You are an expert at summarizing long articles. Proceed to summarize the following text:

You are an expert at summarizing long articles. Proceed to summarize the following text: 
This application also claims priority to U.S. provisional application Ser. No. 60/776586 filed Feb. 24, 2006. 

   FIELD OF THE INVENTION 
   The field of the invention is modular floor tiles. 
   BACKGROUND 
   Interlocking modular tiles provide a quick and easy option to cover a variety of sizes and shaped surface areas. Simple assembly of the tiles allows users to quickly restore and enhance surface appearance of any undesirable characteristics of the floor surface, such as stains and markings. Usually made of durable material, the tiles also serve as a protective layer of existing floor surface. 
   There are many known modular tiles with interlocking elements addressing all manner of various needs. U.S. Pat. No. 5,791,114 to Mandel (Aug. 1998) describes quick assembly interlocking tiles having generally T-shaped connectors. U.S. Pat. No. 6,588,167 to Chang (July, 2003) in which the interlocking elements have a different configuration. U.S. Pat. No. 6,526,705 to MacDonald (March 2003) provides tile with different configuration connectors. While there exist many other tile configurations, many of these are merely for decorative purposes and do not take into consideration the problem of binding, which often exists during installation. Since the connectors have to interlock exactly, slight variations of the tiles tend to grind or “bind” together, causing the tiles to poorly fit around each other. Some of the configuration also creates the problem in which the connectors do not interlock tightly and can cause the floor modules to become disconnected with each other. As one unit of the interlocking tile binds the other, the whole surface of tiles can be uneven, unfitted and unsafe. 
   Thus, there is still a need for improvements to interlocking tiles that allow for greater flexibility and easy of use. 
   This and all other referenced patents and applications are incorporated herein by reference in their entirety. Where a definition or use of a term in a reference, which is incorporated by reference herein is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply. 
   SUMMARY OF THE INVENTION 
   The present invention provides modular floor covering systems and methods in which interlocking tiles have mushroom shaped connectors, allowing the tiles to be relatively free from undesirable binding during installation, and providing improved alignment and guidance of the connectors into corresponding receiving tiles. 
   In a preferred embodiment, a tile has a body and an interlocking cap structure with a first surface and a second surface; a first curved portion connecting the first surface with a radius of R 1  to the second engaging surface with a radius of R 2 , wherein R 1 &gt;R 2 ; and a stem supporting the cap structure. The cap has a mushroom-like shape. 
   The stem also a second surface and a third surface contiguous to the body of the stem. Furthermore, the stem has a second curved portion connecting the second surface with a radius of R 3  to the third engaging surface with a radius of R 4 , wherein R 3 &lt;R 4 . 
   In another preferred embodiment, a system for covering a surface has a tile having a body and an interlocking cap structure having a first surface and a second surface; a first portion connecting the first surface with an angle of L 1  to the second engaging surface with an angle of L 2 , wherein L 1 &gt;L 2 , where (L 1 +L 2 ≦180°), and a stem supporting the cap structure. 
   The stem also has the second surface and a third surface. The second portion connecting the stem to the second surface has an angle of L 3  and the third engaging surface connecting to the stem has an angle of L 4 , and L 3 &lt;L 4 . 
   In preferred embodiments, the body of the tile also has a pattern and a grid around the pattern. The pattern can be raised from the rest of the body. The pattern can be of a square, diamond or other desired shape, The patterns, if raised, is at least 0.04 inches higher than the rest of the grid or the body. 
   In yet another preferred embodiment, a floor block has a grid portion defining a cap structure and a plurality of raised pattern that collectively reduce the thickness of the block by a factor of at least 20% relative to corresponding block without the grid portion. 
   Contemplated interlocking tiles can be fabricated from any suitable material, including for example polycarbonate, plastic, rubber or other polymeric material. 

   
     BRIEF DESCRIPTION OF THE DRAWING 
       FIG. 1  is a plain view of an interlocking tile. 
       FIG. 2  is a close-up perspective view of the interlocking tile. 
       FIG. 3A  is a plain view of the interlocking tiles mating together. 
       FIG. 3B  is a closed up view of the joining pieces of the interlocking tiles. 
       FIG. 3C  is a side cross-section view of the corner piece of the interlocking tile. 
       FIG. 4  is a plain view of an interlocking tile with a surface pattern. 
       FIG. 5  is a vertical cross section view of the interlocking tile with the surface pattern. 
       FIG. 6  is a close-up perspective view of an interlocking tile with a different configuration. 
   

   DETAILED DESCRIPTION 
   The present inventive subject matters provides a modular floor covering system with interlocking tiles that are relatively free from undesirable binding during installation, and providing improved alignment and guidance of the connectors into corresponding receiving tiles. 
   In  FIG. 1  and  FIG. 2 , a modular floor covering system  100  generally comprises tile  10 , cap  20  and stem  30 . 
     FIG. 2  demonstrates a close-up view of cap  20  and stem  30  on tile  10 . Cap  20  is preferably is a male protruding portion  12  that mates with another tile&#39;s female receiving portion  14 . Male protruding portion  12  are connectors of tile  10  and can join other tile by mating with the female receiving portion. 
