More copilot formulas, they lack description

assets/formulas/conversions_and_constants.d4rt

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+[
+  {"name":"Temperature converter","description":"Example of simple formula, just unit conversion","input":[{"name":"Input","unit":"Kelvin"}],"output":{"name":"Output","unit":"Kelvin"},"d4rtCode":"Output = Input;","tags":["converter","temperature"]}
+]

assets/formulas/electromagnetism.d4rt

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+[
+  {"name":"Coulomb's Law","input":[{"name":"q1","unit":"coulomb"},{"name":"q2","unit":"coulomb"},{"name":"r","unit":"meter"}],"output":{"name":"F","unit":"newton"},"d4rtCode":"F = (8.9875517923e9 * q1 * q2) / pow(r, 2);","tags":["physics","electricity","electrostatics"]},
+  {"name":"Ohm's Law","input":[{"name":"I","unit":"ampere"},{"name":"R","unit":"ohm"}],"output":{"name":"V","unit":"volt"},"d4rtCode":"V = I * R;","tags":["physics","electricity","electronics"]},
+  {"name":"Electric Power","input":[{"name":"V","unit":"volt"},{"name":"I","unit":"ampere"}],"output":{"name":"P","unit":"watt"},"d4rtCode":"P = V * I;","tags":["physics","electricity","electronics"]}
+]

assets/formulas/energy_and_power.d4rt

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+[
+  {"name":"Kinetic Energy","input":[{"name":"m","unit":"kilogram"},{"name":"v","unit":"meters per second"}],"output":{"name":"KE","unit":"joule"},"d4rtCode":"KE = 0.5 * m * pow(v, 2);","tags":["physics","energy","mechanics"]},
+  {"name":"Work","input":[{"name":"F","unit":"newton"},{"name":"d","unit":"meter"},{"name":"theta","unit":"degree"}],"output":{"name":"W","unit":"joule"},"d4rtCode":"var thetaRad = theta * (pi / 180); W = F * d * cos(thetaRad);","tags":["physics","energy","mechanics"]},
+  {"name":"Power","input":[{"name":"W","unit":"joule"},{"name":"t","unit":"second"}],"output":{"name":"P","unit":"watt"},"d4rtCode":"P = W / t;","tags":["physics","energy","mechanics"]},
+  {"name":"Mass-Energy Equivalence","input":[{"name":"m","unit":"kilogram"}],"output":{"name":"E","unit":"joule"},"d4rtCode":"E = m * pow(299792458, 2);","tags":["physics","relativity","energy"]}
+]

assets/formulas/fluids_and_pressure.d4rt

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+[
+  {"name":"Density","input":[{"name":"m","unit":"kilogram"},{"name":"V","unit":"cubic meter"}],"output":{"name":"rho","unit":"kilogram per cubic meter"},"d4rtCode":"rho = m / V;","tags":["physics","mechanics","material"]},
+  {"name":"Pressure","input":[{"name":"F","unit":"newton"},{"name":"A","unit":"square meter"}],"output":{"name":"P","unit":"pascal"},"d4rtCode":"P = F / A;","tags":["physics","mechanics","fluid"]},
+  {"name":"Buoyant Force","input":[{"name":"rho","unit":"kilogram per cubic meter"},{"name":"g","unit":"meters per square second"},{"name":"V","unit":"cubic meter"}],"output":{"name":"Fb","unit":"newton"},"d4rtCode":"Fb = rho * g * V;","tags":["physics","fluid","mechanics"]}
+]

