helixmodel copy

"It is of course not surprising that, in these days of short cuts, there should have arisen a movement to get rid of Euclid and to substitute a “royal road to geometry”; the marvel is that a book which was not written for schoolboys but for grown men should have held its own as a school-book for so long… 

It was with reference to such a danger that Dionysius Lardner wrote in 1846:

 “Euclid once superseded, every teacher would esteem his own work the best, and every school would have its own class book. All that rigour and exactitude which have so long excited the admiration of men of science would be at an end. These very words would lose all definite meaning. Every school would have a different standard; matter of assumption in one being matter of demonstration in another; until, at length, GEOMETRY, in the ancient sense of the word, would be altogether frittered away or be only considered as a particular application of Arithmetic and Algebra.” 

It is, perhaps, too early yet to prophesy what will be the ultimate outcome of the new order of things; but it would at least seem possible that history will repeat itself and that, when chaos has come again in geometrical teaching, there will be a return to Euclid more or less complete for the purpose of standardising once more...

Euclid’s work will live long after all the text-books of the present day are superseded and forgotten. It is one of the noblest monuments of antiquity…"

Sir Thomas L. Heath - 'Euclid - The Thirteen Books of the Elements' Vol I ‘preface’ Nov 1908

I would heartily concur with Sir Thomas Heath’s prophetic observation and Dionysius Lardner's 1846 statement regarding the dangerous confusions and misunderstandings that the abandonment of Euclid will lead us toward. At the time of his writing Heath can have had no conception that the chaos he prophesied in mathematics was likely to lead us into quite such an all consuming state of scientific, cultural, and educational dystopia.

The ancient practice of ‘geometry' that many people find so incredibly dry and dull, actually served a key purpose of opening and exercising the mind in an incredibly stringent manner - similar to that which today we might ascribe to the good of physical exercise on the body.

To those biochemist’s who question the importance of geometry and place all their emphasis on the chemistry of molecules I can but press them to contemplate the spacial illustration on the cover of one of their own bibles(below). The element or perhaps I should say atom, is, by its very nature a ‘monad’, and compound groups of monads create molecules of both 2 and 3-dimensional geometric space. Is it so unreasonable to argue that both the proportion’s and regularity exhibited by this supermolecule are in part accounted for by geometric shape and not only the chemical attractions of its parts.   

Scan 1

Furthermore, if geometry really doesn’t play a part in the overall architecture of molecules and supermolecules I would ask how it is that so many viruses acurately exhibit structural combinations and variations of the Platonic solids.


Tetrahedron      -      Octahedron      -     Cube      -      Icosahedron      -      Dodecahedron

Zika Virus

Icosahedron & Dodecahedron

zikavirus copy


Yellow Fever Virus



Cowpea Mosaic Virus



Foot & Mouth Virus

Icosahedron & Dodecahedron

foot&mouthvirus copy2

Nematode Orsay Virus

Truncated Icosahedron


Grouper Nervous Necrosis Virus

Truncated Icosahedron

GrouperNervousNecrosisvirsus copy 2
GrouperNervousNecrosisvirsus copy

Polio Virus

Icosahedron & Dodecahedron

poliovirus copy

Noro Virus



West Nile Virus


Human Papillova Virus

Truncated Icosahedron

Platonic Solids

curtis 1490 med hr