Output a geometry rather than a number

In summary, the conversation discusses the process of analyzing a geometry or function and asking questions about it, with the answer being a number or a function that reduces to a number. The opposite process is also considered, starting with a number and working backwards to output a geometry. An example of this is the prediction of a circular orbit of electrons in the hydrogen atom, where the expected values of energy correspond to the geometry of a sphere. The conversation also mentions the need for topology and metrics in order to create a geometry from a list of numbers or vectors.
  • #1
tickle_monste
69
1
So, in my studies of math so far, we can take a certain geometry (or just any function) and analyze it, and ask questions about it. The answer that's given in all the work I've done so far is a number (or a function that will reduce to a number when solved). Now, let's say I want to do the opposite (or the inverse operation): start with a number and have a function reduce to a geometry rather than another number. Here's an example (actually why I'm motivated to ask this question):

Niels Bohr and those before him predicted a circular (spherical) orbit of electrons in the hydrogen atom. Starting from the idea that the orbit would be circular, we can use this geometry to give an expected value (number) of the energy that would be emitted (or have to be absorbed) in a change of state. The measured values correspond with the expected values which correspond to the geometry of a sphere, which supports the hypothesis.

So, after we've done all this and we have a basic template for finding the numbers from the geometry, what kind of math does it take to work backwards, starting from the numbers, to output the geometry? You can certainly use the same example as I did, but it's not necessary, any example would be great.
 
Physics news on Phys.org
  • #2
To go from a list of numbers or list of lists (position vectors or other types of vectors) to geometry requires some guesswork or extra empirical measurements. A list of numbers is missing a topology that relays how the numbers are connected to each other and a metric that relate distances between the numbers to create a geometry.
 

1. What does it mean to "output a geometry"?

Outputting a geometry means that instead of getting a numerical value as the result of a calculation or measurement, you will get a visual representation of a shape or object, such as a point, line, or polygon.

2. How is outputting a geometry different from outputting a number?

Outputting a geometry is different from outputting a number because a geometry provides a visual representation of a shape or object, while a number is simply a numerical value. A geometry can be more useful for analyzing and understanding spatial data, while a number may be more useful for quantitative analysis.

3. When would you want to output a geometry instead of a number?

You would want to output a geometry instead of a number when working with spatial data, such as mapping or analyzing geographic information. Geometries can provide a more intuitive and visual understanding of the data, whereas numbers may be more abstract and difficult to interpret.

4. Can any type of data be outputted as a geometry?

No, not all types of data can be outputted as a geometry. Geometries are typically used for representing spatial data, such as locations, boundaries, or shapes. Other types of data, such as text or numerical values, may not have a visual representation that can be outputted as a geometry.

5. How can you output a geometry instead of a number in your analysis or code?

The method for outputting a geometry instead of a number will depend on the specific software or programming language being used. However, in general, you will need to use a function or command that is specifically designed for working with spatial data, such as a GIS (Geographic Information System) software or a library for spatial analysis in a programming language like R or Python.

Similar threads

Replies
12
Views
2K
  • Beyond the Standard Models
Replies
3
Views
1K
  • Differential Geometry
Replies
27
Views
5K
Replies
2
Views
177
Replies
3
Views
2K
  • Special and General Relativity
Replies
8
Views
694
  • Differential Geometry
Replies
12
Views
2K
Replies
3
Views
94
Replies
2
Views
3K
Replies
27
Views
983
Back
Top