Differential Geometry
What is the Differential Geometry?
It is mathematical discipline which studies the geometry of smooth shapes and smooth spaces.
Who invented Differential Geometry?
Gaspard Monge and C. F. Gauss
What various fields is Differential Geometry used for? And, what does it help analyze?
You can find applications in various fields such as physics, biology, computer science, and engineering. It helps analyze shape, surfaces and spatial relationships. (Spatial meaning relating to or occupying space.
What is another phrase for "Smooth Spaces"?
Smooth Manifolds
Who were the inventers known for?
Gaspard Monge was a French mathematician, commonly represented as the inventor of descriptive geometry, technical drawings and the father of differential geometry. C. F. Gauss was a German mathematician, astronomer, geodesist, and physicist who contributed to many fields in mathematics and science. He was also known as the father of differential geometry.
How is Differential Geometry used for Physics? And, what are the jobs work in the field of Differential Geometry for physics?
The language in which Albert Einstein’s general theory of relativity is expressed. Jobs: Theoretical physicist, or more specifically, general relativist or a gravitational physicist.
What type of techniques does differential geometry use?
It is uses techniques of differential calculus, integral calculus, linear algebra and multilinear algebra.
Who is the "Modern Father of Differential Geometry"? And, what is he/she known for?
Shiing-Shen Chern is known as the modern father of Differential Geometry. He was a Chinese mathematician, internationally known as the foremost differential geometer in his time.
How is Differential Geometry used for Biology? And, what are the jobs work in the field of Differential Geometry for biology?
Differential Geometry used as a natural mathematical tool when a protein molecule is represented as a space curve. Jobs: Computational biologist, Bioinformatician, or a Structural biologist.
This field have its origins in the study of what?
The field has its origins in the study of spherical geometry.
When was Differential Geometry invented?
Differential Geometry was invented in the early 19th century.
How is Differential Geometry used for Computer Science? And, what are the jobs work in the field of Differential Geometry for computer science?
It is used to analyze shapes and as layers in neural networks, allowing neural networks to model complex systems described by differential equations. Jobs: Machine Learning Researcher or Computational Scientist.
Is Differential used as a tool? If yes, then how is it used as a tool?
Yes, it is a tool which is used to understand how to adapt concepts such as distance between two points, the angle between two crossing curves.
Where was Differential Geometry invented? And, the work laid what?
Differential geometry traces back to its origins in ancient Greece. The work laid the foundation for understanding geometric shapes and their properties.