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Great-circle geodesic domeRelated Patent Categories: Games Using Tangible Projectile, Golf, Ball, Particular Cover (e.g., Size, Material, Dimple Pattern, Etc.), Icosahedral Dimple PatternGreat-circle geodesic dome description/claimsThe Patent Description & Claims data below is from USPTO Patent Application 20060135288, Great-circle geodesic dome. Brief Patent Description - Full Patent Description - Patent Application Claims
[0001] This application claims priority U.S. Provisional Patent Application Ser. No.: 60/651,006, filed 9 Feb. 2005; 60/647,406, filed 28 Jan. 2005; 60/643,149, field 13 Jan. 2005; and 60/637,889, filed 22 Dec. 2004, the complete disclosures of which are incorporated herein by reference. FIELD OF THE INVENTION [0002] A conventional dome comprising a saddle structure or a conventional geodesic dome made of triangular basis elements have elements under tension; whereas, a perfect dome is essentially or entirely under compression since all of weight is equally distributed. Furthermore, a perfect sphere has no unique position on the surface or unique axis. This invention relates to a structure that more closely replicates a perfect sphere or dome using finite elements derived from great circles. In an embodiment, the surface has a characteristic that axes defined by crossings of great-circle elements are not unique. Such an architectural structure or container is anticipated to be stronger and provide more efficiency of material requirements than in conventional systems such as a structure made of triangular basis elements as in the case of a conventional geodesic dome. The structure is also more esthetic and natural. It further permits the construction of near perfect spherical dishes without machining out a solid material which is a very challenging fabrication problem. Broad application in architecture and industry by one skilled in the Art is anticipated and within the scope of the current Invention. BACKGROUND OF THE INVENTION [0003] This Invention relates to a geometrical derivation of a means to generate a perfect sphere using great circles. The disclosure and background are given in the book, R. Mills, The Grand Unified Theory of Classical Quantum Mechanics, January 2006 Edition, BlackLight Power, Inc., Cranbury, N.J.; posted at http://www.blacklightpower.com/bookdownload.shtml ("Mills GUT"), which is incorporated by reference in its entirety. The Chapter One and Appendix III are preferred references which are also incorporated by this reference. SUMMARY OF THE INVENTION [0004] The object of this invention is to provide a sphere or spherical section such as a dome as a universal architectural structure or container, that is a more ideal of a perfect sphere or dome or spherical section using finite elements. [0005] The present invention is a structural system and a method of fabricating the system comprised of finite elements called basis elements such as great circles or partial great circles to form a great-circle geodesic sphere, dome, or arch called a great sphere, dome, and arch, respectively. The structure is generated by forming a pattern of the basis element rotated at incremental angles about a rotational axis from an initial position to define a so-called primary component orbitsphere-cvf. The primary component orbitsphere defines a stationary pattern as well as a structural element called a secondary component orbitsphere-cvf that is constructed according to the pattern of the primary orbitsphere-cvf. The secondary component orbitsphere-cvf is initially oriented at the initial position and is incrementally rotated about the rotational axis to form the great-sphere-type structure. The structure defined as Y.sub.0.sup.0(.phi.,.theta.) may formed according to Eqs. (67-71) of the ANALYTICAL EQUATIONS TO GENERATE THE ORBITSPHERE CURRENT VECTOR FIELD AND THE UNIFORM CURRENT (CHARGE)-DENSITY FUNCTION Y.sub.0.sup.0(.phi.,.theta.) section. [0006] Another embodiment of the Invention comprises a uniform current density function on a two dimensional surface defined as Y.sub.0.sup.0(.phi.,.theta.) and a method and constructing Y.sub.0.sup.0(.phi.,.theta.). The current density function may have a defined angular momentum along two orthogonal axes that is determined by the selection of the desired angular momentum of the basis elements and by the selection the rotational matrices that form the Y.sub.0.sup.0(.phi.,.theta.) with the desired angular momentum projections. The angular momentum components have corresponding magnetic moments in the embodiment wherein the elements are current loops. A further embodiment comprises a uniform mass-density structure with desired angular momentum components. This embodiment is constructed by using mass-flowing elements rather than current elements. BRIEF DESCRIPTION OF THE DRAWINGS [0007] FIG. 1 is the element pattern given by Eq. (1) shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The great circle element that served as a basis element that was initially in the yz-plane is shown as red in