- #1
Jianphys17
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Hi, i would be very interested to start learning hyperbolic geometry, what would be the necessary prerequisites to begin it's study? 
Prerequisites for non Euclidean geometry
- Thread starter Jianphys17
- Start date
In summary, the necessary prerequisites for learning hyperbolic geometry include a good familiarity with vector calculus and basic linear algebra. It is also beneficial to have knowledge of the differential geometry of curves and surfaces in 3-space, but it is not absolutely necessary. However, learning this subject can greatly enhance understanding of hyperbolic geometry.
- #2
zinq
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- 119
A good familiarity with vector calculus and basic linear algebra should suffice.
- #3
Jianphys17
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Ah, but reading the article on wikipedia https://en.wikipedia.org/wiki/Hyperbolic_geometry believed is also required knowledge of differential geometry of surfaces...
- #4
zinq
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The reason I didn't mention hyperbolic geometry specifically is that vector calculus and linear algebra prepare one for a basis course on the differential geometry of curves and surfaces in 3-space. This is just what one would need to understand hyperbolic geometry in the right context (even though a complete hyperbolic plane of constant Gaussian curvature = -1 cannot be embedded in 3-space if it is of differentiability class C2. — Hilbert's theorem).
Hyperbolic geometry is ideally learned as an advanced topic in a course on the differential geometry of curves and surfaces in 3-space. So, the prerequisites are for such a course.
Hyperbolic geometry is ideally learned as an advanced topic in a course on the differential geometry of curves and surfaces in 3-space. So, the prerequisites are for such a course.
- #5
Jianphys17
- 66
- 2
Hence so it would be necessary to learn before some notion of differential geometry of surfaces in 3d-space!
- #6
- 22,183
- 3,321
Jianphys17 said:
No, it is not necessary. Differential hyperbolic geometry is a subset of hyperbolic geometry, but definitely not the only part.
- #7
Jianphys17
- 66
- 2
Thank you for helping me solve this doubt! 
- #8
zinq
- 399
- 119
It is possible that micromass and I have different viewpoints about this issue. I won't say that differential geometry is absolutely necessary if all you want to learn is hyperbolic geometry.
But in my opinion it would greatly enhance your understanding, and would be an extremely wise thing to learn either before or during the time you learn about hyperbolic geometry.
But in my opinion it would greatly enhance your understanding, and would be an extremely wise thing to learn either before or during the time you learn about hyperbolic geometry.
1. What is non Euclidean geometry?
Non Euclidean geometry is a branch of mathematics that explores geometric systems in which the parallel postulate of Euclidean geometry does not hold. In other words, it studies geometries that do not follow the traditional rules of Euclid's geometry.
2. What are the prerequisites for studying non Euclidean geometry?
The main prerequisite for studying non Euclidean geometry is a strong understanding of Euclidean geometry. This includes knowledge of geometric concepts such as points, lines, angles, and shapes, as well as theorems and postulates. A strong foundation in algebra and trigonometry is also helpful.
3. Why is a strong understanding of Euclidean geometry important for studying non Euclidean geometry?
Euclidean geometry serves as the basis for understanding non Euclidean geometry. Many of the concepts and theorems in non Euclidean geometry build upon those in Euclidean geometry. Without a strong foundation in Euclidean geometry, it can be difficult to grasp the principles of non Euclidean geometry.
4. Can anyone study non Euclidean geometry?
Yes, anyone with a strong understanding of Euclidean geometry and the necessary mathematical background can study non Euclidean geometry. It is a complex and advanced topic, so it may require a significant amount of time and effort to fully comprehend.
5. What are some real-world applications of non Euclidean geometry?
Non Euclidean geometry has many real-world applications, particularly in fields such as physics and engineering. For example, Einstein's theory of general relativity, which describes the behavior of gravity, relies on non Euclidean geometry. It is also used in computer graphics and mapping technology.
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