D'Arcy Thompson and Mathematics
Alice Gowenlock and Indre Tuminauskaite
Correspondence about Coordinate Transformations
One of the most recognisable and celebrated parts of On Growth and Form are the Coordinate Transformations of the forms of similar animals.
However, D'Arcy did not invent it without help from his correspondents, which included mathematicians, scientists and artists. Marshall, a mathematician and St Andrews alumnus,
helped Thompson with this part of the book and many fundamental questions were discussed in their correspondence.
Paleontologist and keen Artist, Heilmann, provided many of the drawings seen in On Growth and Form, whilst Neville contributed by writing to Thompson about the mathematics of 3D coordinates.
For more information about coordinate transformations click THIS LINK.
For a more detailed mathematical explanation of the method click THIS LINK.
Thompson tried to improve his knowledge about coordinate transformations prior to writing the book.
He attempted to learn about 3D coordinate transformations and admitted that it would be advantageous to do so as it is the 3D form of the object which should be understood, not just the drawing. D'Arcy also states that there are limitations in dealing with transformations solely in 2D-coordinates.
However, only a short subsection of the chapter on transformations in On Growth and Form mentions 3D coordinates.