The Area of a Square

Insert obvious joke here.

The Area of a Square is determined using advanced calculus and rudimentary geometry, and is expressed as a measurement of distance or length with squared units. The use of finding the area of a square is still a mystery and may never be fully realized.

Origin

The origins of the formula for deriving the area of a square come from the work of the German mathematician, Yens Geldemacher, who finally discovered this geometrical mystery in 1939. Geldemacher combined the formula of the area of a circular disc with a formula created by master mathematician Ross Sacco, which Sacco had developed for use in deriving the area of isosceles, arched triangles. By inscribing a circle inside of a square, and summing the area of the square with the four arched triangles, he was able to closely approximate the area within a square to the nearest thousands place.

$\pi r^{2}$ = the area shaded in red. $4(\int _{0}^{r}-{\sqrt {r^{2}+x^{2}}}+r\,dx)$ = the area shaded in blue. It's that fucking simple.

Yens Geldemacher was originally commissioned for the task by Adolf Hitler, the newly elected leader of Germany. Geldemacher worked as one of the Third Reich’s premiere mathematicians. As a member of Hitler’s elite engineering team, he solved many of the problems regarding rocketry, helped create the Enigma code, and almost successfully created a banana that could fire projectile rounds. Yens Geldemacher’s first great discovery, however, was the formula for solving the area of a square.

Formula

Geldemacher’s formula for determining the area of a square is relatively simple and can be calculated using the combined formula shown below:

$\pi r^{2}+4(\int _{0}^{r}-{\sqrt {r^{2}+x^{2}}}+r\,dx)$

The formula took Geldemacher over two years to discover with non-stop research. The discovery came upon him accidently as he was trying to break what he thought was a British secret code, but what actually turned out to be an early variation of a ”Scrabble” board game called “Criss-Crosswords”.

Research done into Geldemacher’s formula has shown that there is perhaps a much simpler method for computing a square’s area, although such a method is still not known. Geometrics speculate that by dividing the square into equal right triangles a closer and more accurate approximation can be attained. To date, all attempts to uncover the truth behind these speculations have caused three math expert’s heads to asplode.

Speculation aside, Geldemacher’s formula is still the only known method for solving the area of a square, and is taught at the University of California Berkeley as a series of Advanced Geometric/Trigonometric Paranormal and Existential Theory courses.

Utility

History of Use

The exact use of the formula is unknown, and it is widely regarded as ‘folly’ by many renowned mathematicians including Yens Geldemacher himself:

“This monstrosity I have created. I do not know what it can do. I regard it as folly.”

~ Yens Geldemacher on his discovery of the area of a square

A few high ranking members of Hitler’s Nazi party believed that if a square were to be designed as to have an area of approximately 666 units of Roman measurement, a portal to hell could be opened. Since the square was still a mystery, and was regarded by many mathematicians as an “enigma”, its use and practicality were questioned. Even so, Geldemacher was commissioned by Hitler himself to oversee the task, believing access to an army of demons would give him a great military advantage, and allow him to have great success with the ladies.

Hitler's demonic army.

Having found the formula for the area of a square, a large construction project for a portal was begun in 1941. However, the portal lacked the necessary “piece” of the Ark of the Covenant prescribed as belonging to King David of the Jews in the late second century B.C. This plot was foiled by the great archaeologist Indiana Jones, in the infamous “Raiders of the Lost Ark” event. The project, missing one of its key components, had its construction efforts ceased by the Fuhrer. It was speculated by Hitler’s peers that, even with the ark, the scheme would not have been a success. It was even regarded as “hair-brained” by Alfred van Seiden of Luftwaffe command. Van Seiden was killed by a firing squad shortly after stating this.

Modern Use

Modern day use is more experimental and analytical than in years past. Beginning in 1987 with Alexander Fruden’s research into this geometrical mystery, the goal of mathematicians became centralized in uncovering a use for the formula, such as x-ray vision goggles and new types of sexual lubricants.

Alexander Fruden looking suprisingly normal.

Fruden Research

Fruden’s early research became involved in the ultimate function or use of Geldemacher’s Formula. Fruden scrutinized the formula from multiple angles and even went as far as to “break it apart” distributively and analyze it for content he could use to determine its function. In June of 1987, Alexander Fruden concluded that the formula could best be used to solve Rubik’s Cube. This use was considered somewhat laughable by some historians claiming that the Rubik’s Cube would not be invented until more than ten years after Geldemacher’s death. On July 9th, 1987, Fruden claimed he found evidence to support a theory regarding Geldemacher building a time travel device. Two days later, July 11th, Fruden was reported missing after not attending his sponsored lecture on the mathematical implications of smell. Some mathematicians believe Fruden to be factual, and others claim he was a “poo-daddy”.

Vanderschneil Research

The first great discovery pertaining to the area of a square occurred in 1990 after Gerald Montgomery Has Vanderschneil of Austria invented Sq.2, a new formula for whitening teeth and curing glaucoma. Sq.2 was a hit on the Austrian market, but failed to pass FDA regulations in the United States. The exact formula remained a secret until multiple cases of death occurred, due to E. Coli infections, related to users of Vanderschneil’s product. An investigation later shut down the Sq.2 production line after it was discovered that Vanderschneil had gone crazier than a loon and left steaming piles of his “doo-doo” inside the condensing vats. The formula was eventually bought by Gleam Toothpaste Co., for a sum of $200 and a crate of Fruit Roll-Ups.

Harper Findings

In 1994 Dr. Harper Harper Harper, a scientist at Yale University, used Geldemacher’s formula to produced a spreadsheet detailing the results of the 2127 World Series. Dr. Harper used the integral, which he integrated, then squared, and then distributed into a computer, which concluded that the findings were from the year 2127. The arc of the curve, once integrated, was found to be a comparative multiple to MLB statistics for World Series wins/losses. According to Dr. Harper’s complete analysis, the Birmingham Boolahmeister’s lose to the New Boston Pink Sox by a score of 9 runs to 3 after one of the players indefinatively opens a rift in the space time continuum. Although his findings are not known to be completely accurate, his formula is comparative to obvious patterns in steroid usage.