my magic industry

Chapter 210 Geometry

"The formulas and theorems obtained after establishing the various coordinate systems I proposed in "Rune Variations and the Four Basic Rune Theories" all have a major premise, that is, these formulas and theorems are only established on the plane.

And your geometric theory, without your realizing it, is based on the curved surface, or more narrowly: the spherical system! "

Xia Lin took out a pencil recently produced in the industrial park from the inner chest pocket of the mage robe, cast a mage armor as a desktop, put the manuscript paper on it, and began to draw graphics.

The so-called spherical geometry is a geometric system based on a two-dimensional spherical surface. In this system, due to the curvature of the spherical surface, the sum of the interior angles of a triangle will be greater than 180°, and parallel lines will intersect. The established formulas and theorems will also undergo many changes.

Therefore, when Archmage Darien deduced Xia Lin's theory with the set of geometric theories he had researched in the past, a series of inconsistencies naturally appeared.

In the history of Xia Lin's previous life, European geometry, that is, plane geometry, was the first geometric theory recognized by mathematicians, but in an accident, the amazingly talented mathematician Lobachevsky was studying When trying to find the parallel postulate of geometry, a hyperbolic geometry that violates this postulate is discovered.

In this set of geometric theories, the sum of the interior angles of a triangle will even be less than 180°, and parallel lines will also be separated.

This is the earliest appearance of non-Euclidean geometry, and spherical geometry is a set of geometric systems established in the direction roughly opposite to the hyperbolic geometric conditions. This set of geometry plays an extremely important role in the fields of astronomy and navigation. Later It also extended the development of Riemannian geometry.

Xia Lin had never imagined that in this world where unknowns had not even been invented, there would be a mage who independently researched this theory.

After drawing the Poincaré semi-plane model, spherical model and basic plane model, he wrote down the basic postulates and axioms of the three geometric systems of plane geometry, hyperbolic geometry and spherical geometry. Master Lien, the intuitive graphics and concise text immediately attracted his full attention:

"This is……"

Archmage Darien carefully examined these seemingly abstract graphics and text descriptions:
"A straight line can be drawn from any point to any other point; a finite line segment can continue to be extended... A straight line intersects two other straight lines in the same plane, if the sum of the two interior angles on a certain side is less than the sum of two right angles, then the two The straight lines, extended infinitely, intersect on this side."

With the mage's intelligence and comprehension ability, Archmage Darien quickly grasped the meaning of these graphics and words. Combined with his own research results, his face suddenly showed surprise, and he couldn't wait to ask Xia Lin:

"Could it be that your theories are all based on this plane, while my derivation is based on the sphere you drew?"

"That's right, although I don't know how you derived the spherical geometry system, but the fact is exactly what you said!"

Xia Lin put the cap on the pencil, nodded affirmatively and said.

"It's unbelievable... It's really unbelievable... For more than 100 years, I thought that only me and some of my companions in Glory of Thorns were researching these things, but I didn't expect that someone had advanced our achievements to this level!"

Archmage Darien murmured. Seeing his appearance, Mage Uther took the manuscript paper in his hand in surprise, and began to carefully examine what Xia Lin had just written. After studying it for a while, he There was also a little dignified look on his face:
"Master Xia Lin, did you research these all by yourself?"

"Of course not, this knowledge is actually recorded in an ancient book that I bought from a small stall opened by an adventurer team who had explored an ancient ruin when I was wandering on the street of 'Adventurer's Friends'." Yes, the name of that book is 'Elements of Geometry', and therefore, I named this body of knowledge 'Geometry'!"

Xia Lin calmly replied that this reason was naturally not something he came up with on a whim, but the second version that was suspected by Dorothea before and then patched.

The knowledge he brought up in Xinglan Elementary School textbooks is too advanced, unless he wants to be treated as a monster that goes further than a genius, otherwise he has to find a suitable reason to explain the existence of that knowledge In this regard, Xia Lin thought of pretexting the knowledge left over from ancient civilizations.

In this world, the main job of adventurers is to accept the employment of the lords and villages and towns, and expel the wild beasts and even monsters that have entered the realm of human life. But in addition, exploring the wilderness, hunting monsters, picking potions, Magic materials and exploring ruins are also one of their main sources of income.

In these ancient ruins, no matter what things are unearthed, it is possible, such as all kinds of wonders that are more magical and more powerful than magic equipment, are basically produced from the ruins, so even if there are more Some unknown and novel knowledge can also be explained.

As for the so-called "Friends of Adventurers" street, it is actually an alias for several streets near the Adventurer's Guild, where there are usually various adventurers setting up stalls to sell various materials or other items they have obtained through their adventures. The largest marketplace for used gear for adventurers, it's not surprising to see anything there.

"'Geometry original'? That's it, Master Xia Lin, where is the original, can you let me have a look? In exchange, I can exchange with you three intermediate soul cores made by myself. These soul cores The quality is enough to make a mage's servant!"

Archmage Darien also recovered from his thoughts, nodded clearly and begged Xia Lin, and took out a small ebony box from the mage's robe. After opening it, there were three mysterious stones inside. The eight-sided diamond-shaped crystals with faint blue brilliance seem to have a wonderful magic power, which can attract people's eyes to these crystals involuntarily.

"Intermediate soul core!"

Xia Lin couldn't help being a little surprised at the grand master Darien's generosity. In the market, the soul core, a golem's necessary raw material, has a huge gap in price according to the grade.

The price of low-level soul cores that can be used to make ordinary golems is roughly 30 to 50 gold lunds, but the price of intermediate soul cores has soared to 400 to 500 gold lunds.

As for high-level soul cores, they are extremely rare. According to Sophia, soul cores of this quality have completely disappeared from the market. If they appeared, at least they could fetch a high price of more than [-] gold lunt at auction.

Even the maid golem named Gracia next to Sophia, that kind of intelligence is only made of a very high-quality intermediate soul core.

And Archmage Darien actually got three intermediate soul cores, [-] gold lunites, which is not a small sum even for Xia Lin.

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(End of this chapter)