Tetracontaoctagon
In geometry, a tetracontaoctagon (or tetracontakaioctagon) is a forty-eight-sided polygon or 48-gon. The sum of any tetracontaoctagon's interior angles is 8280 degrees.
Regular tetracontaoctagon
The regular tetracontaoctagon is represented by Schläfli symbol {48} and can also be constructed as a truncated icositetragon, t{24}, or a twice-truncated dodecagon, tt{12}, or a thrice-truncated hexagon, ttt{6}, or a fourfold-truncated triangle, tttt{3}.
One interior angle in a regular tetracontaoctagon is 1721⁄2°, meaning that one exterior angle would be 71⁄2°.
The area of a regular tetracontaoctagon is: (with t = edge length)
The tetracontaoctagon appeared in Archimedes' polygon approximation of pi, along with the hexagon (6-gon), dodecagon (12-gon), icositetragon (24-gon), and enneacontahexagon (96-gon).
Construction
Since 48 = 24 × 3, a regular tetracontaoctagon is constructible using a compass and straightedge. As a truncated icositetragon, it can be constructed by an edge-bisection of a regular icositetragon.
Enneacontagon
In geometry, an enneacontagon or enenecontagon (from Ancient Greek ἑννενήκοντα, ninety) is a ninety-sided polygon or 90-gon. The sum of any enneacontagon's interior angles is 15840 degrees.
A regular enneacontagon is represented by Schläfli symbol {90} and can be constructed as a truncated tetracontapentagon, t{45}, which alternates two types of edges.
Regular enneacontagon properties
One interior angle in a regular enneacontagon is 176°, meaning that one exterior angle would be 4°.
The area of a regular enneacontagon is (with t = edge length)
and its inradius is
The circumradius of a regular enneacontagon is
Since 90 = 2 × 32 × 5, a regular enneacontagon is not constructible using a compass and straightedge, but is constructible if the use of an angle trisector is allowed.
Symmetry
The regular enneacontagon has Dih90dihedral symmetry, order 180, represented by 90 lines of reflection. Dih90 has 11 dihedral subgroups: Dih45, (Dih30, Dih15), (Dih18, Dih9), (Dih10, Dih5), (Dih6, Dih3), and (Dih2, Dih1). And 12 more cyclic symmetries: (Z90, Z45), (Z30, Z15), (Z18, Z9), (Z10, Z5), (Z6, Z3), and (Z2, Z1), with Zn representing π/n radian rotational symmetry.
Heptadecagon
In geometry, a heptadecagon is a seventeen-sided polygon or 17-gon.
Regular heptadecagon
A regular heptadecagon is represented by the Schläfli symbol {17}.
Construction
As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon (that is, one that can be constructed using a compass and unmarked straightedge): this was shown by Carl Friedrich Gauss in 1796 at the age of 19. This proof represented the first progress in regular polygon construction in over 2000 years. Gauss's proof relies firstly on the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions, and secondly on his proof that this can be done if the odd prime factors of n are distinct Fermat primes, which are of the form 
. Constructing a regular heptadecagon thus involves finding the cosine of 
in terms of square roots, which involves an equation of degree 17—a Fermat prime. Gauss' book Disquisitiones Arithmeticae gives this as (in modern notation):
List of Invader Zim characters
Invader Zim is an American animated television series created by Jhonen Vasquez and originally aired on Nickelodeon. The recurring cast includes long-term Nickelodeon voice actors Richard Steven Horvitz and Rodger Bumpass, with live-action television actors Kevin McDonald (The Kids in the Hall) and John de Lancie (Star Trek: The Next Generation). Vasquez voices parts in the show. The show was cancelled early in its run and some episodes were unfinished. The show ran for two seasons before its cancellation.
Main characters
Zim
Zim (voiced by Richard Steven Horvitz,Billy West in the pilot and Melissa Fahn as a smeet in "Parent Teacher Night") is an incompetent Irken invader who is foul-tempered, overzealous, impulsive, megalomaniac, and convinced of his own greatness. He dreams of regaining his leaders' trust by taking part in Operation Impending Doom II, so Zim is assigned to Earth, a planet which the Almighty Tallest believe has little to no chance of existing. However, against all odds, Zim makes it to Earth and establishes a base on a fake conquest mission. Because of his very small stature, Zim disguises himself as a human child using a hairpiece to cover his antennae and contact lenses to make his eyes look normal.
Tak (function)
In computer science, the Tak function is a recursive function, named after Ikuo Takeuchi (竹内郁雄). It is defined as follows:
This function is often used as a benchmark for languages with optimization for recursion.
tak() vs. tarai()
The original definition by Takeuchi was as follows:
tarai is short for tarai mawashi, "to pass around" in Japanese.
John McCarthy named this function tak() after Takeuchi.
However, in certain later references, the y somehow got turned into the z. This is a small, but significant difference because the original version benefits significantly by lazy evaluation. Though written in exactly the same manner as others, the Haskell code below runs much faster.
You can easily accelerate this function via memoization yet lazy evaluation still wins.
The best known way to optimize tarai is to use mutually recursive helper function as follows.
Here is an efficient implementation of tarai() in C:
Note the additional check for (x <= y) before z (the third argument) is evaluated, avoiding unnecessary recursive evaluation.
Tak (town)
Tak is a town (thesaban mueang) in north-west Thailand, capital of the Tak Province and the Tak district. As of 2005 the town had a population of 19,900 and an area of 7.27 km². It covers the tambon Rahaeng, Nong Luang, Chiang Ngoen, and Hua Diat. It is on the Ping River, 418 km north-north-west of Bangkok.
Geography
Tak is on the Ping River, which runs from north to south through the town. While the land to the east is fairly flat, the Tenasserim Hills and Dawna Range lie to the west.
Climate
Tak has a tropical savanna climate (Köppen climate classification Aw). Winters are dry and very warm. Temperatures rise until April, which is very hot with the average daily maximum at 38.5 °C (101.3 °F). The monsoon season runs from May through October, with heavy rain and somewhat cooler temperatures during the day, although nights remain warm.
Transportation
Route 105, through Mae Sot, forms one of two major transnational roads through the Tenasserim Hills to Burma. Route 1, also known as the Phahonyothin Road, passes through Tak. On the north side it leads to Lampang, Chiang Rai, and the border with Burma at Mae Sai. On the south side it leads to Kamphaeng Phet, Nakhon Sawan, and Bangkok. Route 12 leads east to Sukhothai, Phitsanulok, Chum Phae, Khon Kaen, Kalasin, and the border with Laos at Mukdahan.
Lie
A lie is a statement that is known or intended by its source to be misleading, inaccurate, or false. The practice of communicating lies is called lying, and a person who communicates a lie may be termed a liar. Lies may be employed to serve a variety of instrumental, interpersonal, or psychological functions for the individuals who use them. Generally, the term "lie" carries a negative connotation, and depending on the context a person who communicates a lie may be subject to social, legal, religious, or criminal sanctions. In certain situations, however, lying is permitted, expected, or even encouraged. Because believing and acting on false information can have serious consequences, scientists and others have attempted to develop reliable methods for distinguishing lies from true statements.
Types
Bad faith
As defined by Sartre, "bad faith" is lying to oneself. Specifically, it is failing to acknowledge one's own ability to act and determine one's possibilities, falling back on the determinations of the various historical and current totalizations which have produced one as if they relieved one of one's freedom to do so.
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