Trachtenberg Speed System

The Trachtenberg Speed System

Who was Trachtenberg?

  • Professor Jakow Trachtenberg was the founder of the Mathematical Institute in Zurich, Switzerland.
  • He was a Russian, born June 17th, 1888, and studied engineering.
  • While still in his early twenties, he became Chief Engineer with 11,000 men under his supervision.
  • After the Czar of Russia was overthrown, he escaped to Germany where he became very critical of Hitler. He was later imprisoned.
  • Most fellow prisoners around him gave up hope and died even before being sent to their death. He realized that if he wanted to stay alive, he had to occupy his mind with something else rather than focus on the hopeless conditions surrounding them. He set his mind on developing methods to perform speed mathematics.
  • With the help of his wife, he escaped from prison and fled to Switzerland.
  • There, he taught his speed math system to young children. It was very successful.

Trachtenberg developed a set of rules (algorithms) to multiply long numbers by numbers from 0 to 12. These rules allow one to dispense with memorizing multiplication tables if that is desired.
Even better, it gives a way to help memorize them, by allowing one to
work out the answer by rule if one cannot remember it by rote. We
perform each rule starting at the far right. The `number’ is the digit
of the multiplicand just above the place that we are currently
computing. The `neighbor’ is the digit immediately to the right of the
`number’. When there is no neighbor, we assume it is zero. We also
write a zero in front of the multiplicand.

Note that the following rules only use the operations of addition, subtraction, doubling, and `halving’.

rules.jpg

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Download the file trach.pdf for some examples. Also see the book: Trachtenberg, Jakow (1960). The Trachtenberg Speed System of Basic Mathematics. Doubleday and Company, Inc.

Memorizing Pi – World Records and Techniques

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