Appendices - Mathematics

To avoid long and involved explanations , the objective of these appendices is to develop deeply what is stated in the main pages: data, explanations and formulation needed for a deep theoretical and practical knowledge.

So, in the main pages the subject will be developed in the minimum extension to be clearly understood with references to the appendices which conclusions will be assumed there.

• Mathematics

  • General

    • Análisis gráfico, interpolación, extrapolación y regresión
    • Ecuaciones diferenciales, Ecuaciones diferenciales, Ecuaciones en derivadas parciales,
    • Ecuaciones de recurrencia
    • Matemática aplicada

  • Funciones Derivadas

    • Tabla de derivadas

  • Geometry

    • Euclidean vector

      • Vectores
      • Dot product
      • Cross product
      • Derivada de un vector

    • Trigonometry

    • Law of Cosines
    • Pythagorean theorem
    • Sagitta of an Arc
    • Calculating the Sagitta of an Arc The construction of so-called flattop guitars and similar instruments involves the use of various fixtures that feature long radius arcs. It is simple to approximate these arcs using bent splines but to do so one needs to know how far to bend the spline for a given radius arc. The key to this is calculating the deflection or displacement of the highest point of the arc from the midpoint of the chord that connects its end points. This quantity is called the sagitta or sag.
    • A Method for Calculating the Area of a Plate A simple paper and pencil method for calculating the area of an arbitrary plate (stringed musical instrument top or bottom) is presented.
    • Calculating Curtate Cycloid Points Curtate cycloid curves are used by some violin makers and guitarmakers for the arching profiles of carved plates. This page contains javascript calculators which generate these curves as series of points with regular x or y intervals.