What is the seven identity theorem?

Answer 1

The Seven Identity Theorem has a long history. It was created in 237 BC by Greek scientist, Archimedes.

On July 7th of 237, Archimedes reportedly woke from a dream. As his close friend, Conon of Samos, reports, the dream consisted of an army of Alexandrians who repeatedly mocked him. One Alexandrian stepped forward and declared, "What does he know? Naught! Dost he understand the true natures of this world? I trow not!" Afterwords, the Alexandrians began whispering the number, "7", over and over again.

In the dream, Archimedes was thoroughly confused about the number 7, wondering if it possibly had an unique identity. He began extensive research on this number.

He made seven immediate connections, some of which are listed: there are 7 days in the week, 7 notes on the musical scale, 7 directions (left, right, up, down, forward, back, center), and so forth.

Interested in geometry, Archimedes made another connection: imagine a cube, which has six sides. Imagine the largest sphere possible fully enclosed within the cube. This is one of the many examples demonstrating that such a figure with six sides will always fit around a seventh figure. Similarly, if a circle of any particular size is drawn, you can draw exactly six circles of the same size around that central circle. You can draw no more and no less if you want each circle to be externally tangent to at least three neighboring circles.

Archimedes proceeded to discovering that if a projectile is launched upwards with a minimum velocity of 49 meters per seconds, the vertex of the trajectory always exceeds 7 meters. This is due to the nature of gravity on Earth. Interestingly, if a projectile is launched upwards with a minimum velocity of 343 meters per seconds, the vertex of the trajectory always exceeds 77 meters.

Around this time, he began experimenting with water displacement and buoyancy. He found that if an object with a mass of 7 grams is released into a container holding precisely 2401 liters of water, the water displaced will be equal to (7*10^-4) liters. If an object with a mass of 7497 grams is released into the same container, the water displaced will be equal to 727 liters.

There are countless applications of the number, "7", in our modern world. The majority of them were discovered by Archimedes. Before he died, he compiled a book plainly titled, "Seven". Inside the book, he compiled his most important discoveries into a list and named the endless ability to generate such useful applications "the Seven Identity Theorem".

When Archimedes died in 212 B.C., the book was found and published. However, people were appalled at the fact that this seemingly normal number, 7, would have so many useful applications. They felt degraded, knowing that they had used the number so many times in their lifetimes without knowing its deeper meaning. To this day, many refuse to speak of it, as doing so would bring back such memories of humiliation.

Nevertheless, nearly all professional mathematicians use the Seven Identity Theorem daily to solve complex problems. To mathematicians, Archimedes is considered the most prominent figure in history for discovering such a valuable theorem and unearthing the mystery of the number, 7.