You can define: A star is a figure which generally consists
of a convex polygon with triangles on its sides.
1st possibility
2nd possibility: You take a regular polygon and reflect the basic triangles of the polygons on a side. 3rd possibility: You take a regular polygon with n corners and turn it around 180/n. Origin and image together form a star. 4th possibility: Give a polygon and draw special diagonals. They form stars. Regular polygons form stars with rich symmetries. The pentagram and the hexgram are the simlest examples. 5th possibility: You take a regular polygon and set isosceles triangles on the sides, which have a large height compared with the basic side. The polygon, which has the points, can degenerate into a circle (far right). 6th possibility: You take any polygon and set arbitrary triangles on the sides.
The first eight pointed star is a silhouette.
The second star is Froebel's star, which is made from four strips. This is explained on another site of my homepage. Origami-Flowers
:a
=1/2*sqr(5)-1/2. This is about 0.62.
The well known German TV journalist Professor Heinz Haber described the golden ratio as follows in the 1960s.
The pentagram is called also Drudenfuss or witch star. This is a reference to a certain topic you can investigate on the internet. I recommend the picture directory of google.com and the search word "pentagram". Sometimes you think you are in the Middle Ages. (This is the same with the hexagram in the next chapter.) My contribution can be: I saw a pentagram at the door of the combined horse/cow stable of a farm in the 1950s. It should keep away diseases from the cattle.
String Game
Those who know the 3d view can see the star three-dimensional. The Kepler-Poinsot Polyhedra
There are three-dimensional stars, which hang in the hall of many houses in December. They have a bulb in the centre so they shine from inside. They are called Sternlampions (=star Chinese lanterns) in German and Moravian stars in English. Among them the "Original Herrnhuter Weihnachtsstern" (Herrnhut Star) is known all over the world.
near Here in Lippe, a district of North Rhine-Westphalia there are many half-timbered houses with a big hall, so that horse and carriage could drive in in former times. Usually there is an inscription outside above the hall with the star (here seven-pointed) of "Burg Sternberg" on one side and on the other side the "lippische Rose" similar to a star.
Origin: http://www.lippe.de/new/allgemein/show.php3?s=3&n=wappen You also find the star and the rose at the historic town hall (1546) of my hometown Bad Salzuflen.
German HERRNHUTER STERNE GMBH
Joachim Mohr
Lena Pauline Hönisch Jurado (besserbasteln.de)
Martin Marheinecke
origamiseiten.de
Wikipedia
English BETSY ROSS
Eric W. Weisstein (World of Mathematics)
Harvey D. Heinz
Suzanne Alejandre and Mutsumi Suzuki
Wikipedia
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