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Add first fundamental form calculator to maths#14554

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Add first fundamental form calculator to maths#14554
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@singhc7 singhc7 commented Apr 14, 2026

This adds a script to calculate the coefficients (e, f, g) of the first fundamental form for parametric surfaces. This mathematical framework is a core concept in differential geometry, used to measure lengths, angles, and areas on a surface.

The implementation uses sympy for symbolic differentiation and simplification. While standard mathematical notation dictates capital E, F, and G for these coefficients, they are implemented as lowercase to strictly adhere to PEP 8 N806 and pass the repository's required Ruff linter pre-commit hooks.

Reference: https://en.wikipedia.org/wiki/First_fundamental_form

Author: singhc7

Describe your change:

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

This adds a script to calculate the coefficients (e, f, g) of the
first fundamental form for parametric surfaces. This mathematical
framework is a core concept in differential geometry, used to measure
lengths, angles, and areas on a surface.

The implementation uses sympy for symbolic differentiation and
simplification. While standard mathematical notation dictates capital
E, F, and G for these coefficients, they are implemented as lowercase
to strictly adhere to PEP 8 N806 and pass the repository's required
Ruff linter pre-commit hooks.

Reference: https://en.wikipedia.org/wiki/First_fundamental_form

Author: singhc7
@singhc7 singhc7 marked this pull request as ready for review April 14, 2026 03:26
@algorithms-keeper algorithms-keeper bot added the awaiting reviews This PR is ready to be reviewed label Apr 14, 2026
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