U.S. patent application number 09/829886 was filed with the patent office on 2002-01-31 for tabletop with a configuration having safety features and maximum seating capacity for a given size.
Invention is credited to Akyuz, Ahmet Fevzican.
Application Number | 20020011197 09/829886 |
Document ID | / |
Family ID | 23632222 |
Filed Date | 2002-01-31 |
United States Patent
Application |
20020011197 |
Kind Code |
A1 |
Akyuz, Ahmet Fevzican |
January 31, 2002 |
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.
Inventors: |
Akyuz, Ahmet Fevzican;
(Istanbul, TR) |
Correspondence
Address: |
ABELMAN FRAYNE & SCHWAB
Attorneys at law
150 East 42nd Street
New York
NY
10017
US
|
Family ID: |
23632222 |
Appl. No.: |
09/829886 |
Filed: |
April 10, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09829886 |
Apr 10, 2001 |
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09412244 |
Oct 5, 1999 |
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Current U.S.
Class: |
108/161 |
Current CPC
Class: |
A47B 13/10 20130101 |
Class at
Publication: |
108/161 |
International
Class: |
A47B 013/00 |
Claims
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 8 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.
Description
FIELD OF THE INVENTION
[0001] This invention generally relates to 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. More particularly, the invention relates to such shapes
as used for items of furniture, windows, doors, and floor
coverings. Still more particularly, the invention relates to such
shapes that have closed, curvilinear outer boundaries and that are
substantially two-dimensional, with no angular corners or sharp
edges in their contour, for use as tabletops, wherein the number of
individuals, who may be seated around the perimeter of a table
incorporating such a tabletop, is maximized for a table of given
dimensions, as measured by a total continuous linear dimension,
with each individual to be seated thereat being allocated a
predetermined amount of linear space around the periphery of the
table.
BACKGROUND OF THE INVENTION
[0002] Plane surfaces such as windows, doors, carpets, tables, and
the surface of furniture and other items have previously been
designed so that those surfaces have boundaries which are
rectangular, square, circular, elliptical, or a combination of
these geometric shapes.
[0003] In general, the closed outer boundary of a geometric shape
is described by the equation (1): 1 x u A u + y v B v = 1 ( 1 )
[0004] where x and y are coordinates of points on the outer
boundary of the geometric shape, with reference to x and y axes
defining an ordinary Cartesian coordinate (x, y) system; and A and
B are the coordinates of the points at which the curve described by
the above equation intersects the x and y axes. Specifically, the
curve intersects the positive x axis at (A, 0), the negative x axis
at (-A, 0), the positive y axis at (0, B), and the negative y axis
at (0, -B). The exponents u and v are the degrees or orders of the
closed curve, and may be any rational numbers, not just integers.
If u=v=2 and A=B, the curve is a circle. If u=v=2 and A is not
equal to B, the curve is an ellipse. If u=v=.infin. and A=B, the
closed curve is a square. Finally, if u=v=.infin. and A is not
equal to B, the closed curve is a rectangle.
[0005] Although the circle and ellipse have commonly been used in
the surfaces previously described, they lack surface area present
with respect to comparably dimensioned squares and rectangles,
respectively. On the other hand, the square and rectangular shapes,
although providing maximum surface area for a given A and B, are
not aesthetically pleasing and have the ergonomic disadvantage of
sharp corners which may cause injury or other discomfort to
users.
[0006] Thus, there exists a need for surfaces shaped such that more
surface area is available than the traditional circular or
elliptical shapes, while eliminating the unattractiveness of and
the hazard of sharp corners of square or rectangular shapes.
SUMMARY OF THE INVENTION
[0007] The invention comprises surfaces, such as table tops, with
boundaries defined by the general analytical curve (1), shown
above, but with the further restriction that 2<u<10 and
2<v<10 (2). The lower limit of 2 defines a circle (when A=B)
or an ellipse (when A B). The upper limit of 10 has been found
empirically to be the limit after which the boundary shape
approximates a rectangle or square, albeit with slightly rounded
corners.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIG. 1 is a graphical representation of two comparative
closed curves for the case of A=4 and B=3 where u=v=2 for one curve
and u=v =3 for the other curve.
