Flat finger loop

A membrane comprising:

• a first opening and a second opening, where the length of the portion of the edge of said first opening between an edge of said first opening and said second opening and bounded by any two points that exist on said portion of the edge of said first opening that are farthest apart along said portion of the edge of said first opening and on separate continuous segments of intersection with the shortest possible path between a first tangent point at which one of two tangent lines, each tangent to both said first opening and said second opening, is tangent to said first opening and a second tangent point where the other of said two tangent lines is tangent to said second opening, where said first tangent point and said second tangent point are chosen so that the length of the shortest possible path between the said first tangent point and said second tangent point through the region between said first opening and said second opening is minimized, and where the length of the portion of the edge of said second opening between an edge of said second opening and said first opening and bounded by any two points that exist on said portion of the edge of said second opening that are farthest apart along said portion of the edge of said second opening and on separate continuous segments of intersection with said shortest possible path between said first tangent point and said second tangent point, differ by at most 10% of the length of the smaller of the two, and such that for any point on the first of said two tangent lines and between and excluding said first opening and said second opening and for any point on the second of said two tangent lines and between and excluding said first opening and said second opening, the shortest possible path between said point on said first of said two tangent lines and said second of said two tangent lines and through the region between said first opening and said second opening is greater in length than the straight line between said first point and said second point;
• such that a plurality of fingers may be inserted through either said opening and out of the other said opening whereby a region of said membrane between said first opening and said second opening changes out of a flat orientation and into a loop orientation and forms a loop around said plurality of fingers that tightly grips said plurality of fingers.

A smartphone case having:

• a first opening and a second opening, each having a shape and orientation with respect to each other such that it is possible to choose two points along the edge of said first opening so that a portion of the edge of said first opening and a straight line through said two points along the edge of said first opening bound a region containing part of said second opening and such that it is possible to choose two points along the edge of said second opening so that a portion of the edge of said second opening and a straight line through said two points along the edge of said second opening bound a region containing part of said first opening;
• whereby the region between said first opening and said second opening is able to contort out of a flat orientation when a plurality of fingers are inserted through one said opening and out of the other said opening, forming a loop around said plurality of fingers and attaching said plurality of fingers to said smartphone case, while said smartphone case remains attached to a smartphone, thus attaching said plurality of fingers to said smartphone, and where said first opening and said second opening are each formed in the shape of a narrow non-inflected curved line having rounded bulbous ends, where a portion of said first opening and said second opening have rounded edge corners, and where said narrow non-inflected curved line is defined as any line segment of any width that is able to fit within the bounds of a region defined by the union of an up to 1 mm wide and up to 20 mm long rectangle tangentially abutting an up to 120 degree portion of a circle with radius of up to 20 mm and where said line begins at the non-abutting end of said rectangular region, and where said narrow non-inflected curved line is joined at either end to the narrow part of an up to 50 mm long teardrop shape with a bulbous end portion with radius of up to 3 mm, and where said second opening is rotated between 160 and 200 degrees with respect to said first opening and spaced apart from said first opening such that the resulting strip of said membrane between said first opening and said second opening has an up to 20 mm width, and where a region of said membrane surrounding said first opening and said second opening is up to 3 mm in thickness and made from a material selected from the group consisting of at least one of the following:
• thermoplastic polyurethane (TPU), polyethylene, polypropylene, polyurethane, vinyl, silicone, a blend of plastics, rubber, natural leather, synthetic leather.