Mathematics Patch Notes

Aug 24, 2010  
(via Spiked Math)
Patch Notes 1.02a
"Mathematics will never be the same."

Introducing Probability 2.0
  • Upgraded probability to include real numbers in the range from 0 to 2.
  • Switching in the monty hall problem is now the same as not switching.
  • Due to high demand, correlation now implies causation.

Graph Theory Features

  • Fixed glitch in the petersen graph so it is no longer a counter-example.
  • Support is no longer offered for hypergraphs.
  • Added a new color to the outdated 4-color theorem. We anticipate at least 7 colors available for planar graphs by patch 1.03.

Number Systems
  • Decimal notation will be phased out next patch. This should fix the long standing bug that 1 = 0.999...
  • Due to loneliness, the set of prime numbers now includes the number 1.
  • Complex numbers have been deemed no longer complex and will now be known as "easy numbers".

Proof Changes

  • Proof by "reference to inaccessible literature" is no longer accessible.
  • A new "proof by picture" widget has been added for mac users.

Miscellaneous

  • Support has been added to allow division by 0 fixing the wormhole bug.
Click to read the comments on this entry...


Math books

Jul 19, 2010  



math-for-dummies



math-for-retarded



sweet-book

I wouldn't mind having this one.
Click to read the comments on this entry...


loop.jpg

(via Reddit)

This was posted by ooglag on Reddit who says it's from John Zelle's Python Programming, although it's pretty common in other text books as well. It also reminds me of google:
http://www.google.ca/search?q=recursion
Click to read the comments on this entry...


Caution!

Apr 3, 2010  
This is in a textbook:

calculus caution

CAUTION!
The area of a washer is pi*R^2-pi*r^2, which you can simplify to pi*(R^2-r^2), but not to pi*(R-r)^2. No matter how tempting it is to make the latter simplification, it's wrong. Don't do it.

Click to read the comments on this entry...


How many digits of pi do you have memorized?



But seriously... is it 3? 5? 10? more than 30? If it's more than 30 pat yourself on the back because that's a great accomplishment! If it's only a few, then no worries. Below we will teach you some techniques that can be used to conquer the digits of pi.

Computations of Pi

Some basic information and a brief time line on computations of the digits of pi:

  • 1540 - 1610: 35 digits determined
    • done by German mathematician Ludolph van Ceulen
    • used a geometric method (just like Archimedes did)
    • proud of his calculation that took a great part of his life
    • he had the digits engraved on his tombstone
  • 1949: 2, 037 digits computed (John von Neumann et al.)
  • 1973: Over one million digits computed
  • 1989: One billion digits computed (Chudnovsky brothers)
  • 2010: 2.7 trillion digits computed (F. Bellard)
  • In the near future: Almost all of them computed?

Who memorizes pi?


This is just a joke. It does bear a tiny bit of truth but the two sets of people aren't mutually exclusive. I am both a scientist and a science fan!

Digits Memorized vs. Year (Graph)

500px-PiDigits.svg.png
Record Holders*: David Fiore
April 1st, 1979:
  • David Fiore wrote down 10,625 decimal places of pi
  • He was 18 years old at the time
  • He is known as the first person to ever break 10,000 decimal places
  • It took him three hours and five minutes

Record Holders*: Creighton Carvello (1944-2008)
June 27th, 1980:
  • Creighton Carvello recited 20,013 decimal places of pi
  • 2003: he recalled 3,500 facts about every FA Cup Final since 1872 (names of referees, goal scorers, teams, crowd attendances, scores, venues...)
  • Memorized the exact sequence of 10,000 words from Ernest Hemingway's The Old Man and the Sea
  • Recited 17 random digits after seeing them for 2 seconds

Record Holders*: Rajan Mahadevan
July 5, 1981:
  • Rajan Mahadevan recited 31,811 digits of pi
  • He discovered his exceptional ability to memorize numbers at the age of 4 during a party hosted by his family
  • During the party, Rajan wandered to a parking lot and committed the license plate numbers of every guest's car for recitation later
  • A quote: "I am not good at remembering words - words confuse my system of memorizing. Numbers, I have no problems at all. I put away huge numbers in something similar to a computer file and I can recall them even after decades."

Record Holders*: Hideaki Tomoyori
March 10th, 1987:
  • Hideaki Tomoyori recited 40,000 decimal places of pi
  • Took him 17 hours 21 minutes (including breaks totaling 4 hours 15 minutes) to recite
  • Took him 10 years to memorize 40,000 decimal places

Record Holders*: Chao Lu
November 20th, 2005:
  • Chao Lu recited 67,890 decimal places of pi
  • Took him 24 hours 4 minutes to recite (with no breaks)
  • Took him 1 year to memorize 100,000 digits (he made a mistake at the 67,891th digit when going for the record)
  • He is the current (official) record holder
  • In 2006, Akira Haraguchi, a retired Japanese engineer, claimed to have recited 100,000 decimal places. This, however, has yet to be verified by Guinness World Records.

Unofficial: Andriy Slyusarchuk
June 17th, 2009:
  • A. Slyusarchuk claims to have 30 million digits memorized
  • The digits are printed in 20 volumes of text
  • He is a neurosurgeon, medical doctor and professor
  • He was able to recite randomly selected sequences from within the first 30 million places of pi
  • Reciting 30 million digits of pi at one digit a second would take 347 days (nonstop)
  • No officially documented attempt to debunk his claims has been successful as of yet

Why memorize pi? To beat Grace!
May 12th, 2008:
  • Grace Hare recited 31 digits of pi
  • It took her 18 seconds
  • She is 3 years old and the youngest record holder

How to memorize pi? Piems!
A piem is a (pi) poem where the length of each word represents a digit of pi
For example, the following piem encodes the string: 3. 141592 65358 9793 23846

Pie
I wish I could determine pi
Eureka! cried the great inventor.
Christmas pudding, Christmas pie
Is the problem's very center.

