Feb 2024 - Euclidean Geometry and Innovation!

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 analysing 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?

Euclidean Geometry which greatly influenced the domination of axiomatic-deductive methods in analytical processes for many centuries has some interesting insights that can help entrepreneurs mainstream innovation across all aspects of their ventures. How? 

                                  

There has always been innovation even without the aid of current methodologies and theories.  A century ago, Henri Ford was able to identify a need outside of the physical context of horses, and innovate a new means of affordable transportation, the Ford Model-T.

The allure of the innovation process lies in its transformative power, turning a mere idea into a tangible and successful reality! The process is all about exploring new market applications, introducing ground breaking methods and diverse sources of supply, as well as reshaping the organizational structures to creating and delivering innovative goods and services.

The axiomatic-deductive process of Euclidean geometry greatly enhances the application of the above-mentioned distinctively central aspects to the process of innovation.

Successful entrepreneurship demands constant innovative efforts across four domains:

customer – what are the current and emerging customer needs;

function -   what functions to be met;

physical – how can these be achieved vis-à-vis the constraints - what are the design parameters;

process – how to build for and deliver to the customer.

It is evident that a logical deductive approach from some core elementary propositions offers a strong building block for success in such efforts.

Three core elementary propositions - the axioms – are the foundational precursors for initiating and maintaining any robust innovation process.

(a) the independence of core functional requirements and the bare-minimization of functional information needs,

(b) the structures, domains and hierarchical framework in which the innovative solutions can develop and

(c) a process for decomposing the solutions from abstract ideas to detailed features that can be integrated into deliverable components of a product or service.

Building on these three elements, entrepreneurs can deduce pathways across each of the four domains and build innovative products and services.