Geometry, the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space, is one of the oldest branches of mathematics; it has evolved from the study of flat surfaces (plane geometry) and rigid three-dimensional objects (solid geometry) to analyzing the most abstract thoughts and images which might be represented and developed in geometric terms. The main branches of geometry are Euclidean Geometry, Analytic Geometry, Projective Geometry, Differential Geometry, Non-Euclidean Geometries, and Topology.
What
can entrepreneurs learn from each of these six branches of geometry?
Analytic geometry was initiated by the French mathematician René Descartes (1596–1650), who introduced rectangular coordinates to locate points and to enable lines and curves to be represented with algebraic equations. It is that branch of Algebra in which the position of the point on the plane can be located using an ordered pair of numbers called as Coordinates. For this reason, it is also called Coordinate geometry or the Cartesian geometry.
The increased interest in curves that resulted in part from the recovery and Latin translation of the classical treatises of Apollonius, Archimedes, and Pappus was an important trend that contributed to the development of analytic geometry. The earlier works of other German and Italian mathematicians was also consolidated by another mathematician Viète into the development of the algebraic tools and practices.
The work of Pappus and Viète in
the development of analytic geometry have a great relevance to some effective
practices (nay tools!) employed by all successful entrepreneurs.
The use of business
connections – networks – have been researched well and is acknowledged as a
powerful tool that can catalyze the entrepreneurial journey. That journey seeks to
build a bridge from known customer needs to unknown profitability scenarios.
Equating these with the help of production and distribution factors is certainly
augmented by use of the “connections”.
Successful businessmen intrinsically
seek to answer the unknown beginning variable (profitability) by using well-understood parameters (market demand, production and distribution factor
efficiencies), proceeding to link them all in multiple ways that will
help them derive the desired value for the unknown.
Analytic geometry has
parallels to what the entrepreneur does!
Pappus had employed an
analytic method for the discovery of theorems and the construction of problems;
in analysis, by contrast to synthesis, he postulated that one can proceed from
what is sought until one arrives at something known.
By laying down an equation among known and unknown magnitudes in an arithmetic problem, and then solving for the unknown, one was, Viète reasoned, following an “analytic” procedure. Viète innovated by introducing the concept of algebraic variable, as well as the concept of parameter. This innovation, considered by historians of mathematics to be a major conceptual advance in algebra, facilitated the study of the symbolic solution of algebraic equations and led to the creation of the first conscious theory of equations.
Unknowns, Parameters and Equations - the basis of much of analytic geometry - have seamlessly infiltrated much of the toolkits of today's entrepreneurs!
