12,072,015

12/07/2015

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.

David

Pearl Harbor Day, and Brain-0 Quiz Answers

12/07/2015

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.

Mr. B's Brain-O Quiz # 36

12/04/2015

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.

1.		Find the name of an animal hidden in the following sentence: “Please, use a ladder.”
2.		The Yankees and the Tigers play 5 baseball games. They each win 3. No ties or disputed games were involved. How could this be?
3.		Most people think that elephants eat a lot, but did you know that elephants each much less than cows?  How is that possible?
4.		Arrange the integers 1 through 15 in a row so that the sum of any 2 adjacent integers is a perfect square.
5.		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.

David

Math Related Christmas Songs

12/01/2015

12,012,015 is the hypotenuse of a right triangle: 12012015^2 = 7207209^2 + 9609612^2.


MATH RELATED CHRISTMAS SONGS:

If you haven't yet started gathering some festive songs to sing before you take your "Christmas Break" (you don't think they're really doing it for Isaac Newtons Birthday or just because it's winter - did you?) it's time to get on it.

Here are some web sites to check out:



Calculus Collapse (Winter Wonderland)--Jennifer Brevell

Calculus the Killer Math Course (Rudolph)--Russ Tilton

We Three Math'maticians (We Three Kings)--Clay Janca

We Three Students of Calculus (We Three Kings)--Edward Coles

Calculus Christmas Carol (Winter Wonderland)--Lisa Judkins

Calculus (Jingle Bells)--Ryan Barlow

Leibniz the Unknown Founder (Rudolph)--Jenna Hartmann

12 Days of Sir Isaac Newton

Samples from Math Horizon Magazine (This includes “Fill the Boards with Differentials” and “Oh Calculus, Oh Calculus”

http://www.calculus-help.com/calculus-carols/ (This includes “Riemann Sums”, “Derivatives, Derivatives”, and “Calculus Class”.

http://sites.csn.edu/gcohen/182/31_christmas.pdf “The Calculus Christmas Carol”

http://www.math.ucla.edu/~barnicle/carols.pdf (This includes: “Twas Just Before the Winter Break” ('Twas In The Moon Of Wintertime), “The First Derivative” (The First Noel), “We Three Dimensions (We Three Kings), “What Function Is This?” (What Child Is This), “Hark! The AP Proctors Sing (Hark, The Herald Angels Sing)”, “O Sum All Your Data” (O Come, All Ye Faithful), “O Little Open Interval (O Little Town of Bethlehem), “Look at the Board” (People, Look East), “All the Spivak I've Forgotten” (Of The Father's Love Begotten). “Joy to the Set” (Joy to the World), “Creator Alme Siderum” (Complex Analysis version), “Infant Holy, Infant Lowly” (Mathematical Logic version), “The Friendly Beasts (Abstract Algebra version), “The Gentzen and the Hilbert” (The Holly and the Ivy).

http://www.pleacher.com/mp/mpoetry/calcsng5.html  One song, “A Calculus Christmas Carol”, sung to the tune of Jingle Bells, and it’s a version I haven’t seen before.

http://homework.zendog.org/songsfall2004.html More calculus songs, and a few carols.  Worth checking out.

http://cchsindy.org/bird/Smart/Calc1/CalculusSongs01_17.pdf is a collection of Calculus songs, but not necessarily Carols.  Worth checking out.

http://shadowfaxrant.blogspot.com/2010/12/12-days-of-calculus-carols.html  This web site is hard to read (for us old folks) but it looks like you could copy the text and print it out in a much clearer form very easily.

https://sites.google.com/site/gdscalculuscarols/  Many interesting and original songs.

 David