|
A megagon is a polygon with 1 million sides (mega-, from the Greek μέγας megas, meaning "great").〔〔Dugopolski, Mark, ''(College Algebra and Trigonometry )'', 2nd ed, Addison-Wesley, 1999. Page 505. ISBN 0-201-34712-1.〕 Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle. == Regular megagon== A regular megagon is represented by Schläfli symbol and can be constructed as a truncated 500000-gon, t, a twice-truncated 250000-gon, tt, a thrice-truncaed 125000-gon, ttt, or a six-fold-truncated 15625-gon, tttttt. A regular megagon has an interior angle of 179.99964°.〔Darling, David J., ''(The universal book of mathematics: from Abracadabra to Zeno's paradoxes )'', John Wiley & Sons, 2004. Page 249. ISBN 0-471-27047-4.〕 The area of a regular megagon with sides of length ''a'' is given by : The perimeter of a regular megagon inscribed in the unit circle is: : which is very close to 2π. In fact, for a circle the size of the Earth's equator, with a circumference of 40,075 kilometres, one edge of a megagon inscribed in such a circle would be about 40 meters long. The difference between the perimeter of the inscribed megagon and the circumference of this circle comes to less than 1/16 millimeters.〔Williamson, Benjamin, ''(An Elementary Treatise on the Differential Calculus )'', Longmans, Green, and Co., 1899. Page 45.〕 Because 1000000 = 26 × 56, the number of sides is not a product of distinct Fermat primes and a power of two. Thus the regular megagon is not a constructible polygon. Indeed, it is not even constructible with the use of neusis or an angle trisector, as the number of sides is neither a product of distinct Pierpont primes, nor a product of powers of two and three. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「megagon」の詳細全文を読む スポンサード リンク
|