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 here.

For a more detailed mathematical explanation of the method click here (or pdf here)

<i>Human and Chimpanzee skulls</i>
Human and Chimpanzee skulls
<i>Human and Chimpanzee skulls</i>
Human and Chimpanzee skulls

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.


Eric Harold Neville

John Marshall

Alfred North Whitehead



Overview & D'Arcy's Life


On Growth and Form


Heilmann & Shufeldt


Maths of Transformations




D'Arcy and Mathematics


Coordinate Transformations


Logarithmic Spirals


Forms of Cells


Forms and Mechanical Efficiency




Wartime and D'Arcy


The Leg as a Pendulum


Recreational Maths


Fibonacci Sequence




All Correspondence Links

Claxton Fidler


Eric Harold Neville


John Marshall


Alfred North Whitehead


Charles Robert Darling


Peter Guthrie Tait


William Peddie


Geoffrey Thomas Bennett


Dorothy Wrinch


Main Index Biographies Index

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Alice Gowenlock & Indre Tuminauskaite © July 2018
Copyright information
School of Mathematics and Statistics
University of St Andrews, Scotland

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