{
  "version": 1,
  "name": "Math & geometry formulas",
  "iconName": "function",
  "colorID": "indigo",
  "detail": "Areas, volumes, algebra and trigonometry in one place",
  "cards": [
    {
      "title": "Area of a circle",
      "concept": "Radius squared times pi.",
      "code": "A = πr²",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Circumference of a circle",
      "concept": "Twice pi times the radius.",
      "code": "C = 2πr",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Area of a triangle",
      "concept": "Half the base times the height.",
      "code": "A = ½ · b · h",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Area of a trapezoid",
      "concept": "Average of the parallel sides times the height.",
      "code": "A = ½ (a + b) · h",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Pythagorean theorem",
      "concept": "In a right triangle, the squares of the legs add up to the square of the hypotenuse.",
      "code": "a² + b² = c²",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Volume of a sphere",
      "concept": "Four thirds pi times the radius cubed.",
      "code": "V = (4/3)πr³",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Surface area of a sphere",
      "concept": "Four pi times the radius squared.",
      "code": "S = 4πr²",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Volume of a cylinder",
      "concept": "Area of the base times the height.",
      "code": "V = πr²h",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Volume of a cone",
      "concept": "A third of the cylinder with the same base and height.",
      "code": "V = ⅓πr²h",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Quadratic formula",
      "concept": "Solves ax² + bx + c = 0.",
      "code": "x = (−b ± √(b² − 4ac)) / 2a",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Discriminant",
      "concept": "Positive: two real roots. Zero: one. Negative: none real.",
      "code": "Δ = b² − 4ac",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Slope of a line",
      "concept": "Rise over run between two points.",
      "code": "m = (y₂ − y₁) / (x₂ − x₁)",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Equation of a line",
      "concept": "Slope-intercept form.",
      "code": "y = mx + b",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Distance between two points",
      "concept": "The Pythagorean theorem in the plane.",
      "code": "d = √((x₂ − x₁)² + (y₂ − y₁)²)",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Midpoint",
      "concept": "Average the coordinates.",
      "code": "M = ((x₁ + x₂)/2, (y₁ + y₂)/2)",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Difference of squares",
      "concept": "A product that collapses.",
      "code": "a² − b² = (a + b)(a − b)",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Square of a sum",
      "concept": "Don't forget the middle term.",
      "code": "(a + b)² = a² + 2ab + b²",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Sine, cosine, tangent",
      "concept": "Opposite, adjacent and hypotenuse: SOH-CAH-TOA.",
      "code": "sin = opp/hyp, cos = adj/hyp, tan = opp/adj",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Fundamental trig identity",
      "concept": "Holds for every angle.",
      "code": "sin²θ + cos²θ = 1",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Law of sines",
      "concept": "Sides over the sine of their opposite angles are equal.",
      "code": "a / sin A = b / sin B = c / sin C",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Law of cosines",
      "concept": "The Pythagorean theorem with a correction.",
      "code": "c² = a² + b² − 2ab cos C",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Degrees to radians",
      "concept": "Multiply by pi over 180.",
      "code": "rad = deg · π / 180",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Sum of an arithmetic series",
      "concept": "Number of terms times the average of first and last.",
      "code": "S = n(a₁ + aₙ) / 2",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Sum of a geometric series",
      "concept": "With ratio r not equal to 1.",
      "code": "S = a(1 − rⁿ) / (1 − r)",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Compound interest",
      "concept": "Amount after t years at rate r, compounded n times a year.",
      "code": "A = P(1 + r/n)^(nt)",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    },
    {
      "title": "Combinations",
      "concept": "Ways to choose k from n when order doesn't matter.",
      "code": "C(n, k) = n! / (k!(n − k)!)",
      "languageID": "none",
      "kindRaw": "formula",
      "styleID": "",
      "notes": "",
      "colorID": "indigo",
      "tags": []
    }
  ],
  "subfolders": []
}