Approachability

Today is the birthday of Michel Rolle born 1652 in Ambert, Basse-Auvergne, France.  Rolle is known for Rolle's Theorem which states that in calculus, any differentiable function that attains equal output values at two distinct points must have a point between those two where the first derivative (the slope of the tangent line to the graph of the function) is zero.

Quote of the day: John Maynard Keynes, "I can't remember my telephone number, but I know it was in the high numbers."

In mathematics, a limit of a function at a input value (x-value) is the output value (y-value) that the function produces as the input value is approach from the right and left of the input value.  For the function to have a limit at that particular input value, the formed output value must be the same from both the left and right sides.

Functions that have asymptotes do not have numerical limits at the asymptote.  As input values approach the particular numerical value where the asymptote exists, the function may increase or decrease without bound.  The asymptote acts as an invisible boundary, a forcefield.

Two famous quips concerning asymptotes I have used in my class:  "You need to know the difference between your asymptote and a hole in the graph."  and "Holy shift!  Did you see the asymptote on that mother function."

Recently, I have had a parent call me and state that I am unapproachable.  I guess the parent was stating the I was asymptotic.  I have thought about that comment since that phone call.  I can be unapproachable.  The part of my personality is my Achilles' Heel.  I have made a conscious effort to be more approachable.  That particular characteristic does not come naturally to me.  I work closely with a colleague and he is warm and welcoming.  I, on the other hand, have to work at it.  I need . . . I require full concentration from myself and from my students when I teach.  I believe that my focus can be alarming and frightening to students.  Often, when I am focused on a problem, I can be gruff and too quick to the point.  I also have a well-defined bubble that surrounds me.  I am not a very "touchy, feely" kind of a guy.  I really work at giving my best instruction to my students.  I just need to create an approachable limit.