March 20th, 2015

I must apologize for my absence - have been in the hospital, but I'm back and ready to post.

By the way, while I was in the hospital I was given a lot of medical advice.  One of my doctors advised me to take a certain medication.  I ask why I should.  He told me that studies indicate that it can reduce my risk of dying by 18%.  I asked to be changed to a different doctor.  My risk of dying is 100%.  I might take a certain medication and live longer, but I will still eventually die.  The staff asked me why I wanted a new doctor. 

I told them "This one got by me."

"What do you mean."

"Well, why did you decide to become a doctor?"

"I wanted to save lives.  Why did you decide to become a Mathematician?"

"I wanted to save lives too!  In fact I may have saved more lives than you have."

"How do you save lives as a mathematician?"

"I help keep the idiots out of med school.  Most doctors know you can't reduce the risk of dying, but they can help prolong my life.  The doctor who has been treating me thinks that a medication can keep me from dying.  I guess he slipped past me."

David

Happy Sequence Day

3/4/2015

Today is Sequence Day.  Todays date written numerically (3/4/2015) contains consecutive digits (0, 1, 2, 3, 4, and 5).

The next date to have this property will be 4/3/2015.

The next one after that is not until 2031!!!


David

Preparing for Pi Day - Resources

3/01/2015

Piphilology: Piphilology comprises the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant "pi".  The word is a play on the word "pi" itself and of the linguistic field of philology.
http://en.wikipedia.org/wiki/Piphilology

Pi World Ranking Lists:
http://pi-world-ranking-list.com/

Pi Word Play from Wolfram Mathworld:
http://mathworld.wolfram.com/PiWordplay.html

Pilish: Pilish is a style of constrained writing in which the lengths of consecutive words match the consecutive digits of the number pi.
http://en.wikipedia.org/wiki/Pilish

Writing in Pilish.
http://www.cadaeic.net/pilish.htm

Pi Day Carols
http://www.teachpi.org/music/pi-day-carols/

Pi Day Songs
http://mathforum.org/te/exchange/hosted/morehouse/songs.pi.html

15 Songs that Mention Pi(e).
http://popdust.com/2013/03/14/songs-that-mention-about-pie-for-pi-day/

Happy Pi Day: 10 YouTube Videos for Math Geeks
http://mashable.com/2013/03/14/pi-day-videos/

Pi Day Videos
http://www.piday.org/topics/videos/

Vi Hart's Song about Tau (2 times pi):
https://www.khanacademy.org/math/recreational-math/vi-hart/pi-tau/v/a-song-about-a-circle-constant

Lucy Kaplansky's Song about Pi
https://www.youtube.com/watch?v=nJkwlnN7VII

The Joy of Pi, Pi Facts, Pi Links:
http://www.joyofpi.com/

Youtube has a ton of videos with songs about pi.  Mathematical Pi, Pi-namite, Pi Day Theme Song, etc.
www.youtube.com

A personal challenge to math music nerds and geeks.  I would like to see a song about Pi that is sung to the tune of "This is the song that never ends".

Good Hunting!



David

Largest Known Prime

1/25/2015

The largest known prime was discovered two years ago by Curtis Cooper.

It is a Mersenne Prime, 2^57,885,161 - 1.

When written in decimal form it is 17,425,170 digits long.

Of course it would be impossible to determine if a number that large is prime or not with out the use of a computer - well, in this case a bunch of computers.  When mathematicians are working on a project like this they are in competition with others for find another large prime to become the next "worlds largest known prime", but they are also competing in the world of computer science to test their algorithms for finding large prime numbers.

Because of this I have challenged myself to memorize this prime number in its binary form (because the computers that verified its "primeness" work in binary.

In binary it is 57,885,161 digits long.  And today I have finished memorizing all of them.  See below:










Wait for it!










Wait for it!










All 57,885,161 digits are "1".

Sometimes I even amaze myself.



David

Peggy Sue Does It Again

Tridecanacci Numbers: 

Gotta LOVE those Italian babes with mathematical skills.  Actually, this Italian babe immigrated from Italy when she was just 3 months old.  In fact she still speaks a little Italian - like "spaghetti", "pizza", "lasagna" and "raviolli" fluently.  She even know the Latin names of more body parts than I known the English names for.

Anyway she has developed a way of remembering the first 31 terms of the tridecanacci sequence, and she only has to remmber 1 number.  Then she takes its inverse, and converts it from a fraction to a decimal expansion.  The tridecanacci numbers are formed by a process similar to the Fibonacci numbers.  However it starts with 11 zeros, and 2 ones, after that each new term is the sum of the previous 13 terms.

1/999,998,999,998,999,998,999,998,999,998,999,998,999, 998,999,998,999,998,999,998,999,998,999,999 =

0.
000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000000  000001  000001  000002  000004  000008  000016  000032  000064  000128  000256  000512  001024  002048  004095  008189  016376  032748  065488  130960  261888…

The first 31 terms of the tridecanacci sequence (OEIS A168084).

She really loves the number 13.

David

Happy Birthday Peggy Sue

Happy Birthday

Happy New Year

Here is your first Interesting Number for 2015!!!

