# Do parellel lines ever meet?

Here's another one of those problems you encounter when things converge to 0.
By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.
Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\
/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.
Is there a flaw in this logic?

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Jamie Frost
Here's another one of those problems you encounter when things converge to 0.
By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.
Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\
/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.
Is there a flaw in this logic?

Well I was also taught that a definition of an infinite distance is the point at which parallel lines meet, infinity is a confusing concept though.
parallel lines meet at infinity. since infinty is "never", no, parallel lines do not ever meet, unless they are the same colinear.
elpaw
unless they are the same colinear.

What does colinear mean?
Invisible
What does colinear mean?

the same line.
elpaw
the same line.

Thank you.
All these concepts are meaningless in the 'real world' though
imasillynarb
All these concepts are meaningless in the 'real world' though

In Further Maths we started doing complex numbers, and i find it weird how they use "imaginary parts" in real-life situations. We haven't done much on it though.
Invisible
In Further Maths we started doing complex numbers, and i find it weird how they use "imaginary parts" in real-life situations. We haven't done much on it though.

Dont know anything about complex numbers Im afraid.

I just remember my chemistry teacher(possibly the smartest person Ive ever known) constantly ranting about how Physicists and Mathematicians come up with loads of bollocks to explain things, and how most of it is totally meaningless and irrelevant.
imasillynarb
Dont know anything about complex numbers Im afraid.

I just remember my chemistry teacher(possibly the smartest person Ive ever known) constantly ranting about how Physicists and Mathematicians come up with loads of bollocks to explain things, and how most of it is totally meaningless and irrelevant.

Well basically, you know when you're trying to solve quadratic equations, when you have a -ve discriminant then there are no REAL Solutions to that equation.

However, what they do is use: i = sq.root (-1)

And you can have imaginary solutions to the equation, in effect. However, they use this concept in real-life situations. As I said, we haven't done much, but it's weird.

For example, you even have graphs called Argand Diagrams, and you can sketch graphs of complex numbers. These are of the form a + bi. There's a real axis and an imaginary axis.

LOL, I'll shut up..
Invisible
Well basically, you know when you're trying to solve quadratic equations, when you have a -ve discriminant then there are no REAL Solutions to that equation.

However, what they do is use: i = sq.root (-1)

And you can have imaginary solutions to the equation, in effect. However, they use this concept in real-life situations. As I said, we haven't done much, but it's weird.

For example, you even have graphs called Argand Diagrams, and you can sketch complex numbers. These are of the form a + bi. There's a real axis and an imaginary axis.

LOL, I'll shut up..

One of my maths teachers tried to tell us about imaginary numbers on bridging week, needless to say at that stage it went right over our heads.
Invisible
In Further Maths we started doing complex numbers, and i find it weird how they use "imaginary parts" in real-life situations. We haven't done much on it though.

One thing you can use complex numbers for in Physics is circuit analysis - eg. when you're dealing with impedances and time varying voltages. 'Complex impedance' doesn't have practical significance, it's just easier to think of it that way.
Yeah, complex numbers are essentially vectors (a real part and an imaginary part), so they can be used to represent quantities that real numbers can't. They're also useful in solving trig problems, because of a handy identity: [cos(x) + isin(x)]^n = cos(nx) + isin(nx), for all rational n.
Jamie Frost
Here's another one of those problems you encounter when things converge to 0.
By definition, parellel lines are always the same distance apart, but my maths teacher argues that what happens an infinite distance across the lines is mathematically vague.
Say you consider the gradient of two lines to the horizontal. If their gradient is 1 they'll meet after a short distance:

\
/

As this gradient becomes smaller, the lines meet after a further distance. Hence as the gradient tends towards 0, then the lines meet at an infinite distance.
Is there a flaw in this logic?

One problem..gradient say is not one, he gradient of one is negativeif they were both one theyd be in same direction and never meet. Complex numbers..... asked my teacher to give an example whyd we would need em...he left the classroom
jaffakidds
Complex numbers..... asked my teacher to give an example whyd we would need em...he left the classroom

Very professional.
imasillynarb
Dont know anything about complex numbers Im afraid.

I just remember my chemistry teacher(possibly the smartest person Ive ever known) constantly ranting about how Physicists and Mathematicians come up with loads of bollocks to explain things, and how most of it is totally meaningless and irrelevant.

Probably because he didn't understand any of it.
Pzyko
Probably because he didn't understand any of it.

Not really,something is only deemed correct until it is disproven by someone else. There are probably theories etc. we see as correct which have flaws in them. Even 4ed made a thread that contradicted the theories about duality.
Invisible
Not really,something is only deemed correct until it is disproven by someone else. There are probably theories etc. we see as correct which have flaws in them. Even 4ed made a thread that contradicted the theories about duality.

Or he didn't understand any of it.
Pzyko
Or he didn't understand any of it.

That's irrelevant, he still isn't wrong in his opinion that it's a load of bollocks. Even the axiom "angles in a triangle add up to 180 degrees" isn't technically correct. A triangle on a sphere doesn't have angles adding up to 180 degrees, I can assure you.
Invisible
That's irrelevant, he still isn't wrong in his opinion that it's a load of bollocks. Even the axiom "angles in a triangle add up to 180 degrees" isn't technically correct. A triangle on a sphere doesn't have angles adding up to 180 degrees, I can assure you.

I triangle on a sphere is a stupid concept because any idiot can see (except, possibly, you) that the lines making up the triangle aren't straight. I can draw a triangle on a flat piece of paper that doesn't have straight edges but has angles that add up to more than 180 degrees. It just wouldn't be a triangle.

So I repeat: he probably didn't understand any of it.