© copyright 2003 Wayne Roberts. All rights reserved.
See also Eutrigon triads and Co-eutrigon triads for two new Pythagoras-like classes of triangle in Euclidean geometry together with their parametric equations, which logically followed when I applied Scale-structure theory to this 'generic class' or scale structure of hybrid-triangle types.
~WR
Asymmetric symmetries in universal and musical scale structures
A natural 'magnetism' towards the formation of Scale Structures in Nature?
The physical principle of Least Action points to the natural formation of Scale Structures
Music and the generic principle of relativity
The fact that music is notatable reflects its scale structure basis and syntax
Real-time improvisation, spontaneity & interaction in the genre of jazz
Synchronicities between 20th century art & science
Beyond style in art — towards higher-dimensional unity in art
Seurat-Einstein, Monet-Maxwell parallels
Cézanne's late Mont Ste Victoire paintings and the 'Aix' factor of abstraction
Matisse and the music of line and space
Kandinsky: law and the counterpoint of intuitive improvisation in art
Pollock and Minkowski's timelines
Escher: under-recognised genius of 20th cenury art
Brewster's kaleidoscope, Op art, and interactive moiré resonances
An application of scale structure theory to number and geometry
Concerning the need for a revision of foundational concepts like the unit
The scale of 'numbers as shapes' and the so-called square numbers
The pivotal importance of the unit of area in math
Scale structure theory of so-called square numbers
Relative units: the natural 'measure' of Nature's scale structures
The theory applied to the geometry of triangles
The equitriangular unit of area (etu)
The area of an equilateral triangle in etu
The areas of a new class of semi-regular triangles (the eutrigon) in etu
Area of a scalene triangle in etu
Is the dominance of right triangles and squares justified from a scale structure perspective?
'New angles' on triangles and their theorems— the Eutrigon Theorem
Eutrigon Theorem (algebraic form) and the Cosine Rule connection
Completing the scale – co-eutrigons and the
Co-eutrigon Theorem
Introduction to a new in-principle naturalism in artistic practice and composition
Some scale structures now available for syntactical inter-relation in covert scale structure art
Conclusions for the arts and sciences
Towards new ways of representing numbers geometrically
Music's inclusiveness of new and old
Questioning the Fundamental Theorem of Arithmetic
Gallery of selected works by the author
Scale structure within irregular quadrilaterals
Theorem I -
the Eutrigon Theorem
Theorem II -
the Co-eutrigon Theorem
Sotto Voce, a covert scale structure composition in watercolour
Principia, a covert scale structure composition in oil on canvas
The Discreteness of Infinity - watercolour on art-science connections