The Circle of Geometry

Today is the birthday of William Metzler born 1863 in Odessa, Ontario, Canada.  Metzler was a Canadian Mathematician who taught at Syracuse University and Albany Teachers Training College.  He published papers in the Proceedings of the European Mathematical Society.  His focus was on the theory of matrices and determinants.

A long time friend, Dick, and I were enjoying each other's company, reminiscing about our high school educational experiences.  After a brief lapse in the conversation, Dick stated "I should send an apology to my high school geometry teacher."  I asked why.  Dick sighed and replied, "I hated that class.  I thought it was so pointless.  Who would of thought that many of my conversations now, are with architects and revolve around geometric relationships and buildings."  I smiled, "The circle of geometry."

The circle of geometry.  I am fascinated by the circle.  The circle has been symbolic of the sun, life, boundary, completion, returning cycles, and unification of two lives as represented by wedding rings.  As I consider the circle, I think a more appropriate symbol for me is the helix.  This geometric shape combines the returning cycles of life and the experiences I gather each year.  As I garner each experience and the circle attempts to complete itself, it rises slightly, never competing the task but starting a new revolution above itself.

In mathematics, a helix is defined as a curve in three-dimensional space for which the tangent at any point makes a fixed angle with an axis.  Springs, screws and hand rails on stairwells are examples of helices.  Helices can be right-handed or left-handed.  At my dad's welding shop, there was a machine that put threads on metal rods.  Most of those threads were right-handed.  What I view as the growth of the helix is called the pitch and is measured parallel to the axis of the helix.  The equation for a helix is a parametric equation.  An example would be: x(t) = cost t; y(t) = sin t; and z(t) = t.  x(t), y(t), and z(t) are functions in three-dimensional space such that at t increases the point (x(t), y(t), z(t)) traces a right-handed helix with a pitch of 2pi radians and a radius of 1 unit about the z-axis.

In music, pitch space is often single or double helices.  These helices often extend out of a circle of fifths to represent an octave equivalency.  The DNA, double helix is probably the most famous geometric shapes known to mankind.

A molecule that encodes the genetic instructions used in the developing and function of all living organisms.  The circle is complete.  The circle of geometry.  The circle of life.