You are here:

Geometry/parallel lines


Hi Scott,

I was taught in school,...a long time ago that two parallel lines meet at infinity. Can that be proved mathematically? How does that gel with the geometric
infinite series 1/1-x which only converges at infinity?

By math, two parallel lines never intersect.  Look at y=0 and y=1.  They are parallel,
but as x increases, the relative difference of 1 in y appears to get smaller
when compared to the size of x.  

When it is said that 1/(1-x) converges to 0 as x goes to infinity means that no matter how small the difference between the number and zero is wanted, an x big enough can be found to make it that small.

For example, since it is known to converge to 0, given any number, no matter how small,
a number n can be found to make the absolute value smaller than the size desired.

If it is to be smaller than 0.1, any n>=11 would work.
If it is to be smaller that 0.01, any n>=101 would work.
If it is to be smaller than 0.001, any n>=1001 would work.

For a limit to exist, no matter how small a choice is chosen,
there exists a value for n such that if x is bigger than that, it works.


All Answers

Answers by Expert:

Ask Experts


Scott A Wilson


I can answer whatever questions you ask except how to trisect an angle. The ones I can answer include constructing parallel lines, dividing a line into n sections, bisecting an angle, splitting an angle in half, and almost anything else that is done in geometry.


I have been assisting people in Geometry since the 80's.

I have an MS at Oregon State and a BS at Oregon State, both with honors.

Awards and Honors
I was the outstanding student in high school in the area of geometry and math in general.

Past/Present Clients
Over 8,500 people, mostly in math, with almost 450 in geometry.

©2017 All rights reserved.