Notice that:
Pie = 3;
I = 1; wish = 4; I = 1; could = 5; determine = 9; pi = 2;
Eureka=6; cried=5; the=3; great=5; inventor=8;
and so on. Thus, each word represents a digit of pi.

My favourite piems!
There's over a bazillion piems and variations (lots and lots). The best ones are:

May I have a large container of coffee right now?
3.141592653

Hey, I need a large motorboat to rescue women and girls.
3.1415926535

God! I need a drink,
Alcoholic of course,
After all those lectures
Involving radical equations.

3.1415 926 5358 979

Long Piems
  • The short story Cadaeic Cadenza encodes 3835 digits
  • It was written in 1996 by Mike Keith
  • Words of length 10 encode the digit 0
  • Words of length 11 (or 12) encode the two consecutive digits 1,1 (or 1,2)
  • 2010: In his book Not A Wake, Keith extends to 10,000 digits of pi

Technique: Grouping Digits
  • Split pi into small groups of digits (like 4 digits or 5, 6, 7, whatever you are comfortable with)
  • Focus on memorizing the first small group
  • Some people find singing it helps
  • When comfortable with the first group, move on to the next
  • Cons: If you lose your spot, you may have to start over.
Grouping Example: (3.14159) (26535) (8979323) (84626) (4338327) (95028) (8419716) (93993) (7510582) (09749) (4459230)

Start by memorizing (3.14159) for a minute... then add the next group (26535) and practice for two minutes. Then add the third group and practice until you are comfortable (REPEAT!!)

Classic Memory Techniques - The Major System
  • Major System: Convert numbers into sounds.
  • Sounds without numbers are used as 'fillers'
  • Form words from the sounds
  • In practice, use 100 'peg words': rat is 41; bar is 94

Classic Memory Techniques - Link System
  1. Start by converting each digit of pi to its corresponding phonetic sound
  2. Group sounds together to create a list of words
  3. Words created should be actions or objects
  4. Alternatively, use your 'fixed' peg words for the number
  5. Use the Link System: Link words together into a long chain by using a sequence of events, a story, or a journey. The CRAZIER the story the BETTER!!
Example: 3.14 15 92 ---> 14 = door; 15 = doll; 92 = pan;

You are standing at the biggest door you have every seen.
You knock at the door and this Raggedy Ann doll answers.
Out of nowhere, she smacks you with a pan she is holding!

Coordinate Method
  • Pros: Can recite starting at any decimal spot (if you lose your spot, you don't have to start over)
  • First 10 decimal places (1415926535) associated with 0
  • Use the Major System to encode as: turtle-pinochle-mall and link it to 0 (saw)
  • Example: Picture yourself using a saw to cut open a turtle who is playing pinochle at the mall
  • Next 10 digits (8979323846) would be linked to 1 in the same manner
  • Next 10 digits linked to 2
  • Repeat.

* Reference for World Record Holders: Pi World Ranking List and Wikipedia
Click to read the comments on this entry...


Poor math book :-(

Feb 13, 2010  
Awwwww



Click to read the comments on this entry...


Need help writing a proof? Need to give your 'kids' some guidelines? Then check out:


Written by Eugenia Cheng, who is at the University of Chicago.

In it you will find:
1 What does a proof look like?
2 Why is writing a proof hard?
3 What sort of things do we try and prove?
4 The general shape of a proof
5 What doesn't a proof look like?
6 Practicalities: how to think up a proof
7 Some more specific shapes of proofs
8 Proof by contradiction
9 Exercises: What is wrong with the following proofs"?

This is a very helpful resource and available freely on Eugenia's website (at least for now...)
Click to read the comments on this entry...


XKCD book is out

Sep 17, 2009  
xkcd_book.png
That's right folks, the first ever XKCD book is now officially out and available. It's available in the xkcd store for a price of $18.
The author, Randall Munroe, says...
"It's been fun putting it all together. It was neat to go back through various huge stacks of old drawings, some on the back of school assignments, and scan them at print resolution. I also had fun with the marginal notes. I'm really excited to finally have it in print, and I'm looking forward to seeing people and signing copies at the release events this weekend. I'm also excited about getting back to work on some other projects which have been on hold for a bit, at least one of which will involve lakes and a recently-acquired Arduino."
Apparently, the book is being published by BreadPig, a company founded by Randall's friend, and their portion of the profits will go to build a school in Laos.
Click to read the comments on this entry...


Written by Clifford Pickover, The Math Book, covers 250 milestones in mathematics. It has information about the Fibonacci series, the Goldbach Conjecture, Benford's Law, the Prisoner's Dilemma, Newcomb's Paradox, Tokarsky's Unilluminable Room, discovery of pi, etc.

the-math-book.jpg

Each two-page spread has an excellent story about a mathematical principle, discovery, puzzle, or person. You can find more information about the book at amazon.com.

Click to read the comments on this entry...


Math Sex Math

Aug 24, 2009  
Mathematics and Sex

These two words seem like they don't go together, but in the book below they certainly do. Dr Clio Cresswell reveals how mathematics can unlock the secrets of love and sex, dating and mating. It's time to shatter the stereotypes in sexual mathematics!

See the description on amazon:

Cover of math sex book


It might be an interesting read, but it seems to be written for a non-mathematician, so mathies beware. But if you're just looking for a book about math sex then this is certainly the book to read.
Click to read the comments on this entry...