End of the World and Non-Euclidean Geometry: Mathematics Note -5 (essay)
The main character of the Journey to the West, Son Goku, was so proud of his power that he went on a rampage in the heavens. Buddha makes a bet whether he can go to the end of the world. He takes the bet, flies clouds, reaches the place where five pillars stand, writes "I'm here" on the pillars, urinates, and returns. However, when he came back, Buddha said, "What you think is the end of the world is nothing more than what is on the palm of your hand." Smelly urine is dripping. Buddha's palm fell over him, and Son Goku fell under the mountain.
Well, this anecdote is also interesting as a topic of "Euclidean geometry" and "non-Euclidean geometry" in mathematics. Euclid's ``Theory: Stoikeia'', a compilation of Greek mathematics, caused a great deal of controversy in later generations. There is only one."
A "postulate" is a truth that can be accepted as correct without proof, but this postulate of parallel lines is more complicated than other postulates. Is it?”, and there were many people who worked hard to prove it. However, the effort was not rewarded, and some people even doubted the parallel postulate. As a result, instead of denying Euclidean geometry, another system of geometry without contradiction was established. These are called "non-Euclidean geometries".
Make the distance between the inner point (which sets up a circle) and the circumference infinite.
Therefore, for humans inside this circle, the circumference is infinitely far away, and no matter how much they walk, they cannot escape from this world. Only the inside of this circle is the whole universe. But for those of us who are looking at this world from the outside, the circumference is at a finite distance within reach. It just shrinks as you get closer. It's an illusion that they look parallel. intersect at infinity.
