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| a picture of 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.
, 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.
, 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?
7 comments:
1. parallel lines are 2 different lines.
2. my answer is they are NOT MEANT for each other coz for being TOGETHER as a couple and being meant for each other means they have to become 1.. parallel as being 2 different lines may never be 1.. (hahah english, dugo nose ko)
then for Non-Euclidean geometry sabi niya nga, IDEAL POINT.. e sa true to life wala namang IDEAL MAN.. di totoo.. hahah. But seriously, if we are going to look at the picture, "yes" it says that "It somehow forms an illusion that the parallel lines meet at the upper center of the figure". Again, an "ILLUSION" meaning UNTRUE. Even how much we want those lines to be together, at the end, they will never meet. --- JC
Yes, it is somehow an illusion,
but in Euclidean Geometry
ideal point exist...
parallel lines intersect!
It only means that,
if you look at the other side of things,
then there is always a possibility.
For the case of parallel lines,
Euclidean Geometry tells us that
these lines do not intersect.
However, there is non-Euclidean Geometry
telling us that parallel lines intersect.
Also,
in Euclidean Geometry
all lines are straight lines.
However, in non-Euclidean Geometry,
curved lines exist...
First of all, PARALLEL LINES po ang pinag uusapan dito, no other lines.
then, fine ulit, ideal point exist, but still an illusion. balibaliktarin mo man ang mundo may mga bagay talagang hindi pwede. it would only give us false hopes in wanting something na di talaga pwede. :) -- JC
It is not an illusion.
Non-Euclidean Geometry exist,
and ideal point exist!
Do not be confined with
the conventional mathematics...
there are a lot more things
to discover in modern and advance mathematics
aside from the basic
that we already know.
with exclamation point?! :p hehehe
yes, there are so many things that needs to be discovered and still needs to be seen.. but sometimes, sa sobrang kakahanap natin ng sagot, it would only leads us into something na nabubuo nalang ng imahinasyon natin. plus, i believe, without the basic knowledge di rin tayo makaka advance, so why focus too much ahead, if we can answer it with what's on hand (the basic)...
confirm ko lang po:
"Yes, it is somehow an illusion,
but in Euclidean Geometry
ideal point exist..." - November 14, 2010 9:50 PM
"However, in non-Euclidean Geometry,
curved lines exist..." - November 14, 2010 9:52 PM
"non-Euclidean geometry, parallel lines intersect at a certain point called the ideal point." - October 31, 2010
>> san po ba talaga ang ideal point sa dalawa? coz i believe, ang ideal point asa curve lines (Non-Euclidean geometry) na..making it not a "PARALLEL LINE" ---- JC
@JC
ideal point is the intersection of two parallel lines...
what i'm trying to say is that,
Euclidean and non-Euclidean Geometry
are two different areas of mathematics.
What we already know
is the Euclidean Geometry.
In Euclidean Geometry,
lines are all straight,
parallel lines do not intersect.
However, in Euclidean Gemeotry,
lines may be curved,
and parallel lines intersect at an ideal point.
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