d4t_formulas/assets/formulas/geometry.d4rt

[
  // Area of Circle
  {
    "name": "Area of Circle",
    "description": r"""
Area enclosed by a circle

$$A = \pi r^2$$

Where:
- $A$: Area (square meters)
- $r$: Radius (meters)
- $\pi$: Pi ($\approx 3.14159$)

The area is proportional to the square of the radius.""",
    "input": [
      {"name": "r", "unit": "meter"}
    ],
    "output": {"name": "A", "unit": "square meter"},
    "d4rtCode": "A = pi * pow(r, 2);",
    "tags": ["geometry", "circle", "area"]
  },

  // Circumference of Circle
  {
    "name": "Circumference of Circle",
    "description": r"""
Perimeter (distance around) a circle

$$C = 2\pi r$$

Where:
- $C$: Circumference (meters)
- $r$: Radius (meters)
- $\pi$: Pi ($\approx 3.14159$)

The circumference is proportional to the radius.""",
    "input": [
      {"name": "r", "unit": "meter"}
    ],
    "output": {"name": "C", "unit": "meter"},
    "d4rtCode": "C = 2 * pi * r;",
    "tags": ["geometry", "circle", "perimeter"]
  },

  // Area of Triangle
  {
    "name": "Area of Triangle",
    "description": r"""
Area enclosed by a triangle

$$A = \frac{1}{2}bh$$

Where:
- $A$: Area (square meters)
- $b$: Base length (meters)
- $h$: Height perpendicular to base (meters)

This formula works for any triangle.""",
    "input": [
      {"name": "b", "unit": "meter"},
      {"name": "h", "unit": "meter"}
    ],
    "output": {"name": "A", "unit": "square meter"},
    "d4rtCode": "A = 0.5 * b * h;",
    "tags": ["geometry", "triangle", "area"]
  },

  // Area of Rectangle
  {
    "name": "Area of Rectangle",
    "description": r"""
Area enclosed by a rectangle

$$A = lw$$

Where:
- $A$: Area (square meters)
- $l$: Length (meters)
- $w$: Width (meters)

The area is the product of length and width.""",
    "input": [
      {"name": "l", "unit": "meter"},
      {"name": "w", "unit": "meter"}
    ],
    "output": {"name": "A", "unit": "square meter"},
    "d4rtCode": "A = l * w;",
    "tags": ["geometry", "rectangle", "area"]
  },

  // Area of Trapezoid
  {
    "name": "Area of Trapezoid",
    "description": r"""
Area enclosed by a trapezoid

$$A = \frac{1}{2}(a+b)h$$

Where:
- $A$: Area (square meters)
- $a, b$: Lengths of parallel sides (meters)
- $h$: Height (perpendicular distance between parallel sides, meters)

The area is the average of parallel sides times height.""",
    "input": [
      {"name": "a", "unit": "meter"},
      {"name": "b", "unit": "meter"},
      {"name": "h", "unit": "meter"}
    ],
    "output": {"name": "A", "unit": "square meter"},
    "d4rtCode": "A = 0.5 * (a + b) * h;",
    "tags": ["geometry", "trapezoid", "area"]
  },

  // Area of Regular Polygon
  {
    "name": "Area of Regular Polygon",
    "description": r"""
Area of a regular polygon with n sides

$$A = \frac{1}{4}ns^2\cot(\frac{\pi}{n})$$

Where:
- $A$: Area (square meters)
- $n$: Number of sides
- $s$: Side length (meters)
- $\pi$: Pi ($\approx 3.14159$)

This formula works for any regular polygon (equal sides and angles).""",
    "input": [
      {"name": "n", "unit": "scalar"},
      {"name": "s", "unit": "meter"}
    ],
    "output": {"name": "A", "unit": "square meter"},
    "d4rtCode": "A = 0.25 * n * pow(s, 2) * (cos(pi/n) / sin(pi/n));",
    "tags": ["geometry", "polygon", "area"]
  },

  // Sum of Interior Angles of Polygon
  {
    "name": "Sum of Interior Angles",
    "description": r"""
Sum of interior angles of a polygon

$$S = (n - 2) \times 180°$$

Where:
- $S$: Sum of interior angles (degrees)
- $n$: Number of sides

This formula works for any simple polygon.""",
    "input": [
      {"name": "n", "unit": "scalar"}
    ],
    "output": {"name": "S", "unit": "degree"},
    "d4rtCode": "S = (n - 2) * 180;",
    "tags": ["geometry", "polygon", "angles"]
  },

  // Heron's Formula (Area of Triangle)
  {
    "name": "Heron's Formula",
    "description": r"""
Area of a triangle using only side lengths

$$A = \sqrt{s(s-a)(s-b)(s-c)}$$

Where:
- $A$: Area (square meters)
- $a, b, c$: Side lengths (meters)
- $s$: Semi-perimeter $= \frac{a+b+c}{2}$

This formula is useful when height is unknown.

**Note:** The side lengths must satisfy the triangle inequality: the sum of any two sides must be greater than the third side (a+b>c, a+c>b, b+c>a). If this condition is not met, the formula returns NaN.""",
    "input": [
      {"name": "a", "unit": "meter"},
      {"name": "b", "unit": "meter"},
      {"name": "c", "unit": "meter"}
    ],
    "output": {"name": "A", "unit": "square meter"},
    "d4rtCode": """
       if( a + b < c || a+c < b || b+c < a ){
          signal( "There is not a valid triangle with those longitudes" );
       }
       var s = (a + b + c) / 2;
       A = sqrt(s * (s - a) * (s - b) * (s - c));
    """,
    "tags": ["geometry", "triangle", "area"]
  }
]