assets/formulas/geometry.d4rt

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+[
+  // Geometry formulas extracted from formulas.d4rt
+  // Area of Circle
+  {
+    "name": "Area of Circle",
+    "description": r'''\nArea enclosed by a circle\n\n$$A = \pi r^2$$\n\nWhere:\n- $A$: Area (square meters)\n- $r$: Radius (meters)\n- $\pi$: Pi ($\approx 3.14159$)\n\nThe area is proportional to the square of the radius.''',
+    "input": [
+      {"name": "r", "unit": "meter"}  // Radius
+    ],
+    "output": {"name": "A", "unit": "square meter"},  // Area
+    "d4rtCode": "A = pi * pow(r, 2);",
+    "tags": ["geometry", "circle", "area"]
+  },
+
+  // Circumference of Circle
+  {
+    "name": "Circumference of Circle",
+    "description": r'''\nPerimeter (distance around) a circle\n\n$$C = 2\pi r$$\n\nWhere:\n- $C$: Circumference (meters)\n- $r$: Radius (meters)\n- $\pi$: Pi ($\approx 3.14159$)\n\nThe circumference is proportional to the radius.''',
+    "input": [
+      {"name": "r", "unit": "meter"}  // Radius
+    ],
+    "output": {"name": "C", "unit": "meter"},  // Circumference
+    "d4rtCode": "C = 2 * pi * r;",
+    "tags": ["geometry", "circle", "perimeter"]
+  },
+
+  // Area of Triangle
+  {
+    "name": "Area of Triangle",
+    "description": r'''\nArea enclosed by a triangle\n\n$$A = \frac{1}{2}bh$$\n\nWhere:\n- $A$: Area (square meters)\n- $b$: Base length (meters)\n- $h$: Height perpendicular to base (meters)\n\nThis formula works for any triangle.''',
+    "input": [
+      {"name": "b", "unit": "meter"},  // Base
+      {"name": "h", "unit": "meter"}   // Height
+    ],
+    "output": {"name": "A", "unit": "square meter"},  // Area
+    "d4rtCode": "A = 0.5 * b * h;",
+    "tags": ["geometry", "triangle", "area"]
+  },
+
+  // Area of Rectangle
+  {
+    "name": "Area of Rectangle",
+    "description": r'''\nArea enclosed by a rectangle\n\n$$A = lw$$\n\nWhere:\n- $A$: Area (square meters)\n- $l$: Length (meters)\n- $w$: Width (meters)\n\nThe area is the product of length and width.''',
+    "input": [
+      {"name": "l", "unit": "meter"},  // Length
+      {"name": "w", "unit": "meter"}   // Width
+    ],
+    "output": {"name": "A", "unit": "square meter"},  // Area
+    "d4rtCode": "A = l * w;",
+    "tags": ["geometry", "rectangle", "area"]
+  },
+
+  // Area of Trapezoid
+  {
+    "name": "Area of Trapezoid",
+    "description": r'''\nArea enclosed by a trapezoid\n\n$$A = \frac{1}{2}(a+b)h$$\n\nWhere:\n- $A$: Area (square meters)\n- $a, b$: Lengths of parallel sides (meters)\n- $h$: Height (perpendicular distance between parallel sides, meters)\n\nThe area is the average of parallel sides times height.''',
+    "input": [
+      {"name": "a", "unit": "meter"},  // Parallel side 1
+      {"name": "b", "unit": "meter"},  // Parallel side 2
+      {"name": "h", "unit": "meter"}   // Height
+    ],
+    "output": {"name": "A", "unit": "square meter"},  // Area
+    "d4rtCode": "A = 0.5 * (a + b) * h;",
+    "tags": ["geometry", "trapezoid", "area"]
+  },
+
+  // Area of Regular Polygon
+  {
+    "name": "Area of Regular Polygon",
+    "description": r'''\nArea of a regular polygon with n sides\n\n$$A = \frac{1}{4}ns^2\cot(\frac{\pi}{n})$$\n\nWhere:\n- $A$: Area (square meters)\n- $n$: Number of sides\n- $s$: Side length (meters)\n- $\pi$: Pi ($\approx 3.14159$)\n\nThis formula works for any regular polygon (equal sides and angles).''',
+    "input": [
+      {"name": "n", "unit": "scalar"},  // Number of sides
+      {"name": "s", "unit": "meter"}    // Side length
+    ],
+    "output": {"name": "A", "unit": "square meter"},  // Area
+    "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'''\nSum of interior angles of a polygon\n\n$$S = (n - 2) \times 180°$$\n\nWhere:\n- $S$: Sum of interior angles (degrees)\n- $n$: Number of sides\n\nThis formula works for any simple polygon.''',
+    "input": [
+      {"name": "n", "unit": "scalar"}  // Number of sides
+    ],
+    "output": {"name": "S", "unit": "degree"},  // Sum of angles
+    "d4rtCode": "S = (n - 2) * 180;",
+    "tags": ["geometry", "polygon", "angles"]
+  },
+
+  // Heron's Formula (Area of Triangle)
+  {
+    "name": "Heron's Formula",
+    "description": r'''\nArea of a triangle using only side lengths\n\n$$A = \sqrt{s(s-a)(s-b)(s-c)}$$\n\nWhere:\n- $A$: Area (square meters)\n- $a, b, c$: Side lengths (meters)\n- $s$: Semi-perimeter $= \frac{a+b+c}{2}$\n\nThis formula is useful when height is unknown.\n\n**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"},  // Side 1
+      {"name": "b", "unit": "meter"},  // Side 2
+      {"name": "c", "unit": "meter"}   // Side 3
+    ],
+    "output": {"name": "A", "unit": "square meter"},  // Area
+    "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"]
+  }
+]

