Friday, October 31, 2014

Mr. B's Brain-O Quiz Number 4

Mr. B’s “BRAIN-O” Quiz
Guaranteed to unclog clogged up brains!

NAME:__________________ DATE:____________ PERIOD:________

Directions: Carefully read and answer the following questions.  Print you answer clearly in the box next to each question.  Questions are worth one zillion nano bonus point each.  However, if you get all five correct, we will double the points for a total of ten zillion nano bonus points.


Using any combination of parentheses and the operation symbols +, -, x, and ÷, how can you arrange the numbers 7, 7, 7, 7 and 7 into a mathematical expression equal to 7?


What number is next in this series:
3, 4, 7, 11, 18, 29, ...?


Scientists in Antarctica that study and film wild life on that continent have never filmed a polar bear attacking a colony of penguins.  Why not?


Name a sport where the defensive team keeps possession of the ball.


Three men check into a hotel.  The manager quotes the room at $30.  The three men pay $10 each.  After the men go up to the room, the manager realizes that he overcharged them, the room is only $25.  He sends the bellboy up with $5 to refund to the men.  The bellboy decides he can make some money.  He pockets $2 and gives the men back $3 ($1 each).  The men divide up the money $1 each. Now, each man paid $9.  $9 times 3 = $27.  The bellboy pocketed $2. $27 and $2 totals $29.  Where's the missing dollar?

It’s not that I’m so smart,
it’s just that I stay with problems longer.

- Albert Einstein

WARNING: For Educational Purposes Only.
Please do not attempt to answer any of these questions
unless you are willing to learn something.

Mr. B’s “Brain-O” Quiz, Volume 1, page 4

Solutions will be posted on Monday.


Thursday, October 30, 2014

Halloween Appropriate Mathematics

Since tomorrow is Halloween, I thought we would address some Halloween Appropriate Mathematics.

Beastly Primes
The Prime Glossary defines two kinds of Beastly primes.  The first type are palindromic primes that have a 666 at the center, which is surrounded by zeros, with either ones or sevens on the end.  The second is a prime number that starts with 666, which is followed by a string of zeros, with either a one or a seven on the end.
The Online Encyclopedia of Integers sequences also describes a set of palindromic primes that have “666” in the middle of the prime (but they do not call it a Beastly prime.  My favorite is 3166613 because it includes the number of the beast, thirteen, and a backwards thirteen.  Spooky!
And they also describe Beastly prime cousins that occur when p is a prime number, and p + 666, and p – 666 are both prime also.  I am not sure if they are referring to all three primes being prime cousins or just the two (p + 666, and p – 666) formed from the original prime p.
Belphegor’s Prime is the most famous Beastly Prime:  1,000,000,000,000,066,600,000,000,000,001.  It consists of a one, 13 zeros, “666”, 13 zeros and another one.  If the 13 ones, and the 666 is not spooky enough, the name Belphegor should be.  Belphegor is one of the seven princes of hell.(representing vanity and sloth, and responsible for helping people make great discoveries or inventions).  This number is also a Palindromic prime and a Naughty prime.  And it has 31 digits (which is 13 backwards).
Belphegor - not your math teacher from last year.

What is interesting is that this number remains prime if you substitute the thirteen zeros on either side of the “666” with 42, 506, 608, 2472, 2623, or 28,291 zeros on each side of the “666”.

Vampire Numbers
Vampire numbers have an even number of digits, and the digits can be rearranged to form two fangs (or factors) whose product is the original number.  For example 1260 is a Vampire number because the digits can be rearranged into 21 and 60, and 21 * 60 = 1260.  OEIS also has a definition of Vampire numbers which can include number with an odd number of digit, fangs (factors) that are not equal sized (have a different number of digits), and might have more than two fangs.  I think a vampire with 3 fangs with a big one on the right just looks funny. 

Witch of Agnesi
Maria Gaetana Agnesi
Maria Gaetana Agnesi was an Italian mathematician and philosopher, who lived in the 18th century.  She was an honorary member of the faculty at the University of Bologna (the university did not teach bologna, it was located in Bologna, Italy).  She is credited with writing the first book that covered both differential and integral calculus.
The "Witch of Agnesi" is the cure going through points M and P.
In her book “Instituzioni analitiche” she discussed a curve earlier studied and constructed by Pierre de Fermat and Guido Grandi.  Grandi called the curve “versoria” (a nautical term meaning “sheet”), but somehow the term was mis-copied or mis-translated into “versiera” which means “she-devil” or “witch”.  So the curve has become known as the "Witch of Agnesi".  It’s not a very scary curve, but if you dressed up as the “Witch of Agnesi” very few people would be able to figure out what you were.
You might want to go see this short video:



Wednesday, October 29, 2014

Math Words: Octothorpe

Octothorpe: In the 1960's when Bell Telephone added two new buttons for push button telephones, they used the * symbol and the # symbol.  Although most people call the * an asterisk, the telephone folks decided to use "star".   other symbol, #, has been called lots of different names such as crosshatch, tic-tac-toe, the pound sign, and the number sign (leave it to the telephone company to put the number sign on one of the two keys without a number); but the term now used by the American telephone industry for the symbol is octothorpe although it is more often called the pound key in conversations with the public.  It seems that the name was made up more or less spontaneously by Bell Engineer Don MacPherson while meeting with their first potential customer.  The octo part was chosen because of the eight points at the ends of the line segments, and the thorpe was in honor of Jim Thorpe, the great Native American athelete.  Why honor Thorpe? At the time MacPherson was working with a group that was trying to restore Thorpe's olympic medals, which had been taken from him when it was found he had played semi-professional baseball prior to his track victories in the Olympics in Sweden.  [It's not math, but I love the story that when the King of Sweden gave him the gold medal, the king said, "You are surely the greatest athlete on the earth".  The modest Thorpe smiled and replied, "Thanks, King."]
There are a host of other names for the # symbol, and many of them can be found at this page from Wikipedia which includes several different stories about the creation of "octothorpe" or "octothorn" and also has this rather interesting clip:
"The pronunciation of # as `pound' is common in the US but a bad idea.  The British Commonwealth has its own, rather more apposite, use of `pound sign.  On British keyboards the UK pound currency symbol often replaces #, with # being elsewhere on the keyboard.  The US usage derives from an old-fashioned commercial practice of using a # suffix to tag pound weights on bills of lading.  The character is usually pronounced `hash' outside the US. There are more culture wars over the correct pronunciation of this character than any other, which has led to the ha ha only serious suggestion that it be pronounced `shibboleth' (see Judges 12:6 in an Old Testament or Tanakh)."  The page also disputes the use of "square" in Britain.