Tuesday, December 22, 2015

Ramanujan's Birthday!


12222015 is a composite, deficient, odd, odious, semiprime, square-free, and wasteful number.  It can be expressed as the sum of all of the integers from 45301 to 45569.

Today is Srinivasa Ramanujan’s Birthday, and a good day to talk about Brithdays and Magic Squares.

(Just a quick reminder - most of you have already decorated the house, bought presents and so forth - but if you haven't there are only 3 days left until Isaac Newton's Birthday!)

Ramanujan was a self-taught Indian mathematician, discovered by the British mathematician G. K. Hardy.  Hardy invited Ramanujan to return to London with him in order to study mathematics.

Ramanujan created his own Magic Square.


Each row, each column and both major diagonal add up to 139.  You might also notice that the four corners add up to 139 also.

And, the two numbers between the top corners add with the two numbers between the bottom corners for a total of 139. 

And, the two numbers between the left corners add with the two numbers from the right corners for a total of 139.

And, the four numbers above, below, to the right of, and to the left of the top left and bottom right corners add up to 139.

And, the four numbers above, below, to the right and to the left of the bottom left and the top right corners add up to 139.

And, the four numbers in the middle of the magic square add up to 139.

Are there more?  Oh yes!

The four numbers in the top left corner add up to 139.  The four numbers in the top right corner add up to 139.  The four numbers in the bottom left corner add up to 139.  AND, the four numbers in the bottom right corner add up to 139.

I’m glad were through ... we are through aren’t we?  Not yet!

The square containing the 88, 17, 10, and 24 (2nd and 3rd rows, 1st and 2nd columns), and the square containing the 9, 16, 25 and 89 (2nd and 3rd rows, 3rd and 4th columns) also add up to 139.

Finally we are at the end.  You may not have noticed, but the icing on the top is that the top row is Ramanujan’s birthday (22/12/1887 – written in the British format (Day/Month/Year) with the year split into two two-digit numbers).

Of course, I could go on about the mathematical mysteries of 139.

Or I could start into a lecture on how to create your own birthday.  (Or, even better, create one for your sweetheart’s birthday.)

Maybe out save those topics for another day.

Email me if you want me to cover either of those topics.



And Arthur Benjamin has a really nerdy paper on how to make birthday magic squares at: https://www.math.hmc.edu/~benjamin/papers/DBMS.pdf .  (But what makes it really nerdy is the picture of him in a nerdy math shirt.)


Thursday, December 17, 2015

The Ten Commandments of Mathematics


The Ten Commandments of Math
1. Thou shalt not divide by zero. 

2. Thou shalt not put other textbooks before thee in math class.

3. Thou shalt show thy work; check thy work and confirm that thy results are reasonable. 

4. Remember thy test days and prepare for them wholly. 

5. Thou shalt honor the correct order of operations. 

6. Thou shalt not do thy math homework in ink! 

7. Thou shalt commit the facts of arithmetic to memory. 

8. Thou shalt do unto one side of an equation what thou doest to the other 

9. Thou shalt not bear false witness against thy original problems; thou shalt copy thy problems accurately and legibly. 

10. Thou shalt not covet thy neighbor's paper, not anything that is thy neighbor's

Source: http://www.teachnet.com/lesson/math/10commforclass.html

Monday, December 7, 2015



12,072,015 = (3^2)(5)(268,267)
It has 12 divisors (1, 3, 5, 9, 15, 45, 268,267, 804,801, 1,341,335 2,414,403, 4,024,005, and 12,072,015), whose sum is σ = 20,924,904.  Its totient is φ = 6,438,384.  The sum of its prime factors is 268278 (or 268275 counting only the distinct ones).  The product of its (nonzero) digits is 140, while the sum is 18.
12,072,015 is a number that cannot be expressed as the sum of three squares.
12,072,015 is digitally balanced in base 2, because in such base it contains all the possible digits an equal number of times.
Almost surely, 212,072,015 is an apocalyptic number.
12,072,015 is a 1,207,203-gonal, 4,024,006-gonal, arithmetic, composite, congruent, deficient, evil, polite, odd, and wasteful number.
It is part of a Pythagorean triple (the short leg of a right triangle): 12,072,015^2 + 294,767,048^2 = 294,767,057^2.


Pearl Harbor Day, and Brain-0 Quiz Answers


Today is the 74th anniversary of the Japanese Attack on Pearl Harbor, and several of the surrounding airfields.  Over 2000 Americans died including civilians, but most were officers and crewmen of just one ship, the USS Arizona.  At the time of the attack Japan had not yet declared war against the U.S.  Most of the ships that were damaged or sunk were refloated, were repaired and upgraded and participated in war to help defeat Japan.

Remember to thank a Veteran for their service.

Answers to Last Fridays Brain-O Quiz:

1.  Seal.
2.  They played other teams.
3.  There are many more cows than elephants.
4.  8, 1, 5, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9 or this order reversed.
5.  He lives at the north pole, where nights are 6 months long.

The average school year in the U.S. is 180 school days, or 36 5 day weeks.  This completes 36 Brain-O Quizes posted on this site.  Feel free to use them with your classes, just don't tell the student's where to look up the answers.

I will continue to post new Brain-O Quizes - so keep checking back.

Friday, December 4, 2015

Mr. B's Brain-O Quiz # 36


Mr. B’s “BRAIN-O” Quiz
Guaranteed to unclog clogged up brains!
NAME:__________________ DATE:____________ PERIOD:_______
Directions: Carefully read and answer the following questions.  Print your answer clearly in the box next to each question.  Questions are worth one million nano bonus points each.  However, if you get all five correct, we will double the points for a total of ten million nano bonus points.

Find the name of an animal hidden in the following sentence: “Please, use a ladder.”


The Yankees and the Tigers play 5 baseball games. They each win 3. No ties or disputed games were involved. How could this be?


Most people think that elephants eat a lot, but did you know that elephants each much less than cows?  How is that possible?


Arrange the integers 1 through 15 in a row so that the sum of any 2 adjacent integers is a perfect square.


A man gets up at 180 times a night, but sleeps at least 7 hours at a time.  Where does he live?

Intelligence is something we are born with.  Thinking is a skill that must be learned.

- Edward de Bono

WARNING: For Educational Purposes Only.
Please do not attempt to answer any of these questions
unless you are willing to learn something.
Answers will be posted on Monday.