[0009] FIG. 2 is a graphical representation of two comparative
closed curves for the case of A=4 and B=3 where u=v=2 for one curve
and u=v=4 for the other curve.
[0010] FIG. 3 is a graphical representation of two comparative
closed curves for the case of A=4 and B=3 where u=v=2 for one curve
and u=v=6 for the other curve.
[0011] FIG. 4 shows a plan view of a table top of an elliptical
shape (u=v=2) where A=46 inches and B=23 inches, and shows outlines
of 23 inch width spaces, each space representing the width needed
for the seating of one person, arranged around the table top.
[0012] FIG. 5 shows a plan view of a table top of a shape where
u=v=4 and where A=46 inches and B=23 inches, and shows outlines of
23 inch width spaces, each space representing the width needed for
the seating of one person, arranged around the table top.
[0013] FIG. 6 is a three-dimensional perspective view of the table
of FIG. 6.
DESCRIPTION OF PREFERRED EMBODIMENTS
[0014] Equation (1) can be converted into the following equation by
multiplying both sides by the factor A.sup.uB.sup.v:
B.sup.vx.sup.u+A.sup.uy.sup.v=A.sup.uB.sup.v (3)
[0015] Setting x=0, one obtains:
A.sup.yy.sup.v=A.sup.uB.sup.v (4)
y=B (5)
[0016] Letting y=0, one further obtains:
B.sup.vx.sup.u=A.sup.uB.sup.v (6)
x=A (7)
[0017] Differentiating equation (3) with respect to x results in: 2
B v ux u - 1 + A u vy v - 1 y x = 0 ( 8 ) 3 y x = - B v ux u - 1 A
u vy v - 1 ( 9 )
[0018] Evaluating 4 y x
[0019] at x=0, one obtains: 5 y x = 0 x = 0 ( 10 )
[0020] Finally, evaluating 6 y x
[0021] represented by the equation (9) at y=0, one obtains: 7 y x =
.infin. y = 0 ( 11 )
[0022] It has been empirically determined that u and v should not
be allowed to reach the value of 10.
[0023] In general, the surface area available increases as the
degree of the curve increases, with the most dramatic increase
occurring from the elliptical shape to the third degree shape.
[0024] FIGS. 1-3, respectively, graphically show the closed curves
for u=v=3, u=v=4, and u=v=6, where A=4 and B=3 for all of FIGS.
1-3. The closed curves are drawn with respect to a Cartesian
coordinate system, wherein the x axis is a first axis of symmetry,
2, for the curves, and the y axis is a second axis of symmetry, 4,
for the curves. Being the axes of a Cartesian coordinate system,
the x and y axes are perpendicular to each other. In all of FIGS.
1-3, the closed curve for u=v=2 and A=4 and B=3, which is an
ellipse, is also drawn with respect to the x and y axes for the
purpose of comparison to the curves for u=v=3, u=v=4, and
u=v=6.
[0025] The use of these boundaries of degree three or higher up to
degree nine can be applied in a myriad of plane surfaces commonly
used. Examples of such applications are tables, doors, windows,
carpets, any plane surface of furniture, or indeed any plane
surface of any object imaginable. Furthermore, although the surface
enclosed by such a shaped boundary may not, in fact, be planar, but
rather curved in three dimensional space (curviplanar surface), the
shape of the boundary described herein can still be used with like
advantages for increased surface area yet pleasing aesthetic
appearance and beneficial ergonomic characteristics.
[0026] A specific example of a tabletop with a shape defined by the
boundary of a closed curve, with A and B being set at actual
physical dimensions, such that A=46 inches and B=23 inches, and
u=v=4 is shown in FIG. 5. Standard individual seating spaces of
23-inch width are arranged about the table. As can be seen in FIG.
5, a total of ten such seating spaces can be arranged around the
table. In contrast, a table top with a boundary, described by a
closed curve with the same values of A and B as FIG. 5, but with
u=v=2 (an ellipse), is shown in FIG. 4. FIG. 4 shows that only
eight 23-inch seating spaces can be arranged comfortably about that
table. The 14-inch seating spaces remaining at each relatively
curved end of the table do not afford comfortable seating
spaces.
[0027] FIG. 6 is a three-dimensional (3-D) perspective view of the
table according to FIG. 5, showing the way in which ten persons may
comfortably be seated.
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