File:Academ Reflections with parallel axis on wallpaper.svg

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Summary

Description
English:
A given translation   may be decomposed into two reflections with parallel axis:  two lines here named  Δ 1  and  Δ 2 If one of the reflections    or    is given, the axis of which is perpendicular to the direction of   the other reflection is unique which fulfills the equality:    There is a unique translation   that transforms Δ 1  into  Δ 2 then     The trapezoid ABCD  is part of the tiling of the top of the drawing, where the triangular elements are green and yellow. Across the line Δ 1 the tiling and ABCD  are transformed by the reflection   the trapezoid ABCD  becomes  A 1 B 1 C 1 D 1 and the elements of the tiling become blue and gray as in this image or this other one. The image of ABCD  through the translation   is the trapezoid  A 2 B 2 C 2 D 2 that is filled by three elements of the first tiling, one green triangle and two yellow.
 
Date
Source Own work
Author Yves Baelde
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Licensing

Arthur Baelde, the copyright holder of this work, hereby publishes it under the following license:
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Attribution: Arthur Baelde
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Captions

A wallpaper covers a half‑plane of edge Δ1. Its reflection under R1 with respect to Δ1 has other colors. Reflection R1 transforms trapezium ABCD into A1B1C1D1, itself reflection of A2B2C2D2 with respect to Δ2. Δ2 ∕∕ Δ1. U transforms Δ1 into Δ2.

Items portrayed in this file

depicts

15 August 2011

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5ee7e148a37cd9cbc8d3ff96713ed38230054408

4,833 byte

600 pixel

600 pixel

File history

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Date/TimeDimensionsUserComment
current06:43, 27 October 2022600 × 600 (5 KB)Arthur Baelde alternation of two colours of the quadrilateral at each transformation by reflection,  and other improvements 

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