D’Arcy Thompson explains in the article the inter-relationship between mathematics and form. The study of form may be descriptive or analytical but lacks precision. But when form is defined with respect to mathematics the quality of precision is imbibed.

D’Arcy Thompson goes on to explain the various methods of incorporating mathematical precision into form. The method of study for this article is plotting of the form on co-ordinates of the Cartesian system to generate proportional diagrams. Thompson’s initial intentions were no more than trying to translate the form of a curve into numbers and words. However, the next step he took intrigued most morphologists, as he went on to analyze the deformation of the form on the co-ordinates, as well as, study the transformation the form inscribed in the co-ordinate network. His analyses makes it likely to discover hidden identities by using mathematical synthesis. This method provides the necessary computations and abstractions and moves from static form to the analysis of dynamic forces underlining this form.

This method of co-ordinates became the foundation for D’Arcy Thompson’s theory of morphological transformations. Using this theory he was able to create related forms. He found that if he referred to the same mathematical function in transformed systems of co-ordinates, these identities are of the same ‘genus’ and variation that occurred in the form due to the “law of growth”.

He concluded the article by stating that if an organic form is studied mathematically it offers a better understating of the relationship between species, their deformation and evaluation cycle.

1. What is the scope of error in this method from collection of data, analyzing the data, plotting the data and then creating deformations?

2. Does the data plotting method vary depending in the size and scale of the species?