   Preferably, cap  20  comprises two regions: top region  22  and middle region  24 . Top region  22  extends across the cap from one side to another. Similarly, bottom region  28  extends from the based of the cap from one side to the other. Outer edge  34  joins from one side of top region  22  and middle region  24  to form a curve and then joins the other side of top region  22  and middle region  24 , and together form a generally mushroom-shape cap structure. 
   Preferably, outer edge  34  connects with top region  22  to form an arch to form an ellipse shape with first radius  26 . Then outer edge  34  preferably curves downward to connect with middle region  24  to form another ellipse with second radius  28 . The downward curves allow for a mushroom-cap like shape, which also preferably means that top radius  26  is greater than middle radius  28 . 
   Generally, a circle is defined by one point and the distance radius, R. However, it is preferred that the arch formed by joining outer edge  34  with top region  22  and middle region  24  is of an ellipse. The ellipse is a natural extension of the circle. Instead of having one radius, the ellipse has two points from one given point. Thus, the ellipse is the sum of distances from two radius R 1  and R 2  from the two points to the one given point. The two points are also called the foci of the ellipses. Top radius  26  is the larger radius of the ellipse formed by joining edge  34  to top region  22  then middle radius  28  which is joined by outer edge  34  to middle region  24 . 
   The ellipse shape on both sides of the cap allow for the cap to form a mushroom-like shape. More importantly, the ellipse shape allows for the tiles to move relatively freely with each other for installation and use. Since most of the tile are used for floor covering have to withstand heavy foot traffic and use, the tiles have to interlock seamlessly. Existing interlocking modular floor fails to allow binding in which the tiles have some freedom in mating. 
   Contiguous to cap  20 , stem  30  supports cap  20  and form a seamless interlocking unit to tile  10 . Similar to cap  20 , stem  30  has middle region  24  and bottom region  32  joined by inner edge  36 . Middle region  24  extends from one side to the other of the stem and the bottom region  32  extends from one tile to another to form a female receiving portion  14 . Female receiving portion  14  receives male protruding portion  10  of another tile to form an interlocking mating mechanism. 
   Preferably, an inverted arch is formed joining inner edge  36  with middle region  24  and bottom region  32 . Similar to the cap, the stem forms an ellipse shape with third radius  42  formed by joining inner edge  36  with middle region  24  and fourth radius  44  formed by joining inner edge  36  with bottom region  32 . Here, preferably, fourth radius  44  is larger than third radius  42 . Logically, third radius  42  is the same length as second radius  28 , and first radius  26  is the same length as fourth radius  42 . The difference is that the curve is inverted for first and second radius as opposed to third and fourth radius. The inverted curve allows for the mating mechanism of the female receiving portion to the male protruding portion. 
   Preferably, the tiles have the male protruding portion and female receiving portion all along the edges to interlock with other tiles. However, it is contemplated that there are pieces where at least one edge of the tile does not have any male protruding portion or female receiving portion. For instance, tiles that are placed on the outer edge against a straight floor do not need to have connectors. 
   In  FIGS. 3A ,  3 B and  3 C, a modular floor covering system  100  comprises the joining of tiles  10  by interlocking male protruding portions  12  of the individual tile to female receiving portions  14  of the adjoining tile. 
     FIG. 3B  and  FIG. 3C  specifically depicts the joining of corner pieces  50 . Corner pieces in general comprises corner male protruding portions  58  mating corner female receiving portion  56 . The corner male protruding portion generally is at the adjacent side of the female receiving portion. 
   Similar to male protruding portion  12  and female protruding portion  14 , there is corner cap  54  and corner stem  52 . The corner cap and stem are different than the other cap and stem pieces in that corner pieces have to accommodate the different configuration presented in a corner. Preferably, corner cap  54  retains the characteristics of cap  20  on one side of the cap. On the other side of the corner cap that joins another corner piece of an adjoining tile, there is no outer edge that joins top region with a first radius followed by the outer edge joining the bottom region with a second radius. Instead, the corner cap has corner side edge portion  58  that connects corner top region  60  to corner middle region  62  with corner angle  66 . Corner angle preferably is a right angle or an angle of 90 degrees. Similarly for corner stem  52 , corner inner edge  58  connects corner middle region  62  to corner bottom region  68  with corner angle  70 . Again, corner angle  70  preferably is a right angle or an angle of 90 degrees. This configuration gives rise to a corner male protruding portion that allows for the mating to the female receiving portion of the adjoining tile. Corner male protruding portion is located on one corner of the tile and the female receiving portion is located at the other corner of the same tile. The 90 degree configuration allows the corner pieces to join together seamlessly yet still retain the mushroom-like shape on the tile to allow for extra room and movement. 
   Other configuration are also contemplated in that the shape contained is not just an ellipse or oval shape. It can be of an angular shape. As shown in  FIG. 4 , tile  100  comprises cap  200  with stem  300 . Similar to a mushroom shape, cap  200  has top region  220  and middle region  240 . Top region  220  extends across the cap from one side to another. Similarly, bottom region  280  extends from the based of the cap from one side to the other. Outer edge  250  joins from one side of top region  220  and middle region  240  to form instead of a curve, a angle, then joins the other side of top region  220  and middle region  240 , and form the same angle. 
