Today is the birthday of Jean Hachette born 1769 in Mézières, Ardennes, France.  He worked on descriptive geometry.  Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art.  I have included examples of four different 2D representations of the same 3D object.

I draw a picture almost every time I solve a problem.  I actually sketch  a diagram on a coordinate plane, label it, and then apply either algebra or trigonometry to solve the problem.  I also use tables to solve problems.  I look for patterns in the tables.  My last step is to graph it on my Casio Prism.  The calculator allows me to examine detail.

I learned using diagrams to solve problems from my father.  I remember when I was young working in his welding shop how he reacted to customers asking him to do a particular job.  He had a pad and pencil in his pocket and as the customer started to talk, my dad would thrust the pad and pencil toward the customer.  Many of the diagrams were rather crude but my father was able to discern the scribble and create the item to the satisfaction of his client.

I recently asked my dad what he enjoyed about his job.  He told me that the challenge of solving a new problem . . . something he had never seen.  I know that the thrill of solving a hard problem continually brings me back to mathematics.  That success does not happen often.  I try to keeping pushing the limits of what I can solve.