ManyFolds in Variety
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2006/7/21
「Generalized fish bases defined on ex-ellipses of a triangle:」 study in math
[Some further variations of the fish base: these contain the cases appeared in the preceding article: Generalized fish bases defined on excircles of a triangle as special ones.]
For an arbitrary triangle, there exist (many) 'ex-ellipses': each of which contacts an edge of the triangle and two others at these extended parts. The following example shows isogonal conjugate relations with respect to a triangle and one of those ex-ellipses [(Apollonius)]:
Applying this fact to a given triangle at each of its vertices, then the following diagram/graphic image will be realized:
The diagram includes six local flatly foldable structures at six foci of three ex-ellipses around a given triangle. It consists of two 'circum-triangles' and creases of flatly foldable structures at those vertices - also foci of the ex-ellipses -, so that the above diagram/graphic image can be divided into two diagrams/graphic images as follows:
Corresponding three pairs of generalized fish bases those hold flatly foldable structures:
>> Click each image to see in larger scales <<
2
For an arbitrary triangle, there exist (many) 'ex-ellipses': each of which contacts an edge of the triangle and two others at these extended parts. The following example shows isogonal conjugate relations with respect to a triangle and one of those ex-ellipses [(Apollonius)]:
Applying this fact to a given triangle at each of its vertices, then the following diagram/graphic image will be realized:
The diagram includes six local flatly foldable structures at six foci of three ex-ellipses around a given triangle. It consists of two 'circum-triangles' and creases of flatly foldable structures at those vertices - also foci of the ex-ellipses -, so that the above diagram/graphic image can be divided into two diagrams/graphic images as follows:
Corresponding three pairs of generalized fish bases those hold flatly foldable structures:
>> Click each image to see in larger scales <<
[Last edited: July 26, 2006]
2
投稿者: kaishonashi
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