Regular octagon


  • Webster's Revised Unabridged Dictionary
    • Regular octagon one in which the sides are all equal, and the angles also are all equal.
    • ***


In literature:

The octagon is nine hundred and fifty feet in diameter and nearly regular in shape.
"The Prehistoric World" by E. A. Allen
It is a regular octagon in shape.
"Bell's Cathedrals: Chichester (1901)" by Hubert C. Corlette
A regular octagon is regular, though an octagon in general is no more regular than any other figure.
"The Atlantic Monthly, Volume 5, No. 28, February, 1860" by Various
These sockets are arranged in the form of a regular octagon, with the ninth in the middle, and are numbered consecutively from one upwards.
"The New Gresham Encyclopedia. Vol. 1 Part 3" by Various
Make the octagon as regular as possible.
"The Century Cook Book" by Mary Ronald

In science:

In order to illustrate what an eigenfunction for the regular octagonal group does look like, we have computed one such eigenfunction following the method exposed in .
Hyperbolic planforms in relation to visual edges and textures perception
Theorem 1.1 When s is irrational, ∆s is a ful l measure set consisting entirely of squares and semi-regular octagons.
The Octagonal PET II: The Topology of the Limit Sets
Say that an extended pyramid of size K is the union of polygons obtained by taking the outer squares in each row and chopping off the corners so as to leave semi-regular octagons.
The Octagonal PET II: The Topology of the Limit Sets
At each of these vertices, the adjacent edge of Oj makes an acute angle with the bottom edge of Xs . (The angle is π/4.) Since the ∆s consists of an open dense (in fact full measure) set of squares and semi-regular octagons, every neighborhood of the two vertices in question must intersect infinitely many tiles of ∆s .
The Octagonal PET II: The Topology of the Limit Sets
If K is a triangle, then two of the vertices v1 and v2 of K have acute angles. (The angle is π/4.) These vertices must be accumulation points of infinitely many tiles, because all the tiles are squares and semi-regular octagons.
The Octagonal PET II: The Topology of the Limit Sets
MR 1362251 (97c:11048) John Smillie and Corinna Ulcigrai, Geodesic flow on the Teichm¨ul ler disk of the regular octagon, cutting sequences and octagon continued fractions maps, Dynamical numbers—interplay between dynamical systems and number theory, Contemp.
Distribution of approximants and geodesic flows
MR 2762132, Beyond Sturmian sequences: coding linear trajectories in the regular octagon, Proc.
Distribution of approximants and geodesic flows

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