Building A Personal Geometric/Algebraic Lexicon
These materials help students systematically develop a "translation" dictionary
between the languages of geometry and symbolics. Students are urged
to keep a small notebook with key "words" or concepts that have exact counterparts
in both algebra and geometry - a figure on the left facing page and the
corresponding formula on the right. For example, vector sums algebraically
are obtained by adding like cartesian coordinates, but geometrically correspond
to "tips-to-tails" addition of arrows. This connection is an important
building block throughout the course such as when we build the parametrization
of an epicycloid from two rotating vectors. (See the vector
geometry section.) Text Section 2.08 starts the Lexicon
in the form of Mathematica commands that draw the geometric side
of the lexicon from the algebraic side. Computing can help build
this translation skill by having students add to the eLexicon with simple
general commands.
Converted by Mathematica
May 7, 2001