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First of all, when trying to collect
the pieces of an ideal triangle geometry it will be required to draw the
limits of the concepts we will be working with. After having a look at
the catalogues by Clark
Kimberling or by Edward
Brisse, we become aware of the variety of the elements and their nearly
unlimited power of combining and transforming.
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For this TTW presentation, I have selected
objects with an own name or the ones without a name but numbered in the
Encyclopaedia of The Triangle Centres, those we have any interesting properties
beyond their definition. The objects dealt with at TTW nearly reach a number
of 260.
-
Some areas are fully discarded, as the
Triangle Cubics or the Quadrilaters; you can see, about them, the webs
of Bernard
Gibert and Chris
van Tienhoven respectively.
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As well as the definitions, TTW contains
an anthology of the properties of its objects, called the Results. The
collection of the Results is now at an advanced stage and outnumbers 2000
- and it will increase, but slowly.
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Some of the Results are alternate definitions.
The author not even knows why the given definitions were selected and does
not guarantee a coherent criterion on this matter.
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