# 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 …..

# Electoral Polling

Terence Tao has written about electoral polling in a very interesting article here. A non-technical gem from a genius….. 🙂

P.S.:

Try out the assembler game mentioned in the last post . Really interesting.

# Beauty of Numbers

I was stumblingupon sites when i came across something really beautiful . Maybe all of u must be aware of it anyways take a look.

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

Further….

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

Further still…..

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Finally…

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321