There are very good links shared among Facebook friends. The links generally refer to short videos, advertisements and articles. This time I really liked one link shared by Kancho. Basically, this video is a dance, know as "America's Got Talent: Impossible". Its amazing. Enjoy !!
Page Rank Algorithm
Google uses Page Rank Algorithm (PRA) to rank web pages so that finding needle in web's haystack can be accomplished. Here is a good tutorial that explains how it finds our pages in the web.
Fun with mathematics II
We can do multiplication by means of visual ways. I have found both video and article that shows how one can compute the multiplication of ANY DIGIT NUMBERS using visual method.
A. Video
I am hundred percent sure that you will enjoy this video. Watch it first and then we discuss the principle behind this approach.
B. Article
Note: I have copied the following paragraphs and a picture from [1]. If you don't understand here, please go to that site.
Example: Multiply 22 by 13.
C. Understanding the LOGIC
Below, I've described the way we did the multiplication in our school and if you have noticed, the same thing is happening in the visual method as well. Here it goes:
Ex1
2 2
x 1 3
-------
6 6
2 2 x
-------------
2 8 6
Ex2:
1 5 6
3 5 8
---------------------------------------
8 40 48
5 25 30 x x
3 15 18 xx x x
-------------------------
5 5 8 4 8 [ while adding , carry should be propagated towards left ]
We know that two non parallel lines always meet exactly at a point. Note that when a number of lines (representing one digit number, e.g. five lines for 5 ) crosses a number of other lines ( which represents another one digit number), then the number of points formed by the crossings is equal to their product.
I understood the logic by referring back to my ways of doing the calculation. It may not be clear to you by my explanation. Better visit the website and read the article in such a case.
References:
A. Video
I am hundred percent sure that you will enjoy this video. Watch it first and then we discuss the principle behind this approach.
B. Article
Note: I have copied the following paragraphs and a picture from [1]. If you don't understand here, please go to that site.
Example: Multiply 22 by 13.
Note: This figure is taken from [1]
Draw 2 lines slanted upward to the right, and then move downward to the right a short distance and draw another 2 lines upward to the right (see the magenta lines in Figure 1). Then draw 1 line slanted downward to the right, and then move upward to the right a short distance and draw another 3 lines slanted downward to the right (the cyan lines in Figure 1).
Now count up the number of intersection points in each corner of the figure. The number of intersection points at left (green-shaded region) will be the first digit of the answer. Sum the number of intersection points at the top and bottom of the square (in the blue-shaded region); this will be the middle digit of the answer. The number of intersection points at right (in the yellow-shaded region) will be the last digit of the answer.
This will work to multiply any two two-digit numbers, but if any of the green, blue, gold sums have 10 or more points in them, be sure to carry the tens digit to the left, just as you would if you were adding.
C. Understanding the LOGIC
Below, I've described the way we did the multiplication in our school and if you have noticed, the same thing is happening in the visual method as well. Here it goes:
Ex1
2 2
x 1 3
-------
6 6
2 2 x
-------------
2 8 6
Ex2:
1 5 6
3 5 8
---------------------------------------
8 40 48
5 25 30 x x
3 15 18 xx x x
-------------------------
5 5 8 4 8 [ while adding , carry should be propagated towards left ]
We know that two non parallel lines always meet exactly at a point. Note that when a number of lines (representing one digit number, e.g. five lines for 5 ) crosses a number of other lines ( which represents another one digit number), then the number of points formed by the crossings is equal to their product.
I understood the logic by referring back to my ways of doing the calculation. It may not be clear to you by my explanation. Better visit the website and read the article in such a case.
References:
- Su, Francis E., et al. "Squaring Quickly." Mudd Math Fun Facts.
Fun with mathematics I
I found many interesting methods to solve mathematical problems. In this blog, I'll post some of them.
How to find square of a number quickly ?
Multiplying two numbers will be easy if one of them is a multiple of 10. There is also a high probability that a person knows the squares of small numbers by heart. If we incorporate these two ideas, we can get a quicker solution to get the square of a number.
Sample problems and Solutions [1] :
It's based on the algebra identity for the difference of squares, but with a twist!
