[ Pobierz całość w formacie PDF ]
.So, who really won the election [261]?Application 20 (Error-Correcting Code).The projective plane of order2, which is modeled by an equilateral triangle together with its incircle andaltitudes, is shown in Figure 3.20(a).There are 7 points (numbered) and 7 lines (one of which is curved); eachline contains three points and each point lies on three lines.This is also knownas the Steiner triple-system of order 7 since each pair of points lies on exactlyone line.The matrix representation is shown in Figure 3.20(b) where the rows92 Applications(a)(b)(c)Figure 3.20: (a) Projective Plane of Order 2.(b) Binary Matrix Representa-tion.(c) Hamming Code of Length 7.[286]represent lines, the columns represent points and the presence of a 1 indicatesthat a point lies on a line or, equivalently, a line contains a point (0 otherwise).The Hamming code of length 7, which contains 8 codewords, is obtained bytaking the complement of the rows of this matrix and appending the zerocodeword (Figure 3.20(c)).It has minimum Hamming distance d = 4 and is asingle-error-correcting code [286].Application 21 (Equilateral Triangle Rule (Speaker Placement)).Stereo playback assumes a symmetrical loudspeaker and listener arrangementwith a 60æ% angle between the loudspeakers and corresponding to an equilateraltriangular configuration (Figure 3.21) [208].Application 22 (Equilateral Triangular Microphone Placement).Hiokaand Hamada [173] have explored an algorithm for speaker direction tracking us-ing microphones located at the vertices of an equilateral triangle (Figure 3.22).In teleconferencing and remote lecturing systems, speaker direction track-ing is essential for focusing the desired speech signal as well as steering thecamera to point at the speaker.For these applications, the accuracy should bespatially uniform for omni-directional tracking and, for practical purposes, asmall number of microphones is desirable.Both of these objectives are achievedby the integrated use of three cross-spectra from the equilateral triangular mi-crophone array.Computer simulations and experimental measurements haveconfirmed that this array possesses uniform omni-directional accuracy and doesnot lose track of the speaker even if he/she moves abruptly.Applications 93Figure 3.21: Equilateral Triangle Rule [280]Figure 3.22: Equilateral Triangular Microphone Array [173]94 Applications(b)(a)Figure 3.23: Loudspeaker Array: (a) Icosahedral Speaker.(b) EquilateralTriangle Array.[13]Application 23 (Icosahedral Speaker).The research team at The Centerfor New Music and Audio Technologies (CNMAT) of UC-Berkeley, in collab-oration with Meyer Sound of Berkeley, California, has created a compact 120-channel approximately spherical loudspeaker for experiments with synthesis ofacoustic signals with real-time programmable directional properties.These directional patterns can reproduce the complete radiative signatureof natural instruments or explore new ideas in spatial audio synthesis.Aspecial hybrid geometry is used that combines the maximal symmetry of atwenty-triangular-faceted icosahedron (Figure 3.23(a)) with the compact pla-nar packing of six circles on an equilateral triangle (Figure 3.23(b) shows theresulting  billiard ball packing.) [13].Application 24 (Superconducting Sierpinski Gasket).In 1986, Gordonet al.[147] reported on their experimental investigations of the properties of asuperconducting Sierpinski gasket (SG) network in a magnetic field.Because of their dilational symmetry, statistical mechanical and transportproblems are exactly solvable on these fractals.Moreover, study of the SGnetwork is inherently interesting because of its lack of translational invarianceand its anomalous (fractal) dimensionalities.The experimental gaskets (Fig-ure 3.24) were of tenth order with elementary triangles of area 1.38 µm2 andproduced excellent quantitative agreement with theoretical predictions.Applications 95Figure 3.24: Superconducting Sierpinski Gasket [147]Figure 3.25: Square Hole Drill (U.S.Patent 4,074,778) [242]96 ApplicationsApplication 25 (Square Hole Drill).In 1978, U.S [ Pobierz caÅ‚ość w formacie PDF ]