gm: add geometric calculation functions

[suleyman-kaya]

This PR adds several geometric calculation functions to the gm module. These functions implement common geometric theorems and calculations, enhancing the module's capabilities for triangle-related computations.

New functions added:

1. Pythagorean Theorem:

// pythagorean_theorem calculates the length of the hypotenuse given the lengths of the other two sides
pub fn pythagorean_theorem(a f64, b f64) f64 {
    return math.sqrt(a * a + b * b)
}

2. Euclidean Theorem:

// euclidean_theorem calculates the lengths of segments created by the altitude to the hypotenuse
pub fn euclidean_theorem(a f64, b f64, c f64) (f64, f64) {
    h := (a * b) / c
    p := (h * h) / a
    q := (h * h) / b
    return p, q
}

3. Triangle Area using Sine:

// triangle_area_sine calculates the area of a triangle given two sides and the angle between them
pub fn triangle_area_sine(a f64, b f64, angle_rad f64) f64 {
    return 0.5 * a * b * math.sin(angle_rad)
}

4. Finding absent length of a triangle using Cosine:

// triangle_missing_side calculates the length of the missing side of a triangle
// given two sides and the angle between them
pub fn triangle_missing_side(a f64, b f64, angle_rad f64) f64 {
    return math.sqrt(a * a + b * b - 2 * a * b * math.cos(angle_rad))
}

5. Triangle Area from Points:

// triangle_area_from_points calculates the area of a triangle given its three vertices
pub fn triangle_area_from_points(p1 &Point, p2 &Point, p3 &Point) f64 {
    a := dist_point_point(p1, p2)
    b := dist_point_point(p2, p3)
    c := dist_point_point(p3, p1)
    s := (a + b + c) / 2  // semi-perimeter
    return math.sqrt(s * (s - a) * (s - b) * (s - c))
}

These functions provide implementations for common geometric calculations, expanding the functionality of the gm module. They utilize existing structures and functions where applicable, such as the Point struct and dist_point_point function.

Important Note:
Currently, there is no test file for this module. Due to time constraints, I haven't been able to create a comprehensive test suite for these new functions. I acknowledge the importance of testing and commit to writing proper tests as soon as my schedule allows. I will submit a follow-up commit with a complete test file, ensuring all tests pass before merging.
This current PR is to get early feedback on the implementations while I work on the test suite.

In the meantime, I've manually verified the functions' basic functionality, but a thorough test suite is pending. I appreciate your understanding and will prioritize creating the tests at my earliest convenience.

Summary by CodeRabbit

• New Features
  • Introduced new functions for advanced geometric computations, including calculations for triangle area, hypotenuse length, and segments created by altitudes.
  • Enhanced the module's capabilities to support comprehensive geometric analysis for users.

[coderabbitai]

Walkthrough

The changes introduce multiple public functions in the gm/basicgm.v file, enhancing the module's geometric computation capabilities. The new functions cover various aspects of triangle geometry, including calculating areas, hypotenuses, and segment lengths using established mathematical theorems.

Changes

Files	Change Summary
gm/basicgm.v	Added five public functions: pythagorean_theorem, euclidean_theorem, triangle_area_sine, triangle_missing_side, and triangle_area_from_points for geometric calculations.

Poem

In the meadow where numbers play,
A triangle danced in a bright array.
With sides to measure and angles to gleam,
New functions have come, like a dream!
Hop, skip, and calculate, oh what fun,
Geometry's magic has only begun! 🐇✨

---

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Actionable comments posted: 0

Review details

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Review profile: CHILL

Commits

Files that changed from the base of the PR and between bdb5c39 and bf4d41b.

Files selected for processing (1)

• gm/basicgm.v (1 hunks)

Additional comments not posted (5)

gm/basicgm.v (5)

167-170: LGTM!

The pythagorean_theorem function correctly implements the Pythagorean theorem to calculate the hypotenuse.

---

172-178: LGTM!

The euclidean_theorem function correctly calculates the lengths of segments created by the altitude to the hypotenuse.

---

180-183: LGTM!

The triangle_area_sine function correctly calculates the area of a triangle using the sine formula.

---

185-189: LGTM!

The triangle_missing_side function correctly implements the law of cosines to calculate the missing side of a triangle.

---

191-197: LGTM!

The triangle_area_from_points function correctly calculates the area of a triangle using Heron's formula.

[suleyman-kaya]

@ulises-jeremias