolled!

That's why it's called junk food

10 interesting facts about junk food

F-6F Hellcat

Nothing unorthdox indeed. Takes off and lands just like the SN-J! No wonder pilots could get into a Hellcat and just fly it off!