Mathematics and LEGOs: The Deeper Meaning of Combined Systems and Networks

Mathematics LEGO Power Law

You’d expect LEGO kits to be somewhat immune from mathematics, but that’s not the case, as Samuel Arbesman of Wired’s Social Dimension demonstrated most recently. However to start out with, it’s necessary to think how humans combine things together, in general.

Read more @ SciTechDaily

How Many Apps Is Too Many?

013111_rg_TooManyApps_01.jpgWith the App store and other PC outlets providing access to thousands of new programs, it begs the question: how many apps is too many? For us, it all depends on what you do with your computer and what kind of programs are necessary to optimize both your personal and professional life. Here’s our personal take on the question…

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Happy Pi Day

image via Wikipedia
image via Wikipedia

Today is Pi Day.3/14, the first three digits  of the transcendental constant pi.

Here is last year’s post on Pi Day.

π is pretty important in maths and number theory. It’s also used a lot in real life to calculate circumferences, volumes and everything related to circles, wheels and anything circular.

I’m actually more interested in the fact that it’s irrational and transcendental, meaning that there is no repetition in the digits, no period to be found, no matter how far you go and that it’s not a solution of a non-zero polynomial equation with rational coefficients. I had a poster in my room before, π @ 1 million digits. I think that I might have posted the 1 million digits in a post last year. It took up a few MBs. Be warned.

Two New Mersenne Primes Discovered

Two new Mersenne primes have been discovered. The smaller of the two was discovered on September 6th by Hans-Michael Elvenich in Langenfeld, Germany:
2^{37,156,667} - 1,

It’s an 11,185,272-digit number which is available for download here. The larger one was discovered first on August 23rd by Edson Smith, who installed the prime-checking software on computers at UCLA. At 12,978,189 digits, it is now the largest known prime:

2^{43,112,609} - 1.

The two numbers were discovered by using a distributed computing project on the Internet called Great Internet Mersenne Prime Search (GIMPS).

A Mersenne number is a positive integer that is one less than a power of two:

\displaystyle M_n=2^n-1.

Only 46 Mersenne numbers are known. Read more over at Wikipedia’s entry.

Pi at 1 Million

I’ve been meaning to do this for a while. I imagine that 1 million numbers should be easily contained in one single post.

Be warned. π at 1 million decimals in a txt file is about 1MB! Look at π.

On your home computer, you can calculate π at 128 million in about 15 minutes. π at 1 billion takes a bit more than 3 hours. That’s a lot of decimals. For now, 1 million is fine and dandy. I’m actually using the first 2000 decimals in a piece of art that I’m creating.

π at 1 million decimals.

Continue reading “Pi at 1 Million”