# A Microblog by Gaurav Tiwari

Thoughts, discoveries and administrative updates from Gaurav Tiwari. All opinions are personal and are not endorsed by any brand or person.

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# Symbian Theme Review: Elegance by Blade

There are thousands of themes on Nokia Store, price ranging from zero to tens of dollars. But there are only a few themes those can make your phone layout stand out of the crowd. Some are free and many are premium. In this very first review at My Symbian blog, I would like to write a personal review of theme which makes me smile when I use that. The review of a Symbian theme which is purely geometrical. The review of a theme which is elegant! And, may be that is why the name of this theme is… Elegance!

Elegance is a theme by Inder Deep a.k.a. Silver Blade (or, simply Blade). Elegance is an abstract natured theme, mainly focusing on custom icons. Compatible to Belle and Belle Feature Pack 1 devices, this theme gives a mid dark look to your phone. All elements are 2.5th dimensional (neither purely 2D nor purely 3D) and the icons are mathematically balanced with a rhombus design. The navigation bar is striped and opaque. The color is however rusty but very smooth and elegant (let me say it again). Theme is very fast on my belle fp1 device and never lets my phone slow. Elegance is packed with more than 700 customized icons and developer told me that he will be adding more icons in future updates.

## Homescreen and Icons

The default wallpaper is blurred and less shiny. Never hurts your eyes, however the design could be improved. Additional wallpaper pack, provided by the developer is beautiful and suits the design of Elegance. I would suggest one to prefer the additional wallpaper pack to default one.

Icons of Elegance are the best ever I have seen. Purely unique and neverseen design lets you feel different. Many colors are used n the icon-pack developing a multi-colored feel. Icons are like quadrilateral buttons giving you feel of pressing thumbs on pillows, 🙂 .

## Topbar Elements

Almost all toggles in the topbar are implemented very cutely. The above image shows all elements open and closed respectively.

## Keyboard

The next best thing of the theme is the keyboard. Shaded black keyboard is nice to both your eyes and ease of writing. Feels very convenient while using and as speedy as default keyboard. BTW, more elegant-ness and smoothness were required.

Calendar and Calling
Dialer however not the perfect but its transparent nature suits the design. Actually, I loved the dialer only due to the transparentness… otherwise nothing new.

The calendar look is quite nice too.

## Web Browsing

The navigation bar of Nokia Browser as well as other tabs are elegantly customized. Feels good when using the buggy Nokia Browser. The theme is very light and never slows the browser down.

## Gallery

The gallery is covered by the element of elegance at top and the strip bar at bottom. Cool looking!

## Music Player

Almost all elements of music player has been changed with this theme.

Easy and smooth scrolling as always.

Over all Elegance is one of the best themes ever made for Symbian and is a must have for your Symbian^3 and Symbian^4 device. You can buy this theme from Nokia Store at a decent price of 1.99 United States Dollars or 35 Indian National Rupees. Price varies in different countries.

# My Five Favs in Math Webcomics

Cartoons and Comics are very useful in the process of explaining complicated topics, in a very light and humorous way. Like:

Source of These Cartoons
Here my five most favorite math-webcomics sites. (Click on images to visit them.)

1. Spiked Math

2. xkcd

3. SMBC COMICS

4. Oh! You math!

5. Abstruse Goose

# The Cattle Problem

This is a famous problem of intermediate analysis, also known as ‘Archimedes’ Cattle Problem Puzzle’, sent by Archimedes to Eratosthenes as a challenge to Alexandrian scholars. In it one is required to find the number of bulls and cows of each of four colors, the eight unknown quantities being connected by nine conditions. These conditions ultimately form a Pell equation which solution is necessary in case of finding the answer of the puzzle. The Greek puzzle is stated below with a little deviation. I have just tried to make the language simpler than the original, hope you’ll be able to grasp the puzzle easily.

O Stranger! If you are intelligent and wise, find the number of cattle of the Sun, who once upon a time grazed on the fields of an Island, divided into four groups (herds) of different colors, one white, another a black, a third yellow and the last dappled color.In each herd were bulls, mighty in number according to these proportions:

• White bulls were equal to a half and a third of the black together with the whole of the yellow.
• The black bulls were equal to the fourth part of the dappled and a fifth, together with, once more, the whole of the yellow.
• The dappled bulls, were equal to a sixth part of the white and a seventh, together with all of the yellow.

So, these were the proportions of bulls, now the proportions of the cows were as following:

• White cows were equal to the third part and a fourth of the whole herd of the black.
• Black cows were equal to the fourth part once more of the dappled and with it a fifth part, when all cattle, including the bulls, went to pasture together. Now the dappled in four parts were equal in number to a fifth part and a sixth of the yellow herd.
• Yellow cows were in number equal to a sixth part and a seventh of the white herd.