accordance with the present invention; [0008] FIG. 2 is the element pattern of the orbitsphere-cvf component of STEP ONE shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The yz-plane great circle element that served as a basis element that was initially in the yz-plane is shown as red in accordance with the present invention; [0009] FIG. 3 is the element pattern of the orbitsphere-cvf component of STEP ONE shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The great circle element that served as a basis element that was initially in the xz-plane is shown as red in accordance with the present invention; [0010] FIG. 4 the element pattern given by Eq. (7) shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The great circle element that served as a basis element that was initially in the xy-plane is shown as red is in accordance with the present invention; [0011] FIG. 5 is the element pattern for the rotation of the xy-plane great circle about the (-i.sub.x,0i.sub.y,i.sub.z)-axis (Eq. (10)) shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The great circle element that served as a basis element that was initially in the xy-plane is shown as red in accordance with the present invention; [0012] FIG. 6 is the element pattern of the orbitsphere-cvf component of STEP TWO shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The great circle element that served as a basis element that was initially in the xy-plane is shown as red in accordance with the present invention; [0013] FIG. 7 is the element pattern of the orbitsphere-cvf component of STEP TWO shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The great circle element that served as a basis element that was initially in the yz-plane is shown as red in accordance with the present invention; [0014] FIG. 8 is the element pattern of the orbitsphere-cvf shown with 6 degree increments of .theta. from the perspective of looking along the z-axis onto which L.sub.R, the resultant vector of the L.sub.xy and L.sub.z components, was aligned in accordance with the present invention; [0015] FIG. 9 is the schematic of the relative dimensions of the component orbitsphere-cvfs (STEP-ONE component shown in blue and STEP-TWO component shown in red) that make-up the orbitsphere-cvf in accordance with the present invention; [0016] FIG. 10 is the element pattern given by Eq. (30) shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The great circle element that served as a basis element that was initially in the yz-plane is shown as red in accordance with the present invention; [0017] FIG. 11 is the element pattern of the orbitsphere-cvf component given by Eq. (33) that is orthogonal to that of STEP ONE shown with 6 degree increments of .theta. from the perspective of looking along the z-axis. The yz-plane great circle element that served as a basis element that was initially in the yz-plane is shown as red in accordance with the present invention; [0018] FIG. 12 is the element pattern given by Eq. (37) shown with 6 degree increments of .theta. from the perspective of looking along the z-axis obtained from Eq. (32) by rotation about the (i.sub.x,-i.sup.y,0i.sub.z)-axis by .pi. using Eq. (34). The great circle element that served as a basis element that was initially in the yz-plane is shown as red in accordance with the present invention; [0019] FIG. 13 is the orbitsphere, a two dimensional spherical shell in accordance with the present invention; [0020] FIG. 14 is a representation of the uniform element pattern of the Y.sub.0.sup.0(.phi.,.theta.) orbitsphere shown with 30 degree increments (N=M=12 in Eq. (67)) of the angle to generate the orbitsphere current-vector field corresponding to Eq. (30) and 30 degree increments of the rotation of this basis element about the (i.sub.x,i.sub.y,0i.sub.z)-axis corresponding to Eq. (4). The perspective is along the z-axis. The great circle element that served as a basis element that was initially in the plane along the (i.sub.x,-i.sub.y,0i.sub.z)- and z-axes of each secondary component orbitsphere-cvf is shown as red. Note that it is stationary over the convolution due to phase matching in accordance with the present invention; Continue reading about Great-circle geodesic dome... Full patent description for Great-circle geodesic dome Brief Patent Description - Full Patent Description - Patent Application Claims Click on the above for other options relating to this Great-circle geodesic dome patent application. ###  How KEYWORD MONITOR works... a FREE service from FreshPatents1. Sign up (takes 30 seconds). 2. Fill in the keywords to be monitored. 3. Each week you receive an email with patent applications related to your keywords. Start now! - Receive info on patent apps like Great-circle geodesic dome or other areas of interest. ### Previous Patent Application: Golf ball Next Patent Application: Mending device for golf grass fields Industry Class: Games using tangible projectile ### FreshPatents.com Support Thank you for viewing the Great-circle geodesic dome patent info. 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