Maths Dojo

Opening note:   Aside from the 20.July 2024 tour of the Maths Dojo, the Mathematics Club of Science Circle is currently in SUMMER RECESS.

The FALL 2024 schedule of Maths Club will resume in the Maths Dojo at 4 PM PDT on Thursday 5.September 2024 

                   and discuss  AMORTIZATION, Finance, interest, paying off loans and the semi-complex relationships to geometric progressions

    so come and discover in yourself the talents your ancestors bequeathed to you!

Welcome to MATHS DOJO – please take off your shoes and step onto the mat.

We will discuss a very important result in geometry and trigonometry: 

     namely, how one derives formulae for 

       SINE AND COSINE TRIGONOMETRIC FUNCTIONS for SUM OF TWO ANGLES:

             sin (α + β) and cos (α + β)

and how this GEOMETRIC INTERPRETATION relates to 

MULTIPLICATION OF 2×2 MATRICES 

as well as 

MULTIPLICATION of COMPLEX NUMBERS IN THE COMPLEX PLANE

with mention of  de Moivre’s Theorem of 1708  

if           Z          =       [  | Z |  *  [  cos ( 𝛉 )   +  i  sin ( 𝛉  ) ]   ^ n   

then      Z ^ n     =    | Z | ^ n  *  [ cos (n 𝛉)   +  i sin (n 𝛉) ]

where symbols such as  ”  z ^ n  ”  indicates that z is multiplied by itself n times (raised to the  nth power) 

and    | Z |    is the “length” of the complex number  Z, considered as a vector in the plane.

This becomes easily validated using PROOF BY INDUCTION (which is nearly as easy as counting n = 1, 2, 3, …, to infinity)!

Don’t be afraid! As The Staple Singers belted out: “Come on and help me! I’ll take you there!  Let me take you there!” so let’s have fun with it!

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Have a HAPPY SUMMER 2024!!!!!