October 31, 2010

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? 


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