Saturday, November 12, 2011

A Function and its Inverse (Office Supply Edition)

A visual representation for the notation of a function and its inverse.

Doesn't work as well if you have the stapler on the outside and the staple remover on the inside. Would've been more useful if instead of x, there were a stack of papers. Maybe if I can find some time or if someone has the time...

(via MathFail)

PS: If you like this, also check out f(a bag of skittles) over at Sweeney Math.
PPS: Quick google search yields this thread over at reddit. Following comment is by trebor89.
The function f(y) = (staple remover (stapler (y)) is NOT the inverse; it's actually the function commonly known as Gödel's Umlautifier. Simply try it on some trivial input: f(a) = ä.

Kaprekar's Constant (6174) in GeoGebra

While doing a little browsing, I came across Kaprekar's Constant. I remember reading about it a few years ago but I never did anything with it. I finally decided to play with it a little using GeoGebra. Here's a description from Wikipedia:
6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:
  1. Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)
  2. Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
  3. Subtract the smaller number from the bigger number.
  4. Go back to step 2.
The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524:
  1. 5432 – 2345 = 3087
  2. 8730 – 0378 = 8352
  3. 8532 – 2358 = 6174
The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4:
Here's a screenshot of the GeoGebra applet:
If you'd like a copy just click on "File" then "Save As" and save a copy on your computer. Click on the "Play" button on the bottom left of the applet to begin the animation.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Friday, November 11, 2011

11/11/11 Creative Day

If the number zero were 陰 (yin) and the number one were 陽 (yang), today (11/11/11) would make up the first hexagram of the 易經 (I-Ching/Yì Jīng) or the Book of Changes. The first of 64 hexagrams, 乾 (ch'ien/qián) is the only hexagram that matches our date with 6 yangs. It is sometimes translated as "the creative," "heaven," or "force."

The hexagram is depicted below on the left. In the middle is the Chinese character for ch'ien/qián in ancient script font and on the right is the same character is a modern script.

Drumroll...

I hereby proclaim 11:11:11 AM of 11/11/11 to be the Creative Moment of Creative Day... to be repeated every 100 years if we ignore the first two digits of the four-digit year. We sort of missed the first and only real 11/11/11.

Go forth and create something on this Creative Day! It's as good a reason as any.

PS: 3000-4000 years ago, I'm sure the authors of I-Ching had in mind this date and moment based on a calendar and time system not yet invented or adopted.

PPS: Somehow, the 40,271th cycle of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom on 315th rotation of the 2011th revolution of the 3rd wandering star big enough to be rounded by its own gravity around an yellow dwarf calculated using a system agreed upon on the 55th rotation of the 1582th revolution since some arbitrary time around a ball of fusing atoms is special.