PARALLEL LINES

a picture of parallel lines

What are parallel lines?

If we describe two individuals as parallel lines, will that mean that they will never meet each other? Does that mean they are not meant for each other? Does that mean that they will never be together? If your answer is "YES", then think again. Maybe you don't know yet the definition of parallel lines.

In Euclidean geometry, parallel lines are lines on a plane that do not intersect or meet. It can be extended on both directions. Further, the perpendicular distance between the lines remains constant. 

The symbol for parallel is II. If line LO is parallel to line VE , then we can write LO II VE.

However, in non-Euclidean geometry, parallel lines intersect at a certain point called the ideal point.

To visualize the ideal point, let us look at a picture of a pond in Wright Park, Baguio City, Philippines. 

In the picture above, the sides of the pond represent parallel lines extended infinitely upward. It somehow forms an illusion that the parallel lines meet at the upper center of the figure. It is somewhat triangular in form. The intersection on the upper center is the ideal point. 

If I ask you now,

1. What are parallel lines? How would you answer?

2. If two individuals are described as parallel lines, would that mean they are not meant for   

    each other? Why? 

Read More

MAZES

maze by Jie Xu and Craig S. Kaplan

Mazes are also generated by using a computer with inputs from a human designer. They consider the complexity and aesthetic factors of the maze. Some of these are constructed through the interconnected vortices forming sets of paths like the figures below:

The Polyhedron
by Jie Xu and Craig S. Kaplan

The Tumbling Blocks
by  Jie Xu and Craig S. Kaplan

Some of the mazes are generated by the use of images like the following: 

Pres. Lincoln
by Jie Xu and Craig S. Kaplan

The Sphinx
by Jie Xu and Craig S. Kaplan

Would you like to try solving these mazes? It's a test of patience, determination and spatial skills. Good luck!

Note: The use of the images above is permitted by the owners, Jie Xu and Craig S. Kaplan. You can visit their web page at  http://www.cgl.uwaterloo.ca/~csk/projects/mazes/

Read More

MATH TALK

Photo Courtesy: Michal Zacharzewski/stock.xchng

A couple is attending a school party. The guy fetch the girl at their house. 


The girl asked : "How do I look? 


The guy answered: "You are so tan c/sin c"


The girl asked: "What do you mean?"


The guy answered: "tan c/sin c is equal to (sin c/cos c)/sin c, 
                                    which is equal to 1/cos c. 
                                    Lastly, 1/cos c is equal to sec c.
                                    You are so sec c!" 


What a wonderful world of mathematics!
If mathematics could have been integrated in our daily life as light as this, then the subject itself could have been universally appreciated and used by everybody.http://www.sxc.hu/pic/m/m/mz/mzacha/1182634_silhouette.jpg

Read More

DAYS OF THE MONTHS

     
         THE DAYS OF THE MONTHS

Thirty days hath September,

April June and November.

February has twenty-eight alone,

All the rest have thirty - one,

Excepting Leap Year - that's the time

When February's days are twenty - nine. 

Did anyone share or teach this poem to you when you were starting to memorize the exact number of days for every month of the year?


I guess it's effective when you create a jingle from it - using a common song you easily remember. Otherwise, memorize the poem as is.


I still remember during my elementary days when some items in our periodical examination involve the number of days of specified months. One of my classmates tried to recite (murmur) the poem repeatedly. Unfortunately, he forgot the exact arrangement of the months in the poem. He ended up guessing the answers for the items.


Luckily, a week before the examination, one of my relatives shared a technique of easily remembering the number of days of every month without even memorizing the poem. It helped me a lot remembering the exact number of days. Raymond Blum, the author of the book Mathamusement, called this as the knuckles method. It is called knuckles method because it uses the knuckles and the spaces between the fingers as representations of each month of the year.


Make two fists, with palm down. From left to right, the knuckle formed at the base of your baby finger represents January. The space between the baby finger and the ring finger represents February. The knuckle at the base of your ring finger represents March. Continue the process until you reach December. Take note that when you reach July (represented by the knuckle of the index finger of your left hand), proceed with the knuckle of the index finger of your right hand, which represents August.


The months represented by the knuckles have 31 days. These are January, March, May, July, August, October, December.


The months represented by the spaces between the knuckles have 30 days, except for February. These months are April, June, September and November. February is exempted because during a common year it has 28 days but during a leap year it has 29 days. This happens only every four (4) years.Year 2008 is a leap year. The next one will be on 2012.


The next time someone asks you about the exact number of days of every month, use your knuckles!  


            

Read More