## Touch Pilot S01E01 (Fox)

I was initially surprised that Kiefer Sutherland was back on network television, but I have always like 24 so I was actually looking forward to the series on Fox. This series was written and created by Tim Kring, who’s known for Heroes. The series uses some of the techniques from that series, so if you’ve watched Heroes, you’ll feel a familiar when watching this. This series is about a dad struggling with his autistic son, who can see strange patterns in numbers. Everything ends up connected, and Martin Bohm soon discovers this.

While I wanted to like the series, I have to say that I was disappointed, mainly because of the  mathematical elements in the series, which are rudimentary to say the least. It’s definitely not a show aimed at anyone familiar with numbers, patterns, and sequences. That being said, the pilot was watched by over 12 million people and the series was picked up for a full season, so maybe it will improve. I’ll give it a shot to see where it goes, but I wasn’t that impressed.

## Irrational Numbers Clock is Perfectly Rational (If You’re a Mathematician)

The Irrational Numbers Clock is slightly more complicated that the Unit Circle Radian Wall Clock. Also, the fact that it looks like a blackboard has a certain scholarly appeal. While I am a mathematician, anyone with high-school math should be able to read this clock. That’s not because they’ll know what all these irrational numbers are, it’s just that all you just need to do is look at the position of the hands to figure out the time.

## Sieve Of Eratosthene

I saw this today while I was taking Wikipedia Offline thanks to Google Gears and I liked it.

In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. It is the predecessor to the modern Sieve of Atkin, which is faster but more complex. It was created by Eratosthenes, an ancient Greek mathematician. Wheel factorization is often applied on the list of integers to be checked for primality, before the Sieve of Eratosthenes is used, to increase the speed.

A prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. An infinitude of prime numbers exists, as demonstrated by Euclid in about 300 BC. The first thirty prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113

## Rational Numbers

In mathematics, a rational number is a number which can be expressed as a ratio of two integers. Non-integer rational numbers (commonly called fractions) are usually written as the vulgar fraction a / b, where b is not zero. a is called the numerator, and b the denominator.

Each rational number can be written in infinitely many forms, such as 3 / 6 = 2 / 4 = 1 / 2, but it is said to be in simplest form when a and b have no common divisors except 1 (i.e., they are coprime). Every non-zero rational number has exactly one simplest form of this type with a positive denominator. A fraction in this simplest form is said to be an irreducible fraction, or a fraction in reduced form.

The decimal expansion of a rational number is eventually periodic (in the case of a finite expansion the zeroes which implicitly follow it form the periodic part). The same is true for any other integral base above one, and is also true when rational numbers are considered to be p-adic numbers rather than real numbers. Conversely, if the expansion of a number for one base is periodic, it is periodic for all bases and the number is rational. A real number that is not a rational number is called an irrational number.

The set of all rational numbers, which constitutes a field, is denoted $\mathbb{Q}$. Using the set-builder notation, $\mathbb{Q}$ is defined as

$\mathbb{Q} = \left\{\frac{m}{n} : m \in \mathbb{Z}, n \in \mathbb{Z}, n \ne 0 \right\},$

where $\mathbb{Z}$ denotes the set of integers.

## Irrational Numbers

In mathematics, an irrational number is any real number that is not a rational number — that is, it is a number which cannot be expressed as a fraction m/n, where m and n are integers, with n non-zero. Informally, this means numbers that cannot be represented as simple fractions. It can be deduced that they also cannot be represented as terminating or repeating decimals, but the idea is more profound than that. While it may seem strange at first hearing, almost all real numbers are irrational, in a sense which is defined more precisely below. Perhaps[1][2] the most well known irrational numbers are π and $\scriptstyle\sqrt{2}$.

$\Bbb{R}$ \ $\mathbb{Q}$ denotes the irrational numbers.

Having read the above recap on rational and irrational numbers, try answering the following multiple choice question which I had in a test today:

Which of the following is the first false statement?

(a) Between two different rational numbers, we can always find another rational number.
(b) Between two different rational numbers, we can always find an irrational number.
(c) Between two different irrational numbers, we can always find a rational number.
(d) Between two different irrational numbers, we can always find another irrational number.
(e) 0 = 1.