finite & infinite

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In his series Landline, New York-based artist Aakash Nihalani cleverly pierces human torsos throughout Brooklyn with three-dimensional isometric rectangles and squares made out of neon tape. The artist’s keen eye for perspective is evident in the optical illusions, which are produced with tape, paper, corrugated plastic, and magnets.

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착시

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Partner Yoga

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PI

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

http://www.yatzer.com/Metropol-Parasol-The-World-s-Largest-Wooden-Structure-J-MAYER-H-Architects

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Pi http://www.cafepress.com/+golden_ratio_math_clock_wall_clock,790584759

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Dizzy.A 3D-printed version of the Penrose Triangle illusion, created with partial inverted cubes.

(The 3D model is available under the “Attribution/Non-Commercial/Share-Alike” license here)

By Chylld (Own work) [CC-BY-SA-3.0], via Wikimedia Commons

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Orderly tangle hexagon

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Orderly tangles F(x)=2*floor{(x+2)/2} x:polygon 3-gon (3,4,3,4) 4-gon (3,4,4,4) 5-gon (3,5,3,5) 6-gon (3,4,4,5) (3,5,3,5) (3,5,3,6)

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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

From gallery.bridgesmathart.org/exhibitions/

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Conwar's rational tangles

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

Sequence:TTTRT 0/1 -(T)→1/1-(T)→2/1 -(T)→3/1(R)→ −1/3-(T)→2/3 Solution:RTTRTT 2/3-(R)→−3/2-(T)→−1/2-(T)→1/2(R)→−2/1-(T)→−1/1-(T)→0/1

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A : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, … B : 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, … C : 1, 6, 10, 14, 15, 21, 22, 26, …

【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

-1 : ω(n) = Ω(n) & ω(n)≡1 (mod 2) 0 : ω(n)≠Ω(n) 1 : ω(n) = Ω(n) & ω(n)≡0 (mod 2) A(-1) : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 30, … B (0) : 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, … C (1) : 1, 6, 10, 14, 15, 21, 22, 26, …