The aim of this activity is to explore the geometry underlying the emblems of the Tokyo 2020 emblems shown above.[br]Both are made using a tessellation of the regular dodecagon with three kinds of rhombi. Then, each rhombus is replaced by the rectangle joining the midpoints of its edges. Below you have two applets to produce each of these emblems.[br][b]How does it work ?[/b][br]By dragging the green points on the grid in the dodecagon and rotating them with the circular point, try to tessellate the dodecagon (without the white hole) with these three kinds of pieces.[br]With this applet you can show the [url=https://en.wikipedia.org/wiki/Varignon%27s_theorem]Varignon[/url] rectangle inside each rhombus by setting the opacity (blue) at max level and lowering that of the rhombi (pink).

The Tokyo Olympics 2020 emblems are based on this construction.[br][br]Tokyo 2020 emblems :[br][url=https://olympics.com/tokyo-2020/en/games/emblem/]https://olympics.com/tokyo-2020/en/games/emblem/[br][br][/url]See this geogebra applet to understand the emblem for the paralympics :[br][url=https://www.geogebra.org/m/fhqxvgpj]https://www.geogebra.org/m/fhqxvgpj[br][/url][br]See this article for more math about these emblems (spoiler)[br][url=https://archive.bridgesmathart.org/2017/bridges2017-423.pdf]https://archive.bridgesmathart.org/2017/bridges2017-423.pdf[/url][br][br]Checkerboard Patterns with Black Rectangles (spoiler)[br][url=https://www.dmg.tuwien.ac.at/geom/ig/publications/checkerboard/checkerboard.pdf]https://www.dmg.tuwien.ac.at/geom/ig/publications/checkerboard/checkerboard.pdf[/url]