Trigo Song

Pretty generic one.

Eddy Current Tubes

Dropping a magnet down a copper tube to observe the effects of eddy currents.

I will Derive!

Parody of "I Will Survive"

Google Billboard

Saw this on "The World According to Google", a documentary on CNA last night.

This a billboard that was put up by google for the purpose of job application. Find the answer, key in that website and you will end up at their job application site.

e is the base that is first introduced to our students under natural logarithm but a common misconception because when we teach it with the concept of exponential, e does not derive its letter from the word exponential. e is called e because it's Euler's Number in honor of one of the greatest number theorist and possibly mathematician Leonhard Euler. Interesting too is that Euler didn't come up with logarithms but it was accredited to John Napier. Euler just worked on a mathematics problem I believed that was unsolved and found that it led to this constant e. Something along the lines of, what does 1/0! + 1/1! + 1/2! + 1/3! + 1/4! converge to as well as proving that e is an irrational number?

Btw, just in case you are still thinking, the answer is 7427466391.

Integer Sequences

Online encyclopedia of Integer Sequences

This website allows you to figure out sequences. For example, trying keying in the first few numbers of the Fibonacci Sequence. It will not only give you the rest, it tells you the name, commentaries about the sequence and the reference. Quite useful for puzzles too.

The Mathematics of Monopoly

Monopoly is an amazing game of mathematics and economics. Its the perfect introduction for Markov Chains which deals with probabilities when your future states are independant of your past states, much like the random walk problems when studying brownian motion.

Using a simulator, you can compile the probability of each space on a monopoly board and the results can be found on this website for the US version.

http://www.tkcs-collins.com/truman/monopoly/monopoly.shtml

This brute force method of estimating the probabilities is called the Monte Carlo Method which you just roll 2 dices constantly and count how many times you hit each square and just compilte the stats that way.

A faster way is to use a computer. Here is an animation for the probabilities from the 1st turn to the 40th turn.

http://www.bewersdorff-online.de/amonopoly/

Just click to start the animation and you can see the probabilities generate.

Benford's Law

Benford's Law states that if d is the first digit of a number occuring in real life, that digit should occur with probability P(d) = lg (d+1) - lg d. The space between log scales.

P(1) = lg 2 - lg 1 = 0.301
P(2) = lg 3 - lg 2 = 0.176
P(3) = lg 4 - lg 3 = 0.125
P(4) = lg 5 - lg 4 = 0.097
P(5) = lg 6 - lg 5 = 0.079
P(6) = lg 7 - lg 6 = 0.067
P(7) = lg 8 - lg 7 = 0.058
P(8) = lg 9 - lg 8 = 0.051
P(9) = lg 10 - lg 9 = 0.046

What does this imply??? If you were to compile all the numbers in your bank books and if were to take a look at the first digit, they should follow this distribution in the long run. This is a way that IRS have learnt to spot people who fudge numbers in their books. People who fake their numbers tend to distribute their numbers more "randomly" but thats not true in real life.

Its actually quite counter-intuitive as people assume that if numbers are random, they should be equally distributed. However, numbers in real life are not completely random. Numbers starting with '1' occurs more than 6 times more than '9'.