54^2 = 50 * 58 + 4^2 = 2916.
42^2 = 40 * 44 + 2^2 = 1764.
37^2 = 34 * 40 + 3^2 = 1369.
Logic
a2 = (a-b)(a+b) + b2.
How to find square of a TWO DIGIT number that ENDS in 5?
Here again, I've taken examples from [1]. Its very easy to calculate the square of a given two digit number if it ends in 5.
Remember three things
* Two digit number
* Ends in 5
* Find square
Sample problems and Solutions
45^2 = 2025
85^2 = 7225, etc.
Logic:
If the first digit is N and the second digit is 5, then the last 2 digits of the answer will be 25, and the preceding digits will be N*(N+1).
References:
How to find square of a number quickly ?
Multiplying two numbers will be easy if one of them is a multiple of 10. There is also a high probability that a person knows the squares of small numbers by heart. If we incorporate these two ideas, we can get a quicker solution to get the square of a number.
Sample problems and Solutions [1] :
It's based on the algebra identity for the difference of squares, but with a twist!
54^2 = 50 * 58 + 4^2 = 2916.
42^2 = 40 * 44 + 2^2 = 1764.
37^2 = 34 * 40 + 3^2 = 1369.
Logic
a2 = (a-b)(a+b) + b2.
How to find square of a TWO DIGIT number that ENDS in 5?
Here again, I've taken examples from [1]. Its very easy to calculate the square of a given two digit number if it ends in 5.
Remember three things
* Two digit number
* Ends in 5
* Find square
Sample problems and Solutions
45^2 = 2025
85^2 = 7225, etc.
Logic:
If the first digit is N and the second digit is 5, then the last 2 digits of the answer will be 25, and the preceding digits will be N*(N+1).
References:
- Su, Francis E., et al. "Squaring Quickly." Mudd Math Fun Facts.
Using Multiple Search Engines
I just found a useful website. It is really useful because it saves user's time by presenting the results of a query from two different search engines. In other words, with same input effort, one can get results from two search engines. As an example, if I want to search NEPAL in Google, I would be happy if I can get the results for NEPAL from other search engine e.g. Yahoo, on side-by-side. This would be much interesting if your screen is big enough.
Happy browsing !!
Using TreeTagger
I recently used TreeTagger to get the part-of-speech (POS) of English and French texts. As mentioned in its original website [1], TreeTagger is a language independent tool used for annotating text with part-of-speech and lemma information.
Installation is pretty easy. One just needs to follow the instructions given in the website. After the installation it will tell you something like :
You should add /home/nobal/TreeTagger/cmd and /home/nobal/TreeTagger/bin to the command search path.
And here is how you can add path (in ubuntu) :
export PATH
Don't forget to restart the terminal to get the effects. To verify, use this command:
echo $PATH
External Links:
[1]. TreeTagger
Installation is pretty easy. One just needs to follow the instructions given in the website. After the installation it will tell you something like :
You should add /home/nobal/TreeTagger/cmd and /home/nobal/TreeTagger/bin to the command search path.
And here is how you can add path (in ubuntu) :
sudo gedit /etc/bash.bashrc
at the end of file
PATH=$PATH:~/TreeTagger/bin:~/TreeTagger/cmdat the end of file
export PATH
Don't forget to restart the terminal to get the effects. To verify, use this command:
echo $PATH
External Links:
[1]. TreeTagger
Lexical Similarity Measure
My last post described the Levenshtein's algorithm for finding the differences between two sequences which does so by means of "edit distance" metric. Recently, I read an algorithm that utilizes the same metric to calculate the lexical similarity measure between two strings Li and Lj:
SM(Li, Lj ) := max(0 , (min( |Li|, |Lj| ) - ed(Li,Lj) ) / min(|Li|, |Lj|))
where
|Li| and |Lj| are the lengths of Li and Lj ,
ed(Li, Lj) is the edit distance between Li and Lj
This method can be applied for comparing two set of strings as well. Details can be found in the paper: A. Maedche and S. Staab, "Measuring Similarity between Ontologies", Karlsruhe, Germany.
