set forth below is a description of what are believed to be the preferred embodiments and / or best examples of the invention claimed . future and present alternatives and modifications to this preferred embodiment are contemplated . any alternatives or modifications which make insubstantial changes in function , in purpose , in structure , or in result are intended to be covered by the claims of this patent . in accordance with a preferred embodiment of this invention , an aglet 10 is shown in fig1 - 3 . aglet 10 preferably consists of a solid shape with a tapering design . the fibers of lace 20 may be fused directly to the internal surface area of neck 15 using a common adhesive such as , for example , epoxy resin or glue . preferably , aglet 10 includes inner and outer axes of curvature 11 , 12 , respectively , which converge at apex 16 . a tangent line intersects a preferred outer axis of curvature at about 0 ° at the neck , and at about 30 ° at the apex , with the axis of curvature gradually increasing from neck to apex through that curvature ; however , a greater degree of curvature , even to 90 ° or 180 °, may be desired given the particular use . preferably , the inner and outer axes of curvature form a logarithmic arc although , again , various other curvatures may be desired given the particular use . thus , in a preferred embodiment , the respective sides 14 of aglet 10 may taper with converging inverse logarithmic arcs that intersect to form apex 16 of aglet 10 . an increasing ( from neck to apex ) and , most preferred a logarithmic , arc is preferred because tests have shown that an aglet displaying a fixed radius outer axis of curvature is more likely to get caught in an eyelet during lacing or unlacing when the curvature is oriented opposite the direction of pull on the lace . surprisingly , it was found that an aglet displaying a logarithmic arc is more likely to rotate into proper orientation because the increase in the curvature is gradual . apex 16 is preferably pointed , as shown in fig1 - 2 , to facilitate threading through eyelets but may also be rounded or novelty - shaped , such as fang - shaped , caricature - shaped , etc . in one preferred embodiment , aglet 10 is approximately 2 . 75 centimeters in length “ l ” ( fig1 ), and is composed of a solid , non - brittle material , preferably a polymeric material , which may be bonded to the lace material . most preferably , aglet 10 is composed of an injection - molded polymer which adheres to the lace fiber ends . referring to fig2 , the lace material may extend within the aglet over a preferred distance of about one - fourth of the aglet &# 39 ; s length , or more , and also may be incorporated in the neck portion 15 of a molten aglet during the aglet manufacturing process . in a preferred embodiment , the cross - sectional diameter of aglet 10 decreases from the neck to the apex , and is preferably at least one millimeter narrower than a lace eyelet at its widest point , again to facilitate threading through the eyelet . the cross - sectional shape of the aglet may be circular ( e . g ., a 0 . 45 cm diameter ), as shown in fig3 , to facilitate rotation of the aglet to its proper orientation during lacing and unlacing . using a preferred 0 . 45 cm diameter , the fig2 aglet has an overall width “ w ” of 0 . 9 cm in a preferred embodiment . the cross - sectional shape of the aglet may also be ovoid or polygonal , or even irregular at points along its length to accommodate novelty . as shown in fig1 - 3 , neck portion 15 of aglet 10 may be textured or include flutes 17 so as to provide resistance for the aglet to be rolled between the fingers for proper orientation when threading the lace through the eyelets . as also shown in fig1 - 2 , neck 15 may also be tapered or beveled slightly circumferentially to minimize snagging when the lace and aglet are pulled through an eyelet during unlacing . as an example , 0 . 05 cm radius corners 18 may be used . referring now to fig4 - 6 , when used properly , the preferably narrow apex 16 and the curvature of the aglet may facilitate the introduction of the attached lace through eyelets 25 located within the typically rigid flanges 30 of athletic footwear 22 , requiring lacing at relatively awkward lace angles . the solid but flexible composition of aglets 10 may also resist deterioration after repeated lacing and unlacing . other changes and modifications constituting insubstantial differences from the present invention , such as those expressed here or others left unexpressed but apparent to those of ordinary skill in the art , can be made without departing from the spirit and scope of the present invention and without diminishing its attendant advantages . it is , therefore , intended that such changes and modifications be covered by the following claims .
an aglet for facilitating the threading of a lace on footwear , the aglet having a curved , tapering shape connected to the lace , a neck , an apex , and differing inner and outer axes of curvature converging at the apex .