Understanding Isometries in R2 and R3: A Comprehensive Breakdown

Posted by on Jan 10, 2025 in Computing and Communications | 0 comments

Understanding Isometries in R2

Theory

It retains the standard distance i = A · AT = Id. Det = +1 or -1.

Vector fix: v ∈ P associates at v ∈ P 1SI F ∈ G = Tv, then F o G also. Det H = Det G · Det F.

Equations: Tv(x, y) = (x, y). Base service: Tv = Cne · Tn · Cne-1

Note: A * I must be symmetrical.

CNE

  1. Find a point on the axis or plane (one that satisfies the equation).
  2. From the equation equal to 0, if you are caught, separate subjects. If not equal to 0, they are roofed and left all depending on
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