Relationship Geometry (or, A Great Friend is a Rubik's Cube)

I loved high school geometry.  Did you?  Measuring lines, bisecting angles, drawing circles and arcs... This is just plain fun to me!

Since my youngest is in 10th grade, this year is my last opportunity to teach geometry.  Working with him on lines, segments, rays, and angles got me thinking...

Every relationship can be illustrated in geometry!

Yeah, I know, you're rolling your eyes.  But bear with me.

You are a point.  We'll call you Point A.

But no man is an island, so we'll add me to the picture.  I'll be Point B.

 Two islands!  Helloooo over there!

Now, if you and I were to connect in some sort of relationship, whether a work-related one or a friendship, we could be illustrated by a line segment.

This is us, joined in an exclusive relationship.  No other points are involved, no other lives affected.  Just you and me.  On the surface this can appear to be a good thing, as in a marriage or a "best friendship."  But an exclusive relationship tends to become ingrown.  There's too much pressure on one person to support the entire weight of another.  A line segment relationship just isn't going anywhere.

(Please don't misunderstand -- I'm not a bigamist, and I'm not advocating infidelity!  I'm just saying that in marriages, your spouse isn't the only friend you should have.  He/she should ideally be your closest friend, but not your only one.)

I observed an exclusive relationship one time, shortly after we moved to NY.  I was talking with a lady in a social situation, and we hit it off fairly well.  The next time I saw her, I spoke with her briefly again, just a friendly contact.  Everything seemed fine.  The next time I spoke to her, though, she felt compelled to inform me, "I already have a best friend, and I don't have the time to invest in other relationships."

I was amazed.  I wasn't asking her for anything at all beyond the mere politeness due a person you see frequently.  But she was evidently absorbed in her relationship with another person to the extent that she couldn't afford mere pleasantries on a repeated basis.  What a shame.

(P.S.  This lady's best friend died last winter.  I wonder how she coped with the disintegration of her entire universe.)

Okay, moving on, another type of relationship.  Ray AB illustrates a one-way relationship.

We typically see this in a parent-young child relationship, or in other caregiver situations where the receiving of one without giving back is normal. 

A people pleaser, however, often winds up in relationships -- again, whether work-related or in social circles -- where they give to others who dominate them in such a way that they never receive any return on their relationship investment.  They become doormats.

Anne Hathaway played this part well in the movie Bride Wars.  Until she decided to quit catering to everyone else, she was used by self-centered people to further their own agendas.  This is not a truly beneficial relationship for either the giver or the receiver, and is doomed to failure when the giver exhausts his resources or the receiver finds someone who can give them more.


In a relationship between two healthy adults, however, this should not be the norm.  The ideal would be illustrated by Line AB:

 
Both points are interacting with each other as well as extending their reach outward.





As relationships interact, we can find another example of exclusivity as seen below.

 

All points interact with each other, provided the points are invited inside the circle.  This is fine in a business situation, on a committee, for instance, but in relationships it's called a clique.  As with other exclusive relationships, it will eventually become ingrown and suffocate.  Good friendships should be made stronger by including others.




So far, everything we've looked at has been 1- or 2-dimensional.  A growing relationship, however, should become 3-dimensional, developing depth as the people get to know each other.

 
The many facets of their personalities and experiences combine to create a solid relationship that can stand on its own, largely unaffected by outside forces.

And a GREAT relationship becomes like a Rubik's Cube, always stuck together no matter which way circumstances turn it!