equidistant

Did you ever pay attention when your maths teacher was talking about corresponding angles and congruent lines? Think back to one of the first lessons, specifically, parallel lines. Two lines the same distance apart, within the same plane and travelling in the same direction. Regardless of how much these two lines have in common, they never intersect nor meet. Over the last years, I've come to realise that I can't overcome this parallelism obstacle.

But I suppose, like most things, it depends on how you choose to approach the problem. With conventional geometry, the parallel lines remain within constant distance and fail to meet, even at infinity. Consider ecliptic geometry, eventually the parallel lines close the distance between one another and intersect. Alternatively, hyperbolic geometry dictates the lines swerve further from the point of intersection.

What if relationships are just like Euclid's parallel postulate? Well so far, the hyperbolic approach hasn't been successful for me. I suppose when you people know each other for long enough, they begin to notice the patterns in each other's behaviour. I'm always slow to notice these things, I really should be more attentive. I really need to focus and figure out how to overcome the parallelism hurdle.

Image credit: santib