finite & infinite

Metropol Parasol Redevelopment of Plaza de la Encarnacion, Seville, Spain Sliceform

This is a geometrical composition where a basic decagonal shape exhibits 5-fold and 10-fold rotational symmetry. In it we can observe an interplay of various geometrical shapes from Penrose tilings P1 and P2 (thick and thin Penrose rhombs, and kites and darts), as well as pentagons, triangles, and pentagonal stars on different size scales. The composition also displays self-similarity and golden mean relations.

Artist Teja Krasek

Twist : (==) -(T)→ (-/-)              x              x+1 Rotates : (-/-) -(R)→  (-\-)                  x              -1/x

【Q】 A,B,C Classification standard?

Möbius function μ(n)=(-1)^ω(n)  ; ω(n) = Ω(n)       =0             ; ω(n)≠Ω(n)

ω (omega) or Ω (big omega) functions, which count the number of prime factors of integers.

Ω(n) : the number of prime factors of n ft. ω(n) : the number of disticnt prime factors of n ft. 【ex】24=2*2*2*3 Ω(24)=3+1=4, ω(24)=2