Mathematics Formulas and Concepts

Posted on Nov 28, 2024 in Electronics

Mathematics Formulas & Concepts

Geometric Formulas

  • Area of a polygon: A = Fn / 2 (where F is the number of sides and n is the length of each side)
  • Volume of a pyramid: V = Abase * h / 3 (where Abase is the area of the base and h is the height)
  • Area of a circle: A = 4πR2
  • Volume of a sphere: V = 4πR3 / 3

Apothem

  • Triangle: m = √3 / 6
  • Square: m = a / 2
  • Hexagon: a3 = m / 2

Regular Tetrahedra

  • Height: h = a√6 / 3
  • Area: AT = a2√3 / 2
  • Distance between two points (DAB): √((XA-XB)² + (YA-YB)2)

Lines and Angles

  • Area of a triangle: Atri = |D| / 2 (where D is the determinant)
  • Parallel lines: m1 = m2
  • Perpendicular lines: m1 = -1/m2
  • Distance from a point to a line (dP.R): |ax + by + c| / √a² + b²
  • Angle between two lines: tanθ = |m1 – m2| / |1 + m1*m2|
  • Angle of a vertical line: tanθ = 1/m1

Complex Numbers

  • Conjugate: z = a + bi, z’ = a – bi
  • Polar form: Z = r(cosθ + i sinθ)
  • Quadrants: x = real, y = imaginary

Other Formulas

  • Slope: m = (y3 – y1) / (x3 – x1)
  • Equation of a line: x + y = 3