My Math Clock

Absolutely arbit post ….. I am doing an intern in Zeus Numerix in Pune again this summer and am working on some really interesting stuff . All throughout the day I am generally in front of the PC studying ebooks and writing in C/C++. A change would have been kinda nice …  I decided to make a clock except that all the numbers would be represented by their mathematical significance …..(Just to get some experience on woodwork ,etc. ….. 😛 ) I got the mechanism for the clock from a local watch maker . For the base I decided to use  wood from an old unwanted cupboard . A hacksaw , hammer were good enough to cut a piece approximately 18cm x 14cm x 1cm . To drill a hole so that the mechanism could be put in place I visited our electrician . To smoothen the surfaces I used a sand paper lying around my house .For the layout of the clock i.e. the numbers etc. I used Scribus along with $\LaTeX$ .

Finally the layout or background looked like this ….. I did also add a $t$ denoting for the time variable …. 😉

I referred to Wikipedia for the significance of the numbers …..

$\sqrt[3]{1728} = 12$ —- I choose 1728 coz its 1 less than 1729 . The smallest number to represented as a sum of 2 cubes .

$0! = 1$ —- Coz 0! = 1 ….

$\left ( 0010\right )_{10}$ —- 0010 in base 10 is 2 .

$FermatPrime\left[ 0\right ] = 3$ —- 3 is the first Fermat Prime . All numbers satisfying $F_{n} = 2^{2^{ \overset{n} {}}} + 1$

$2 \uparrow\uparrow\uparrow 2 = 4$ —- thats the way 4 represented in Knuth’s Up Arrow Notation .

$\left ( 2\varphi - 1 \right )^2 = 5$ —- where $\varphi$ is the golden ratio $\varphi = \frac{1+\sqrt{5}}{2}$

$\mid S_{3} \mid = 6$ —- 6 is the cardinality of the smallest non-abelian group .

$M_{3} = 7$  —- 7 is the 3 Mersenne Prime .

$F_{6} = 8$ —- 8 is the 6th Fibonacci Number .

$3^{2^{1}} = 9$ —- 9 is an exponential factorial .

$\left ( 1010\right )_2 = 10$ —- 1010 in binary is 10 in decimal (base 10)

$\frac{\Phi_2(10)}{\gcd(\Phi_2(10),2)} = 11^{c} , {c} \in \mathbb{N}$ —- 11 is the second unique prime….

Finally, after the assembly it looked like this ……

a better pic sometime sooner …..

Sage – Open Source Mathematics Software

Sage - Open Source Mathematics Software

Sage is an open source mathematics software with a mission of creating an alternative to softwares like Mathematica,Maple,MATLAB,etc.

Sage can be used to study general and advanced, pure and applied mathematics. This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra and much more.

Will try it out and post on it later. The software along with the reviews look good for loads of my work .

My Intern

Today was  the last day of my intern.Its been a wonderful learning experience at Zeus Numerix.I thank my mentor Sudhir M. and the HR at ZN for giving me the opportunity to work at ZN for the past two months.I have some fond memories and also great new friends :Chaitanya and Nek . It was a nice time with Sriram(yup he came all the way to Pune to work here…. 🙂 )and enjoyed going around for movies with you guys (Irrespective of the movies ).All the best to all you guys in your future endeavours…..

The intern clearly highlighted the key difference in studying theory and making industry class products – these are  the most precious points i have taken from this intern.Its all about applying the most basic points in theory which seem so very trivial and looking at a problem till u find a perspective of solving it elegantly  rather than simply brute forcing ur way through it.Its hard to do so and took me most of the time of the intern in learning and internalising it.Hopefully, when i face such tasks in future i would probably be better at handling them.

Thank You guys once again.

Bye , cya next post will be just before leaving for NITT.cant wait for meeting evry1 out there……

Jai Gurudev!!!

Some cute hacks in Linux.

Adding aliases permanently:open the .bashrc file in ur favorite editor and add the aliases there have them permanently.

man pages formatted as text :

Take for example : man apropos . It looks great on console but sucks when u list it out to a text file.Try this out:

man apropos | col -bx > myfile.txt

The preceding command writes the man page to myfile.txt, without backspaces (the -b) and with spaces substituted for tabs (-x).

This one is from Mihai Patrascu’s site: http://web.mit.edu/~mip/www/probs.html.

Compressing a file system

Suppose you want to back up a partition of your hard drive, and you want to compress it to save space. So, you take your favorite compression utiliy, and have it compress /dev/hd??. But the compressed file turns out to be much larger than the amount of data on that partition. Why, and how do you fix it?

This is because the compressor doesn’t know that the free blocks on disk are actually free. These blocks typically contain junk left over from deleted files, and the compressor treats them as data. An easy and cute fix is: mount /dev/hd?? /mnt ; cat /dev/zero > /mnt/fill ; rm /mnt/fill ; umount /mnt. This will zero out all free blocks, and the compressor will only work hard to compress the actual data.