Megagon
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| Megagon | |
|---|---|
 Even if drawn at the size of the Earth, a regular megagon would be very difficult to distinguish from a circle. | |
| Type | Regular polygon |
| Edges and vertices | 1000000 |
| Schläfli symbol |
{1000000} t{500000} |
| Coxeter diagram |
     |
| Symmetry group | Dihedral (D1000000) |
| Internal angle (degrees) | 179.99964° |
| Properties | convex, cyclic, equilateral, isogonal, isotoxal |
A megagon is a polygon with 1 million sides (from mega-).[1][2]
Properties
A regular megagon has an interior angle of 179.99964°.[1]
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, with a circumference of 40,075 kilometres, the difference between the perimeter of the megagon and the circumference of the circle comes to less than 1/16 millimeters.[3]
Philosophical application
As with René Descartes' example of the chiliagon, the million-sided polygon has been used as an illustration of a well-defined concept that cannot be visualised.[4][5][6][7][8][9][10]
The megagon is also used as an illustration of the convergence of regular polygons to a circle.[11]
References
- ↑ 1.0 1.1 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.
- ↑ Dugopolski, Mark, College Algebra and Trigonometry, 2nd ed, Addison-Wesley, 1999. Page 505. ISBN 0-201-34712-1.
- ↑ Williamson, Benjamin, An Elementary Treatise on the Differential Calculus, Longmans, Green, and Co., 1899. Page 45.
- ↑ McCormick, John Francis, Scholastic Metaphysics, Loyola University Press, 1928, p. 18.
- ↑ Merrill, John Calhoun and Odell, S. Jack, Philosophy and Journalism, Longman, 1983, p. 47, ISBN 0-582-28157-1.
- ↑ Hospers, John, An Introduction to Philosophical Analysis, 4th ed, Routledge, 1997, p. 56, ISBN 0-415-15792-7.
- ↑ Mandik, Pete, Key Terms in Philosophy of Mind, Continuum International Publishing Group, 2010, p. 26, ISBN 1-84706-349-7.
- ↑ Kenny, Anthony, The Rise of Modern Philosophy, Oxford University Press, 2006, p. 124, ISBN 0-19-875277-6.
- ↑ Balmes, James, Fundamental Philosophy, Vol II, Sadlier and Co., Boston, 1856, p. 27.
- ↑ Potter, Vincent G., On Understanding Understanding: A Philosophy of Knowledge, 2nd ed, Fordham University Press, 1993, p. 86, ISBN 0-8232-1486-9.
- ↑ Russell, Bertrand, History of Western Philosophy, reprint edition, Routledge, 2004, p. 202, ISBN 0-415-32505-6.
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