assets/formulas/materials_elasticity.d4rt

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+[
+  {"name":"Hooke's Law","input":[{"name":"k","unit":"newton per meter"},{"name":"x","unit":"meter"}],"output":{"name":"F","unit":"newton"},"d4rtCode":"F = -k * x;","tags":["physics","elasticity","oscillations"]}
+]

assets/formulas/medical_and_bio.d4rt

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+[
+  {"name":"Apgar Score","input":[{"name":"HeartRate","values":["Absent","< 100 bpm>","> 100 bpm"]},{"name":"Breathing","values":["Absent","Weak, irregular","Strong, robust cry"]},{"name":"MuscleTone","values":["None","Some","Flexed arms/leg, resists extension"]},{"name":"Reflexes","values":["No response","Grimace on aggressive stimulation","Cry on stimulation"]},{"name":"SkinColor","values":["Blue or pale","Blue extremities, pink body","Pink"]}],"output":{"name":"Result","unit":"string"},"d4rtCode":"var total = indexOf(\"HeartRate\") + indexOf(\"Breathing\") + indexOf(\"MuscleTone\") + indexOf(\"Reflexes\") + indexOf(\"SkinColor\"); late var interpretation; if( total < 4 ) { interpretation = 'Critical condition'; } else if( total < 7 ){ interpretation = 'Needs assistance'; } else { interpretation = 'Normal'; } Result = 'Score: \$total - \$interpretation';","tags":["medical","pediatrics","assessment"]}
+]

assets/formulas/misc_math.d4rt

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+[
+  {"name":"Compare price per mass","description":"Compares two products by their price per mass and returns which is cheaper, including price per kg for each product.","input":[{"name":"price1","unit":"currency"},{"name":"mass1","unit":"kilogram"},{"name":"price2","unit":"currency"},{"name":"mass2","unit":"kilogram"}],"output":{"name":"Result","unit":"string"},"d4rtCode":"var p1 = price1 / mass1; var p2 = price2 / mass2; if (p1 < p2) { Result = 'first product is cheaper at \$\{p1.toStringAsFixed(2)\} currency/kg vs \$\{p2.toStringAsFixed(2)\} currency/kg'; } else if (p2 < p1) { Result = 'second product is cheaper at \$\{p2.toStringAsFixed(2)\} currency/kg vs \$\{p1.toStringAsFixed(2)\} currency/kg'; } else { Result = 'both products have the same price per mass at \$\{p1.toStringAsFixed(2)\} currency/kg'; }","tags":["comparison","shopping","economics"]}
+]

assets/formulas/optics.d4rt

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+[
+  {"name":"Snell's Law","input":[{"name":"n1","unit":"scalar"},{"name":"n2","unit":"scalar"},{"name":"theta1","unit":"degree"}],"output":{"name":"theta2","unit":"degree"},"d4rtCode":"var theta1Rad = theta1 * (pi / 180); var sinTheta2 = (n1 * sin(theta1Rad)) / n2; theta2 = asin(sinTheta2) * (180 / pi);","tags":["physics","optics","light"]}
+]

assets/formulas/thermodynamics.d4rt

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+[
+  {"name":"Ideal Gas Law","input":[{"name":"n","unit":"mole"},{"name":"T","unit":"kelvin"},{"name":"V","unit":"cubic meter"}],"output":{"name":"P","unit":"pascal"},"d4rtCode":"P = (n * 8.314462618 * T) / V;","tags":["physics","thermodynamics","gas"]}
+]