Keeping above conditions in focus, find the number of cattle of the Sun, giving separately the number of well-fed bulls and again the number of females according to each color. But come, this solution is not complete unless you understand  all these conditions regarding the cattle of the Sun:

• When the white bulls mingled their number with the black, they stood firm, equal in depth and breadth. Number of bulls in a row were equal to the number of columns.
• When the yellow and the dappled bulls were gathered into one herd they stood in such a manner that their number, beginning from one, grew slowly greater till it completed a triangular figure, there being no bulls of other colors in their midst nor none of them lacking.

Find the number of cows and bulls of each color separately.

Solution:

#### $W$

= number of white bulls
$B$ = number of black bulls
$Y$ = number of yellow bulls
$D$ = number of dappled bulls
$w$ = number of white cows
$b$ = number of black cows
$y$ = number of yellow cows
$d$ = number of dappled cows

The relations come as:

•   $W = (\frac{1}{2} + \frac{1}{3})B + Y$ The white bulls were equal to a half and a third of the black bulls together with the whole of the yellow bulls.
• $B = (\frac{1}{4} + \frac{1}{5})D + Y$ The black [bulls] were equal to the fourth part of the dappled bulls and a fifth, together with, once more, the whole of the yellow bulls
•   $D = (\frac{1}{6} + \frac{1}{7})W + Y$ The remaining bulls, the dappled, were equal to a sixth part of the white bulls and a seventh, together with all of the yellow bulls
•   $w = (\frac{1}{3} + \frac{1}{4})(B + b)$ The white cows were equal to the third part and a fourth of the whole herd of the black.
•   $b = (\frac{1}{4} + \frac{1}{5})(D + d)$ The black cows were equal to the fourth part once more of the dappled and with it a fifth part, when all, including the bulls, went to pasture together.
•   $d = (\frac{1}{5} + \frac{1}{6})(Y + y)$ the dappled cows in four parts [in totality] were equal in number to a fifth part and a sixth of the yellow herd.
•  $y = (\frac{1}{6} + \frac{1}{7})(W + w)$ the yellow cows were in number equal to a sixth part and a seventh of the white herd.

The arrangement on solving gives following relations in W,B,D,Y,w,b,d and y. which is a system of seven equations with eight unknowns. It is indeterminate, and has infinitely many solutions and form the following matrix:

 6 -5 -6 0 0 0 0 0 0 20 -20 -9 0 0 0 0 -13 0 -42 42 0 0 0 0 0 -7 0 0 12 -7 0 0 0 0 0 -9 0 20 0 -9 0 0 -11 0 0 0 -11 30 -13 0 0 0 -13 0 42 0

Which yields the following solutions

 W = 10,366,482k B = 7,460,514k Y = 4,149,387k D = 7,358,060k w = 7,206,360k b = 4,893,246k y = 5,439,213k d = 3,515,820k

where $k$ is an arbitrary constant, which can be equal to either 1 or 2 or 3 … etc. Again, from the second part of the problem:

White bulls + black bulls = a square number, $W+B=10366482k +7460514k$= a square number. or $W+B=17,826,996k$ =a square number$2 \cdot 2\cdot 3 \cdot 11 \cdot 29 \cdot 4657 k = \textrm{a square number}$ . Thus $k$ atleast be $3 \cdot 11 \cdot 29 \cdot 4657$ or in general be $3\cdot 11\cdot 29 \cdot 4657 \cdot r^2=4456749r^2$ where $r$ is any integer. Again, Dappled bulls + yellow bulls = a triangular number.or, $Y + D = \textrm{a triangular number}$ where triangular numbers are numbers of the form $1 + 2 + 3 + 4 + 5 + \ldots + m =\frac{m(m+1)}{2}$ . where $m$ is some positive integer. Thus $4,149,387k + 7,358,060k =\frac{m(m+1)}{2}$ or $11,507,447k =\frac{m(m+1)}{2}$ . Putting $k=4456749 r^2$ we have $11,507,447 \times 4,456,749 r^2 = \frac{m(m+1)}{2}$ or $102,571,605,819,606 r^2 = m(m + 1)$ . The problem is now to find the values of $r$ and $m$ that we can find the value of $k$ and thus the solution of the problem.
The computer generated answers for smallest solutions are  at my Pastebin Account.
Recently, Ilan Vardi of Occidental College (Los Angeles, California, USA) developed simple explicit formulas to generate solutions to the cattle problem.Click here to read his paper on the cattle problem.

References and Further Readings: Weisstein, Eric W. “Archimedes’ Cattle Problem.”  From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/ArchimedesCattleProblem.html Archimedes’s Cattle Problem http://en.wikipedia.org/wiki/Archimedes%27_cattle_problem Archemedes’s Cattle Problem http://math.nyu.edu/~crorres/Archimedes/Cattle/Statement.html The Archemedes’s Cattle Problem http://www.maa.org/devlin/devlin_02_04.html

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