B.2 ODEMA: PRODUK SOUVENIRS DAN ASESORIS Keterangan : Disain (kiri) dan produk (kanan) 28
Description (above): Ornaments are put inside the office as decoration (Parhusip,2014) Description (above) Ornaments in middle and small sizes are used as accessories for Hypocycloid dance (Parhusip,2014) presented in mathematics promotion November 2013 di BU UKSW, Indonesia. 29
800 600 400 200 0-200 -400-600 -800-800 -600-400 -200 0 200 400 600 800 1 x 10-4 0.8 0.6 0.4 0.2 0-0.2-0.4-0.6-0.8-1 -1-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 x 10-4 1.5 x 1015 30 1 20 0.5 10 0 0-0.5-10 -1-20 -1.5-1.5-1 -0.5 0 0.5 1 1.5 x 10 15-30 -30-20 -10 0 10 20 30 Keterangan : Motif-motif yang dicetak pada tas dengan formulasi yang diekspresikan pada tas (dapat sebagai souvenir) 30
6 x 1011 4 2 0-2 -4-6 -6-4 -2 0 2 4 6 x 10 11 3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 Keterangan : Beberapa disain motif (atas) yang diterapkan sebagai disain motif untuk souvenir kaleng 31
3 2 1 0-1 -2-3 -3-2 -1 0 1 2 3 Keterangan : Disain (kiri) dan hasil produk berupa hiasan di kepala/bando (kanan) Keterangan : Disain (kiri) dan hasil produk berupa hiasan di berupa bros (kanan) 32
GELAS SOUVENIR 3 2 1 0-1 -2-3 -4-3 -2-1 0 1 2 3 4 Keterangan : Motif (atas) dan produk gelas yang ditempeli disain motif di atas dengan formula yang ditempelkan pada gelas tersebut 33
Keterangan : Disain (atas) dan hasil produk berupa hiasan di berupa bros dan hiasan rambut (kanan) 34
1 x 106 0.8 0.6 0.4 0.2 0-0.2-0.4-0.6-0.8-1 -1-0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1 x 10 6 Keterangan : Disain (atas) dan produk (tengah) dan bawah berupa taplak dan tas 35
Description. Accessories designs and ornaments (second row) 36
Description : Hypocycloid curves are considered to be the domains for complex mappings, i.e. f(z) =sin(z) (first row) and f ( z) 1/ z z (second row). Mathematical ornaments (ODEMA) made of copper polished by silver (shown by second coloumn) The patterned have been published in poster presentation ICM 2014 and in International Journal of Statistics and MathematicsVol. 1(3), pp. 016-023, August, 2014. 37
Keterangan : ODEMA dengan nama ROCKET MATH untuk hiasan taman yang dibuat berdasarkan pemetaan fungsi komplek, dapat juga untuk pohon hias (pohon Natal) 38
Keterangan : Disain 2 dimensi dalam bentuk ornament hiasan yang dikemas dalam kerdus hitam 39
Keterangan : Disain (atas) dan Motif yang diperoleh digambarkan pada ukuran besar dan dengan manic-manik dan dikemas 40
PART C ODEMA 3D DESIGNED Description : Some ornaments here are designed by generalizing hypocycloid equations into 3 dimentional based on spherical coordinates. Some are also defined by the triple equations created by each derivative. The equation for 3 dimensional 3D hypocycloid : a x sin a b cos bcos 1 (s.1) b a y sin a b sin bsin 1 (s.2) b z cos ; r / sin (s.3) The other surfaces are obtained by generalizing equation of ball. Instead of power of 2 for each term for a ball equation, one uses the p- power, i.e p p p p x y z r. (s.4) C.1 ODEMA Disain Sanggul FLY CAKE The second derivative of hypocycloid for a=1;p=1;q=4;b=p/q Keterangan : Disain (kiri dan produk berupa sanggul (kanan) yang dibuat oleh LIRA (Yayasan Limbah Rambut) di Blotongan Salatiga. 41
Mathematical background : Hypocycloid equation innovated into 3 dimensional with Z= cos dimana r / sin dan r x 2 y 2 surf(dxdt,dydphi,z) surf(dxdphi,dydt,z) 42
FIVE CUTS Description : surfaces of hypocycloid for p=1;q=6; a=1;b=-(p/q); ALIENT HEAD Description : surfaces of derivatives hypocycloid p=1;q=6; a=1;b=-(p/q); 43
z-axis C.2 ODEMA- (Math ART) Mathematical background : surfaces designed from function variables 2 0-2 -2 0 y-axis 2 2 0 x-axis -2 x 2 1 y 2 z 1 e u / 6 2 e cos u cos v / 2 u / 6 1 e sin u cos v / 2 u / 3 sin u / 6 v e sin( v) 2 Keterangan : Ornaments designed by using resin (oleh Ary Souvenir Jogja) 44
Description : Design(left) and its surface (right) of p=2/8=1/4 in Eq.(s.4) dx dy dz ; ;, for 45
Description : Design(left) and its Surface of with a=5;b=1; dx dy dz ; ; of 3d Hypocycloid dx dy dz Description (above) Surface of ; ; of 3d Hypocycloid : p=1;q=4; a=1;b=-(p/q); 46
Description : Derivative of hypocycloid p=1;q=6; a=1;b=-(p/q). 47
Keterangan : Twin Cups, generalization of balls (Week balls, with p=) Surface of Derivative of hypocycloid dx dy dz,, p=1;q=4;a=1;b=-(p/q); 48
Description : Surface of Derivative of hypocycloid p=1;q=4;a=1;b=-(p/q); dx dy,, z Description : ODEMA of x p y p z p r p for p / 7 49
The used equation is C.4 ODEMA Generalized Balls (Masih hanya disain) x p y p z p r from the real part of the triple (x,y,z) for a fix value of r) p for all surfaces (below) and drawn 3D ASTROID P=2/3 =6/9 p=6/1 P=6/2 Bola P=6/3 50
p=6/4 p=6/5 p=6/7 p=6/8 p=6/10 51
Description. Surfaces created for k p /, k=1,2,3,,15. 52
Description : Collections surfaces of dx dy dz ; ;. 53
C.5 ODEMA TWIN CUPS Surfaces below are collected into one family TWIN CUPS since the behavior of surfaces are similar. The surfaces here are created from the derivatives of generalized balls for p=2/3 which is 3D astroid. Twin Cups-V dx dy dz ; ; Twin Cups-N dy dy dz ; ; Description : Twin Cups-P (left and right are the same) Two surfaces are drawn together, dx dy dz ; ; and dy dy dz ; ; 54
C.6 ODEMA PARKING PARK Description A family of parking surfaces from generalizatio of balls equation p=13/3 p=14/3 p=15/3 p=16/3 55
C.7 ODEMA LOVE GUN Surfaces below are defined by generalized balls equations p=1/2 p=1/3 p=1/4 Surfaces of dy dy dz ; ; p=1/5 56
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