Navidezni prehod Venere preko Sončeve ploskve 6.6.2012 Objavljeno 6. junija, 2012 , Vinc Velika Plešivica (45°31′N 15°18′E / 45.517°N 15.3°E), 6.6.2011 ob 5:45, fotoaparat Nikon, objektiv Tamron 80-300mm Tele-Macro, filter 5,25″ računalniška disketa.
Any regular poyogln can be drawn using a straightedge, compass, and protractor. In ancient Greece, it was the custom to attempt to draw regular poyoglns using only a straightedge and compass. Since the Mira is equivalent to a compass for many of its functions, we shall also include the Mira. Gauss found that any regular poyogln of n sides can be constructed with an unmarked ruler and a compass if all of the following conditions are met:Each odd factor of n is unique.Each odd factor of n is prime.Each odd factor of n is of the form2^2 k + 1, for some integer kThis expression takes on the following values for different substitutions for k.k 0 1 2 3 4 52^2 k + 1 3 5 17 257 65537 4294967297Of the six numbers shown, all but the last are prime. Therefore, the numbers 3, 5, 17, 257, and 65537 can all be factors of n, where n is the number of sides of a regular poyogln. However, there can be no other odd factors of n.It would be possible to construct a regular 60-sided poyogln with a compass and a straightedge, since the only odd factors of 60 are 3 and 5, and each different odd factor is unique. On the other hand, it is impossible to construct a regular 100-sided poyogln with a compass and a straightedge, since 100 has more than one factor of 5. A 21-sided regular poyogln cannot be constructed with compass and straightedge because 21 has an odd factor of 7, which is not in the table above. The values of n less than 100 for which a regular n-sided poyogln can be constructed using only a compass and straightedge are listed below:3 4 5 6 8 10 12 15 16 17 20 2430 32 34 40 48 51 60 64 68 80 85 96If a regular poyogln has the number of its sides other than in the above list, it can be constructed by using a protractor in addition to the compass and straightedge. In each case, a circle is drawn, the circle is divided into a number of arcs equal to the number of sides of the regular poyogln, and the endpoints of the arcs are connected together with segments. To construct a regular nonagon (9 sides) mark off 40 degrees of arc around the circle for each side and connect the mark