2006-09-04 10:06:36 · 71 answers · asked by Ulas C 2 in Science & Mathematics ➔ Mathematics
Consider an isosceles triangle (where 2 side are equal in length) - if you increases the length of the two equal sides the angle subtended by these lines decreases; as the length of the lines tend to infinity, so the angle tends to zero and the lines are therefore parallel. But as it is a triangle they must meet at infinity!
Equally, if your car could drive through an infinite field of snow in a perfectly straight line, the tyre tracks would never meet.
So I'm afraid the answer to this question is clearly both yes and no.
Added:
And if you're not convinced that the the lines are parallel at infinity, consider this:
1÷9 = 0.1111111111111111111111111111...
2÷9 = 0.2222222222222222222222222222...
3÷9 = 0.3333333333333333333333333333...
4÷9 = 0.4444444444444444444444444444...
5÷9 = 0.5555555555555555555555555555...
6÷9 = 0.6666666666666666666666666666...
7÷9 = 0.7777777777777777777777777777...
8÷9 = 0.8888888888888888888888888888...
9÷9 = 0.9999999999999999999999999999...
But 9÷9 is quite obviously =1 therefore
0.9999999999999999999999999999... = 1
So you might argue that at infinity there is still a small distance between the lines of the triangle, but the above equation shows that this is not the case.
Discuss ...
2006-09-04 11:46:17 · answer #1 · answered by Friseal 3 · 1⤊ 3⤋
According to Euclidean geometry form a point outside a straight line there is one and only one straight line parallel to the first. These two lines do not intersect. According to Riemann geometry there is not such a line. They are always intersect at infinity. According to the geometry of Lobachevsky there are many lines that are never intersect. So this is an axiom, you accepted or not
2006-09-04 10:35:49 · answer #2 · answered by Dimos F 4 · 1⤊ 0⤋
They never intersect in the plane even at infinity.
However take a long thin strip of paper with parallel sides; put some glue on the ends, but twist one end and then glue them together. Now run your finger along one of the parallel sides, you will find the line continuous: so without removing your finger you are moving from one parallel side to the other; the mobius strip
2006-09-04 10:21:11 · answer #3 · answered by Anonymous · 0⤊ 0⤋
No, parallel lines never intersect each other. Not even at infinity. That's why they are called parallel.
2006-09-04 19:57:21 · answer #4 · answered by yousufsons 2 · 0⤊ 0⤋
Well, the definition is "two parallel lines never intersect OR they intersect in infinity", because we actually don't know what happens in infinity, so we can say nothing about it. That's why we have to suppose this hypothesis.
2006-09-04 10:15:56 · answer #5 · answered by Francesco 2 · 0⤊ 1⤋
Never. Not in 1 or n dimensions. Parallel lines never intersect.
2006-09-04 11:39:53 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Parallell lines are two or more straight lines that remain equidistant from each other.
Since the whole concept of a parallel line is that they are always the same distance apart, they cannot ever intersect.
2006-09-04 11:23:09 · answer #7 · answered by Anonymous · 0⤊ 0⤋
No they don't. By Definition. Parallel lines never intersect. Fact!
:)
2006-09-04 10:48:14 · answer #8 · answered by Jimbo 2 · 0⤊ 0⤋
Yes, Because light is a wave and will refract and bend the lines to at some point meet in infinity, they start off parallel but will not remain so.
2006-09-04 10:19:11 · answer #9 · answered by cloud600 1 · 0⤊ 0⤋
No by definition any two lines that don't intersect are said to be parallel.
2006-09-04 22:11:58 · answer #10 · answered by migelito 5 · 0⤊ 0⤋