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The pentagon was Archimedes' first attempt to "square the circle." The calculations are shown here.

A pentagon is a five-sided polygon used to rule the world. Commonly, the term "pentagon" may or may not be used to refer to things pertaining to the White House.

Five pentagons can be arranged around an identical pentagon to form the first iteration of a "pentaflake," which itself has the shape of a pentagon with five triangular wedges removed. You will not need to know this for the final exam, though - so don't bother taking notes.

In a very important work of modern literature, Euclid showed how to inscribe a regular pentagon in a circle. Ptolemy also gave a ruler and compass construction for the pentagon in his epoch-making work The Almagest. While Ptolemy's construction has a simplicity of 16, a geometric construction using Carlyle circles can be made with the geometrography symbol π, which has even more simplicity (See diagram PEN15, to the right). By the way, you WILL need to know that for the test.

Geometric pentagons[edit]

"Ten-hut! We will now learn to field strip, clean and reassemble a standard, Army-issue Pentagon."

Okay, listen up, I'm only going through this once and I want you to save all your question asking for the end of my little presentation - that includes you, Krausman!

Do not confuse a pentagon with a pentagram or pentacle. Pentagrams are for heavy metal deviants and little sissy goth boys, while pentacles are for hippies. If I see any of you ugly dogfaces playing with either of these, I'll have you tossed out of the service, and you can go back to playing tea-parties with your dolls in your little pink cubby houses, you got that?

First, carefully unscrew the wingnuts holding the upper left hand line, using a counterclockwise motion. COUNTERCLOCKWISE, stupid! Opposite to the way Mickey's big hand goes!

Once this line is gone, you will find that the lower left hand line snaps out, allowing you to grab the bottom...

Did I say something fucking funny, Rodriguez? Huh? Do I look like a comedian? Can I borrow some of your lipstick to paint me a

fucking clown smile

? Drop and gimme fifty, maggot!!! You're nothing but a candy-ass college kid to me, buddy!

The U.S. Goverment spent 1.4 billion dollars to put this sign up for terrorist prevention.

Once the bottom has been cracked, the righthand lines may be detatched by means of a standard army issue lugwrench. You may as well get used to this ladies. Tomorrow, you're going to do it blindfolded.

Pentagon power[edit]

The Pentagon (also known as The Pictogon) was built during World War III in Washington DC, and contains the principle HQ of the United States Department of Defense. Prior to that, the United States War Office was based in a series of temporary structures - a secret location in caves beneath an undisclosed mountain, on a satellite orbiting the Earth, in a bunker south of 8-Mile, Detroit, for a brief period in a network of embassies around the world, once in a comandeered alien aircraft vessel, and most recently in a watchtower on the surface of the moon. None of these locations however, proved adequate.

The Pentagon is a massive erection six point six million (6,600,000) square feet, and to date no other countries have been able to match this feat of American engineering! Attempts to one-up the Pentagon only existed up to the 1970s, because all attempts to do so ended in bankruptcy for the opposing government party... What's that Floondekker? I missed 9/11? I did not miss it, you good for nothing faggot! Oh, you actually are gay are you? Sorry, that was so insensitive of me. Where was I... I did not miss it, you goddamned butch breeder! I deliberately skipped over it! - You see, we in the USA are a forward looking people! We do not dwell in the tragedies of the past - we actively work to create the tragedies of the future! Remember the Marine Corps motto - "If you remember the mistakes of the past, the terrorists have already won."

Now drop and disassemble!!

You pitiful excuse for a US Marine, do you even know what a Kepler-Poinsot solid is? Huh? You call that up there a geometric definition? A Kepler-Poinsot solid is a regular non-convex polyhedron, all the faces of which are identical regular polygons and which has the same number of faces meeting at all its vertices! You're on Kitchen Detail for a month, you worthless maggot! Maybe some study of the external topography of potatoes will teach you to have some more respect for regular polyhedra!

Drawing a pentagon[edit]

Construction of the Rhombicuboctahedron finished in 1979, but was taken over by an alien posing as a media icon in 2008.

The following elegant construction for the pentagon is from an extremely well-known architectural engineer (1893). Given a point, a circle may be constructed of any desired radius, and a diameter drawn through the center. The diameter perpendicular to the original diameter may be constructed by finding the perpendicular bisector. Call the upper endpoint of this perpendicular diameter X. For the pentagon, find the midpoint of it and call it a beaver. Draw two circles, and bisect them, calling the intersection point with the peaks Mount Nippoluses. Draw a line parallel to this, and the first two points of the pentagon should be equally spread... just see diagram PEN15 if you get confused.