Tabletop with a configuration having safety features and maximum seating capacity for a given size

Abstract

Surfaces of objects and the shapes thereof, which are two-dimensional, closed, curvilinear and three-dimensional, closed, curviplanar in nature, and which have outer boundaries that are defined according to a mathematical expression, such that the shapes have no discontinuities, irregularities, inflection or transition points about their periphery that result in potentially unsafe or dangerous angular, sharp corners or edges in the contours of the shapes, and are otherwise also generally ergonomically beneficial and aesthetically pleasing, are disclosed. The shapes are useful in providing surfaces for objects such as items of furniture, windows, doors, and floor coverings. The shapes are particularly useful for providing surfaces for tabletops that also maximize the number of individuals, who may be seated around the perimeter of a table, for a table of given dimensions, with each individual to be seated thereat being allocated a predetermined amount of linear space around the periphery of the table.

What is claimed is:  
     
         1 . A surface of an object, comprising a shape having a closed, curvilinear outer boundary, the outer boundary of the shape being defined by a curve having a mathematical expression I  
       
         
           
             
               
                 
                   
                     
                       
                         
                           x 
                           u 
                         
                         
                           A 
                           u 
                         
                       
                       + 
                       
                         
                           y 
                           v 
                         
                         
                           B 
                           v 
                         
                       
                     
                     = 
                     1 
                   
                 
                 
                   
                     ( 
                     I 
                     ) 
                   
                 
               
             
           
           
           
               
           
         
       
       wherein: 
 x and y are coordinates of points (x, y) on the curve, as measured with reference to x and y axes of a standard Cartesian (x, y) coordinate system, from the origin ( 0 ,  0 );  
 A and B are respectively coordinates of positive x and y intercepts of the curve, as measured with reference to the x and y axes of the standard Cartesian coordinate system, the positive x and y intercepts having respective coordinates A=(A,  0 ) and B=( 0 , B); and  
 u and v are orders of the curve, wherein u and v are each rational numbers in the range of from 2 to 10, and wherein u and v alternatively are the same or are different.  
 
     
     
         2 . The surface of an object according to  claim 1 , wherein the object is selected from the group consisting of: an item of furniture; a door; a window; and a floor covering.  
     
     
         3 . The surface according to  claim 2 , wherein the object is an item of furniture.  
     
     
         4 . The surface according to  claim 3 , wherein the item of furniture is a tabletop.  
     
     
         5 . The surface according to  claim 2 , wherein the object is a floor covering.  
     
     
         6 . The surface according to  claim 5 , wherein the floor covering is selected from the group consisting of: a mat; a rug; and a carpet.  
     
     
         7 . The surface according to  claim 5 , wherein the floor covering is free laying and not wall-to-wall.  
     
     
         8 . The surface according to  claim 1 , which is a flat planar surface existing in two dimensions.  
     
     
         9 . The surface according to  claim 1 , which is a curvi-planar surface existing in three dimensions.  
     
     
         10 . The surface according to  claim 1 , wherein A=4, B=3, and u=v= from about 2 to about 6.  
     
     
         11 . The surface according to  claim 1 , wherein A=2, B=1, and 2<u=v<10.  
     
     
         12 . A surface for a table top according to  claim 1 , wherein a relative ratio of the dimensions of A:B is 2:1; A has an absolute dimension of from about 40 to 50 inches; B has an absolute dimension of from about 20 to 25 inches; and u=v=4.