2015¹³⁷ = 

484,933,196,777,114,074,143,958,601,296,047,191,303,238,888,
328,493,788,893,417,124,636,461,282,535,535,197,030,813,992,
895,783,308,595,683,263,188,351,090,196,322,513,839,445,959,
271,157,649,518,041,540,183,146,596,171,102,022,830,089,650,
292,177,587,797,290,188,691,282,775,436,095,410,100,384,042,
181,289,460,837,638,885,592,477,530,746,168,643,702,581,379,
873,363,475,885,265,666,608,606,690,825,611,326,960,945,242,
512,576,880,699,871,340,946,150,843,683,152,340,103,534,181,
032,663,014,193,776,820,682,723,644,342,223,985,362,021,659,
566,308,072,475,404,600,254,478,282,295,167,446,136,474,609,
375

2015 = 4 + 8 + 4 + 9 + 3 + 3 + 1 + 9 + 6 + 7 + 7 + 7 + 1 + 1 +
4 + 0 + 7 + 4 + 1 + 4 + 3 + 9 + 5 + 8 + 6 + 0 + 1 + 2 + 9 + 6 +
0 + 4 + 7 + 1 + 9 + 1 + 3 + 0 + 3 + 2 + 3 + 8 + 8 + 8 + 8 + 3 +
2 + 8 + 4 + 9 + 3 + 7 + 8 + 8 + 8 + 9 + 3 + 4 + 1 + 7 + 1 + 2 +
4 + 6 + 3 + 6 + 4 + 6 + 1 + 2 + 8 + 2 + 5 + 3 + 5 + 5 + 3 + 5 +
1 + 9 + 7 + 0 + 3 + 0 + 8 + 1 + 3 + 9 + 9 + 2 + 8 + 9 + 5 + 7 +
8 + 3 + 3 + 0 + 8 + 5 + 9 + 5 + 6 + 8 + 3 + 2 + 6 + 3 + 1 + 8 +
8 + 3 + 5 + 1 + 0 + 9 + 0 + 1 + 9 + 6 + 3 + 2 + 2 + 5 + 1 + 3 +
8 + 3 + 9 + 4 + 4 + 5 + 9 + 5 + 9 + 2 + 7 + 1 + 1 + 5 + 7 + 6 +
4 + 9 + 5 + 1 + 8 + 0 + 4 + 1 + 5 + 4 + 0 + 1 + 8 + 3 + 1 + 4 +
6 + 5 + 9 + 6 + 1 + 7 + 1 + 1 + 0 + 2 + 0 + 2 + 2 + 8 + 3 + 0 +
0 + 8 + 9 + 6 + 5 + 0 + 2 + 9 + 2 + 1 + 7 + 7 + 5 + 8 + 7 + 7 +
9 + 7 + 2 + 9 + 0 + 1 + 8 + 8 + 6 + 9 + 1 + 2 + 8 + 2 + 7 + 7 +
5 + 4 + 3 + 6 + 0 + 9 + 5 + 4 + 1 + 0 + 1 + 0 + 0 + 3 + 8 + 4 +
0 + 4 + 2 + 1 + 8 + 1 + 2 + 8 + 9 + 4 + 6 + 0 + 8 + 3 + 7 + 6 +
3 + 8 + 8 + 8 + 5 + 5 + 9 + 2 + 4 + 7 + 7 + 5 + 3 + 0 + 7 + 4 +
6 + 1 + 6 + 8 + 6 + 4 + 3 + 7 + 0 + 2 + 5 + 8 + 1 + 3 + 7 + 9 +
8 + 7 + 3 + 3 + 6 + 3 + 4 + 7 + 5 + 8 + 8 + 5 + 2 + 6 + 5 + 6 +
6 + 6 + 6 + 0 + 8 + 6 + 0 + 6 + 6 + 9 + 0 + 8 + 2 + 5 + 6 + 1 +
1 + 3 + 2 + 6 + 9 + 6 + 0 + 9 + 4 + 5 + 2 + 4 + 2 + 5 + 1 + 2 +
5 + 7 + 6 + 8 + 8 + 0 + 6 + 9 + 9 + 8 + 7 + 1 + 3 + 4 + 0 + 9 +
4 + 6 + 1 + 5 + 0 + 8 + 4 + 3 + 6 + 8 + 3 + 1 + 5 + 2 + 3 + 4 +
0 + 1 + 0 + 3 + 5 + 3 + 4 + 1 + 8 + 1 + 0 + 3 + 2 + 6 + 6 + 3 +
0 + 1 + 4 + 1 + 9 + 3 + 7 + 7 + 6 + 8 + 2 + 0 + 6 + 8 + 2 + 7 +
2 + 3 + 6 + 4 + 4 + 3 + 4 + 2 + 2 + 2 + 3 + 9 + 8 + 5 + 3 + 6 +
2 + 0 + 2 + 1 + 6 + 5 + 9 + 5 + 6 + 6 + 3 + 0 + 8 + 0 + 7 + 2 +
4 + 7 + 5 + 4 + 0 + 4 + 6 + 0 + 0 + 2 + 5 + 4 + 4 + 7 + 8 + 2 +
8 + 2 + 2 + 9 + 5 + 1 + 6 + 7 + 4 + 4 + 6 + 1 + 3 + 6 + 4 + 7 +
4 + 6 + 0 + 9 + 3 + 7 + 5

2015 equals the sum of the digits of its 137^th power.

REFERENCES:

http://www.futilitycloset.com/2012/03/16/math-notes-101/

Happy New Year!!!

David