Google recently added a cool calulator

feature.

Simply enter a math formula like “5 *

5” into Google and it will return a results page with the answer.

Asking Google: “The

answer to life, the universe and everything” returns the calculator and the answer 42,

based on the calculation by Deep Thought, the super computer in the Douglas Adam’s classic

“Life the Universe and Everything”.

Google also links to a Wikipedia

entry that explains how 6 * 9 = 42 (hint: not base 10) and how code written

in C using macros also correctly multiplies 6*9=42. I also work in building

42 which makes it that much more special ðŸ™‚

Another cool feature I discovered is that Google does factorials. Entering 4! and

you’ll see 4*3*2*1 (x * x-1) or 24. This reminded me of French mathematician

Blaise Pascal who’s Pascal triangle solves probabability questions. For example, look

at the triangle below:

1 1 1 2 1 2 1 3 1 3 3 1 4 1 4 6 4 1 5 1 5 10 10 5 1 6 1 6 15 20 15 6 1

Both parents sum to be the total of each child:

1 2 3

and

4 6 10

The numbers horizontally represents the possibilities of elements being picked.

Let’s use the 4th row and letters A, B, C, D as examples. The fourth row represents

the numbers 1, 4, 6, 4, 1 which represent the probability of choosing 0, 1, 2, 3,

and 4 of the letters. Let’s look at each of these:

0 – There is only one option for picking none of the letters.

1 – Since there are four unique letters, there are four unique possibilities.

2 – There are six ways of picking exactly two letters: AB, AC, AD, BC, BD, CD.

3 – There are four ways of picking three out of the four elements, simply choose which

letter you are not going to pick.

4 – There is only one way to select all of the letters.

Whew, with that explained, we can look at the mathematical formula for this:

N!/(R!(N!-R!)) where N represents the number of elements and R represents the number

of matches.

Using our example above, where N is 4 and we’ll set 2 as the number of matches,

we get:

4!/(2!(4-2)!).

Google correctly answers this as 6, matching the value in Pascal’s triangle.

If you didn’t have Google, you can represent Pascal’s formula in C#

with the code below:

class f { //Factorial private static long fac(long x) { for(long i=x-1;i>0;i--) { x *= i; } return x; } public static long Pascal(long n, long r) { return fac(n)/(fac(r) * fac(n-r)); } }

Another interesting mathematical pattern in Pascal’s triangle is the Fibonacci sequence

on the triangle diagonals.

Fibonacci # | Diagonal #’s |

1 | 1 |

2 | 1+1 |

3 | 1+2 |

5 | 1+3+1 |

8 | 1+4+1 |

Cool stuff, now do we call Google’s calculator a web service?

Bonjour

Please direct me to a good math forum to discuss problems in statistics

thank you

Philip Shapiro