This text appears to be a detailed explanation of the concept of rotation factors, their relationship to position numbers, and the derivation of equations related to these mathematical concepts. It covers topics like the fundamental equation of position vector rotation, the existence of rotation factor sets, and the classification of numbers into real numbers and rotation factors.
Sure, here are the key facts extracted from the provided text:
1. The author of the paper is Chu Jiang Lu.
2. The paper discusses the derivation of the imaginary unit and Euler's formula from first principles.
3. The paper explores the fundamentals of the imaginary unit and complex numbers.
4. The imaginary unit has been proven to be real.
5. The text mentions the concept of rotation factors as a new type of numbers.
6. Rotation factors can change vector directions, unlike real numbers.
7. The rotation factor of angle 0 is 1, and for angle Pi, it's -1.
8. The concept of orthogonal rotation factors, denoted as Q half pi, is introduced.
9. The text discusses the fundamental equation of position vector rotation.
10. Rotation factors are applicable to position numbers.
11. The rotation factor formula is derived, showing their existence for all angles.
12. Position numbers are formed by real numbers and rotation factors.
13. Real numbers stretch the magnitude of position numbers without changing their direction.
These are the key factual points from the text without including opinions or interpretations.