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# Category Archives: Fun Stuff

## Claim for a Prime Number Formula

Dr. SMRH Moosavi has claimed that he had derived a general formula for finding the $n$-th prime number. More details can be found here at PrimeNumbersFormula.com and a brief discussion here at Math.SE titled  “Formula for the nth prime number: discovered?

SOME MORE EXCERPTS ARE HERE:

General Formula

Prime Numbers Formula For $k$-th prime numberGeneral Formula

## WordPress URL Shortening: An Interesting Consequence

Long post and page URLs can be annoying. There are times when you may want to edit WordPress slugs for long titled posts or pages, so you can share a shorter link with friends. Here’s an example: http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/ (one of the most popular posts from my blog). Would you like to write these (about) hundred characters? Or would you like to use WP.ME link shortener, which for this post was http://wp.me/p14tlY-hv ? Well, second idea sounds better than first one. But you’ll never get the same satisfaction from it because blog URL http://wpgaurav.wordpress.com is not visible, and also looks odd when typed in address bar. What then? This post is on some choices you might want to try. But before we go, let me explain what slug is?
A slug is a few words that describe a post or a page. Slugs are usually an URL friendly version of the post title (which has been automatically generated by WordPress), but a slug can be anything you like. Slugs are meant to be used with permalinks as they help describe what the content at the URL is. The post slug is the part of the URL after the date in a post’s URL. When the default post slug is created, all letters will be converted to lowercase, spaces will be exchanged with dashes, and any special characters will be removed. You can modify the post slug by clicking the Edit button next to it in visual editor. When you’re finished editing, click Save and then Update Post/Page. »via WordPress Codex

# How to shorten a WordPress post or page slug with a more efficient way?

Here are some interesting ways to define a personalised, very short and share-friendly version of URL for your post.

1. Eliminate the ‘time-stamp’ from the slug and
http://wpgaurav.wordpress.com/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
redirects to the same post at
http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
So it got a little shorter.
2. Want it to be even shorter? Then cut one or more characters from the URL: For example:
http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is/
http://wpgaurav.wordpress.com/derivative-of-x-squared-is-2x-or-x/
etc.  are equivalent and redirect to the same post.
3. Want it be shorter still? Then eliminate everything but single word. e.g., http://wpgaurav.wordpress.com/derivative/
Looks cool, no? Yes, Just like a Page URL on WordPress.com! And it redirects to the same post as all other links above.
4. Is the word too long for you? Then abbreviate it to
http://wpgaurav.wordpress.com/der/
5. Want it be still shorter? Try the shortest, a single letter: http://wpgaurav.wordpress.com/d/ ! Well, it does not redirect to http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
Where does it go? It goes to d’ Alembert’s Test of Convergence . Reason is specified below at point 2.

Here are some points, which follow and guide you on shortening URLs:

1. Hyphens are not important when considering shortened-urls.
2. Any URL of the type http://wpgaurav.wordpress.com/d redirects to a post/page which slug starts with ‘d’. If there are two posts having slugs starting with the same letter of the alphabet (here d),then it will, in alpahabetical order, redirect to that post which first word (if same then second word) comes first in English Dictionary. For example http://wpgaurav.wordpress.com/d will redirect to http://wpgaurav.wordpress.com/d-alembert/ rather than to http://wpgaurav.wordpress.com/derivative/
3. If two/more posts have the same slugs and you are using an identical shortener that it might go to any of them, then that will (should) redirect to the post which was published earlier.
4. Some slugs are not allowedin posts or pages on WordPress.com and they are:
• Periods(.) are not allowed in slugs.
• /activate/
• /category/
• /feed/
• /i/
• /next/
• /signup/
• /tag/
• /wp-content/
5. You can not shorten your post URLs /page URLs (this way) until published.
6. This trick also works for self hosted WordPress.org blogs.

So, are you going to experiment with your WordPress.com Post URLs?

Disclaimer: There is no technical basis for these shortening tricks. They are soley based on experiments with WordPress.com slugs. This post was made under supervision of timethief, I am grateful to her. I would also like to say thanks to Ganesh Dhamodkar, who was the guy I tested all these with.
Feel free to comment if you are getting any problem in shortening URLs or if just want to say ‘Hi’.

Long URL for this Post: http://wpgaurav.wordpress.com/2011/11/24/wordpress-url-shortening/

Short URL for this post: http://wpgaurav.wordpress.com/wor/

## 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.

Longhorn Cows in the Southwestern Sun, By T.Paden

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.
(more…)

## A Yes No Puzzle

This is not just math, but a very good test for linguistic reasoning. If you are serious about this test and think that you’ve a sharp [at least average] brain then read the statement (only) below –summarize it –find the conclusion and then answer that whether summary of the statement is Yes or No.
[And if you're not serious about the test ...then read the whole post to know what the stupid author was trying to tell you. ]

## Blog of the Month Awards – October 2011

Reader’s brain is variable. It changes according to what it read. I have changed the pattern of selection and style of writing about BLOG OF THE MONTH. At the beginning of August, I planned that I will select some blogs from the education blog-o-sphere and will award to appreciate them for their excellent work. I know these awards will probably never make a difference but hope too that they’ll keep their good works on. So, here is the list of my 10 most favorite blogs, one of which, Gowers’s Weblog, is my Blog of The Month, for October 2011.

## The problem of the Hundred Fowls

This is a popular Chinese problem, on Linear Diophantine equations, which in wording seems as a puzzle or riddle. However, when used algebraic notations, it looks obvious. The problems states :

 If a cock is worth 5 coins, a hen 3 coins, and three chickens together 1 coin, how many cocks, hens and chickens, totaling 100 in number, can be bought for 100 coins?

This puzzle in terms of algebraic equations can be written as $5x+3y+\frac{1}{3}z=100$ and $x+y+z=100$
where $x, y, z$ being the number of cocks, hens and chicks respectively.
We find that there are two equations with three unknown quantities. So eliminating one of the unknowns, by putting $z=100-x-y$ from second equation into first one such that $5x+3y+\frac{1}{3} (100-x-y)=100$
or, $15x+9y+100-x-y=300$
or, $14x+8y=200$
or, $7x+4y=100$.
Which is a linear Diophantine equation (with only two unknown quantities).
The equation $7x+4y=100$ has the general solution   [links to WolframAlpha] $x=4 t$ and $y=25-7t$, so that $z=75+3t$ where $t$ is an arbitrary integer.
Now, since $x, y, z$ are the number of creatures, hence $x, y, z >0$ and thus $4t >0$ , $25-7t >0$ and $75+3t >0$ which imply that $0 < t < 3\frac{4}{7}$. And because t must have integer values, we have $t=1,2,3$. Which gives the following three solutions:

 Values of $t$ No. Of cocks ( $x=4 t$ ) No. Of hens ($y=25-7t$) No. Of chicks ($z=75+3t$) 1 4 18 78 2 8 11 81 3 12 4 84

So there are the three ways to chose the number of cocks, hens and chicken totaling 100 to buy for 100 coins.

Problem Sources:
Elementary Number Theory
David M. Burton, 2006
McGrawHill Publications

Wikipedia article on Diophantine Equations

Image Credit

## Into the Mandelbrot set

The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognizable two-dimensional fractal shape. More detail on Wikipedia..