# Megagon

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:

$2000000 \sin\frac{\pi}{1000000}$

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. ^ a b 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.
2. ^ Dugopolski, Mark, College Algebra and Trigonometry, 2nd ed, Addison-Wesley, 1999. Page 505. ISBN 0-201-34712-1.
3. ^ Williamson, Benjamin, An Elementary Treatise on the Differential Calculus, Longmans, Green, and Co., 1899. Page 45.
4. ^ McCormick, John Francis, Scholastic Metaphysics, Loyola University Press, 1928, p. 18.
5. ^ Merrill, John Calhoun and Odell, S. Jack, Philosophy and Journalism, Longman, 1983, p. 47, ISBN 0-582-28157-1.
6. ^ Hospers, John, An Introduction to Philosophical Analysis, 4th ed, Routledge, 1997, p. 56, ISBN 0-415-15792-7.
7. ^ Mandik, Pete, Key Terms in Philosophy of Mind, Continuum International Publishing Group, 2010, p. 26, ISBN 1-84706-349-7.
8. ^ Kenny, Anthony, The Rise of Modern Philosophy, Oxford University Press, 2006, p. 124, ISBN 0-19-875277-6.
9. ^ Balmes, James, Fundamental Philosophy, Vol II, Sadlier and Co., Boston, 1856, p. 27.
10. ^ Potter, Vincent G., On Understanding Understanding: A Philosophy of Knowledge, 2nd ed, Fordham University Press, 1993, p. 86, ISBN 0-8232-1486-9.
11. ^ Russell, Bertrand, History of Western Philosophy, reprint edition, Routledge, 2004, p. 202, ISBN 0-415-32505-6.

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