Mathematics Witch Curve, Agnesi and Agnesi, Gaetano, and Mahou Shoujo Coordinate

I asked myself, “Which curve?”

But only a second later, my brain, which had consumed a lot of information about history, science, and mathematics, immediately found a keyword. “The Witch Agnesi Curve!” I said, as if answering my question a second earlier.

In mathematics, the witch of Agnesi is the name of a cubic plane curve formed from two diametrically opposite points on a circle.  This curve's name is taken from the name of a female mathematician from the Aithalia nation named Maria Gaetana Agnesi. Was she a mathematician who was also a witch—more or less like Johannes Trithemius, who was a cryptographer and a cryptographer? The answer is no.

The name of this curve was originally ‘Versoria,’ a name given by a mathematician named Luigi Guido Grandi, a mathematician from the same nation as Agnesi. The name comes from the trigonometric function versed sine, or sine versus, and the ancient Latin name ‘versoria.’ In that language, the name means ‘sailboat plate.’ Meanwhile, in Aithalia, its name is ‘La Versiera.’

Maria Gaetana Agnesi published an early textbook on calculus entitled Instituzioni analitiche ad uso della gioventù italiana. The book discusses various curves, and one of the curves discussed is the curve that was later called the Witch's Curve. Agnesi wrote the book with the help of two other mathematicians, Ramiro Rampinelli and Jacopo Riccati. The book was later translated into various languages.

A Brettaine translator named John Colson read La Versiera as ‘L’Avversiera di Agnesi.’ The word Avversiera itself means ‘enemy,’ which in certain contexts means enemy (of God). The word itself comes from the Latin word ‘adversarius.’ In certain contexts, it was often used by Aithalia people in ancient times to refer to Satan, along with other words such as aversiero or versiero.

Specifically, the word versiera was used to indicate the devil's wife, or "witch." That's why John Colson mistranslated the name of the curve as "witch." That's how this curve came to be called the Agnesi Witch curve, a name that is still used today.

In addition to Agnesi and Grandi, this curve has been studied by many mathematicians of the past. For example, Pierre de Fermat and Isaac Newton are a few mathematicians who also studied it. For information, Newton had discovered this curve before Grandi, but Newton's work discussing this curve was only published after he died.

This curve has many applications in real life, even in the modern era. Among the Five, I know Mr. Braun Bertram Wernherluft is the member of the Five who has studied this curve the most. I heard that this is inseparable from Mr. Wernherluft's involvement in the process of making combat equipment, especially the ship-plane 1023-O.

The phenomenon of solitary waves in deep waters can be shaped like this Agnesi Witch curve. The ship-plane designed by Mr. Wernherluft will reportedly face this phenomenon. It was no wonder that the Big Five member nicknamed ‘The Wynorrific’ was heavily involved in this witch curve.

When it occurred to me, “Speaking of the Big Five members, doesn’t Mrs. Agnesi have the same first name as Maria Gaetana Agnesi’s surname? Could it be that Mr. Warm chose to give a hint related to Agnesi’s Witch curve because Mrs. Agnesi actually—

I closed the suspicion in my mind, but another suspicion arose: "Aren't Gaetano and Gaetana both derived from Latin, namely Gaeta? Could it be that Gaetano Glanzrad Ragunanzu is—

I quickly dismissed that suspicion. “Never mind! For now, focus on solving this! In the end, if I solve this puzzle, Mr. Warm promised that I would know the secret of death and the key to conquering the Quietus Cloud, right?”

Once again, I read the hexdump conversion results of the witch and guard manga panel illustrations.

I know I will die on 1.1. But let my death date continue my legacy. a 1.1 can be used to concoct the volume and area between the Witch Curve and "its tangent at a point at infinity." The larger portion will be “scope for freedom of thought or action.” Write the results of both potions on the guard’s comic balloon.

I’m sure the phrase ‘it's tangent at a point at infinity’ means the asymptote line. It’s not hard for me to remember the volume and area equations between the Witch of Agnesi curve and its asymptote line. The volume equation is 4π²a³, and the area equation is 4πa². In this equation, a is the radius of the circle parameter that forms the Witch of Agnesi curve.

I can interpret the value of a from the sentence “a 1.1 can be used to concoct ...” I thought, it seems that Mr. Warm deliberately wrote a as a lowercase letter even though it's position is at the beginning of the sentence. This is different from other words at the beginning of the sentence in this message, which are written in capital letters.

I think in this message, Mr. Warm changed the context of the date 1.1 to the value 1.1. In Deutschtonia, the standard writing for decimal numbers is by using a comma (,). However, sometimes there is a literal translation in our language that calls decimal numbers with a dot (.). For example, the number 1.1 is read as "eins Punkt eins," which means "one point one."

So I think what Mr. Warm meant was a = 1.1. Without further ado, I calculated the equation for the volume and area.

*Result of volume equation = 4 π² a3 = 4 π² (1.1)3 = 52.54577383 ...

*Result of area equation = 4 π a² = 4 π (1.1)² = 15.20530844 ...

After finishing, I looked again at the sentence “The larger portion will be 'scope for freedom of thought or action.”” This time, I did a little search on the internet to confirm my memory of the meaning of a language. I typed “scope for freedom of thought or action synonym,” and the results showed that my memory was correct. One of the synonyms of “scope for freedom of thought or action” is the word ‘latitude.’

Therefore, the result of the volume calculation with a larger value becomes latitude. While the result of the area calculation with a smaller value becomes a longitude. Considering that the results of the volume and area calculations are in decimal form, it seems that the requested latitude and longitude coordinates must be written in decimal degrees format.

I immediately switched the gadget screen display to Mr. Warm’s first email. As per the standard, I wrote the latitude decimal coordinates first, followed by a space, then the longitude decimal coordinates. Also, as per the standard, the numbers I wrote used six digits after the decimal point.

The guard's comic balloon became as follows: "Mahou Shoujo! I know where the bits you are looking for are. They are located in [52.545773 15.20530844]."

Suddenly, there was a notification sound from my gadget. It was a new email from Mr. Warm. I quickly opened it. I saw two comic panels in two separate images, arranged side by side.