What is a fifty-six angled regular polygon?

Question

I was reading Thrice-Greatest Hermes, Vol. 1 by G.R.S. Mead and he presented a regular polygon that is attributed to the Greek Typhon. He says "The Pythagorics also seem to consider Typhon a daimonic power; for they say that Typhon was produced on the six-and-fiftieth even measure; and again that the power(1) of the equilateral triangle is that of Hades and Dionysus and Ares; that of the square is that of Rhea and Aphroditē and Demeter and Hestia (that is, Hera); that of the dodecagon, that of Zeus; and that of the fifty-six angled regular polygon, that of Typhon—as Eudoxus relates.(2)"

The notes on that entry say

(1) "A “power” in Pythagorean technology is the side of a square (or, perhaps, of any equilateral polygon) in geometry; and in arithmetic the square root, or that which being multiplied into itself produces the square."

(2) "Eudoxus seems to have been Plutarch’s authority for his statements regarding Pythagorean doctrine; cf. vi., lii., lxii. The Typhonic figure might be generated by “sevening” the interior angles of a regular octagon and producing the radii to the circumference of the circumscribed circle, or by “eighting” the interior angles of a regular heptagon."

Does anyone know how this regular polygon is created or what it might look like? I do not know how to go about "sevening" or "eighting" an interior angle. Any help would be appreciated

Answer 1

Construction by ruler and compass construction rules (as the ancient Greeks did) is not possible for the regular heptagon, nor for the regular 56-gon. This result is the Gauss-Wantzel theorem (Gauss 1801, Wantzel 1837). See http://en.wikipedia.org/wiki/Constructible_polygon . Of course such polygons exist. But they cannot be constucted by the restrictive ruler/compass rules.



Here is a picture of a regular 56-gon (link below). There is a small circle at each corner only so you can see where it is, otherwise the figure would appear to just be a circle.



http://i42.tinypic.com/2h7mcy8.jpg

Answer 2

First, I assume we are talking about a two dimensional, regular polygon. Using a straight edge and compass, I do not think 'sevening" is possible but "eighting' is simply dividing the angle in half four times. Using math and a protractor, it is a simple, but tedious, process.

The internal angles of a regular N-gon is equal to 180 degrees - 360 degrees / N. For a 56 sided polygon this would be 356.786 degrees. A circle is 360 degrees so this would look a lot like a circle. Using a CAD or drawing program is your best bet.

Answer 3

polygon 56 angles-->56 sides

unless of very very large sides it looks just like an circle

see this to get an idea of 50 sided.60 sided polygons look like

50 sided http://en.wikipedia.org/wiki/File:Regular_polygon_50.svg

60 sided http://en.wikipedia.org/wiki/File:Regular_polygon_60.svg

Answer 4

It's possible yeah

Answer 5

Thanks for the answers everyone <3