   Preferably, outer edge  250  connects with top region  220  to form a trapezoid-like shape with first angle  260 . Then outer edge  250  preferably curves downward to connect with middle region  240  to form a straight line with that has second angle  280 . First angle  260  preferably is greater than second angle  280 . The sum of first angle and second angle should not exceed 180 degrees. 
   Contiguous to cap  220 , stem  300  supports cap  220  and form a seamless interlocking unit for tile  10 . Similar to cap  220 , stem  300  has middle region  240  and bottom region  320  joined by inner edge  350 . Middle region  240  extends from one side to the other of the stem and the bottom region  320  extends from one tile to another to form a female receiving portion. Female receiving portion receives male protruding portion of another tile to form an interlocking mating mechanism. 
   Preferably, a line is formed joining inner edge  350  with middle region  240  and bottom region  320 . Similar to the cap, the stem forms the straight line with third angle  380  by joining inner edge  350  with middle region  240  and fourth angle  360  formed by joining inner edge  350  with bottom region  320 . Here, preferably, fourth angle  360  is larger than third angle  380 . Again, like first and second angle, the sum of third and fourth angle is no larger than 180 degrees. 
   In general, a modular floor system can have tiles that are made of one kind of material and have a smooth surface. It is contemplated, however, that the tile can have a surface pattern in which different shapes and sizes of patterns are set in the body of the tile. 
   As shown in  FIG. 5 , a tile  100  comprises connectors  13  that have male protruding portion  12  and female protruding portion  14  with body  13  in which pattern  16  is set with surrounding grooves  15 . Specifically, pattern  16  is arranged in an orderly fashion that fills the body of the tile. Pattern  16  can be a square, rectangular, triangle, oval or any other desirable shape and pattern. It is also contemplated that the pattern  16  can comprises a combination of different shape within one tile. 
   Pattern  16  preferably are formed on the tile by mold injection. It is contemplated that when the tile is manufactured, the blocks or patterns are formed when the tile is formed. It is also possible that the basic mold of the tile with the mushroom-shape like caps and stems are formed first and then blocks and patterns are later on added onto the tile. 
   The modular floor covering system can be made of any suitable material or mixture of materials commonly known for floor covering, including clay, stone, wood, polymeric materials, recycled materials and especially material selected from the list consisting of vinyl, rubber, linoleum, and resin. Generally, a co-polymeric material is preferred for conventional modular flooring covering system. 
   For example, a preferred formulation of the modular floor covering system has PVC Resin: 32.8%; Calcium Carbonate: 24.9%; Dioctyl Phthalate: 39.8%; Lead (as lead stearate) 2.2%; Titianium Dioxide: 0.18%; Alumina: 0.11%; Benzophenone: 0.05% and dyes: 0.05%. In general, sporting flooring that requires greater use and abuse may require less expensive and synthetic rubber polymers. The mushroom-like shape of the tiles and the material flexibility provides a combinations of specific product application and requirement. It also provides for competitive cost advantages in the marketplace without comprising utility or quality. 
   Tiles can be any practical width, thickness, and length. With a given tile, the surface can be of one smooth material in which there are no ridges or grooves. With a patterned tile, the surface can contain ridges and grooves between the connectors and within the pattern as shown in  FIG. 5 . Cap can also be any practical width, thickness, and length that corresponds with the overall length, width, thickness of the tile. The width, thickness and length of pattern also can be flexible depending on the desired characteristics of the look and feel of the tiles. 
   In one preferred embodiment as shown in  FIG. 6 , a side vertical cross section of the tile is shown. The thickness of tile preferably is at least 0.25 inches. It is contemplated that as long as the structural integrity of the tiles are maintained, the tiles can be any thickness. For example, tiles used for heavy duty sporting purposes is contemplated to have a greater thickness. Depending on the material formulation and construction, groove thickness  19  can be different than pattern thickness  21 . Having groove thickness  19  be less than that of pattern thickness  21 , at least 20% of material can be saved. Similarly, connector thickness  17  can also be less than the groove thickness and pattern thickness to save material. The patterns, if raised, preferably is at least 0.04 inches higher than the rest of the grid or the body to not only save material but maintain structural integrity. 
   Having the unique mushroom shape of the connectors allow for the tiles to interlock in a more efficient way. Tiles do not have to be aligned exactly during installation and yet they retain durability after installation. Even though the thickness of the connector is less, the structural integrity still stands with the present connector shape. It is also possible, although not desirable from a manufacturing cost standpoint, for different ridges on a given tile to be made of different materials, densities, shapes, colors and so forth. 
   It should be apparent to those skilled in the art that many more modifications besides those already described are possible without departing from the inventive concepts herein. Moreover, in interpreting the disclosure, all terms should be interpreted in the broadest possible manner consistent with the context. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps could be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced. Where the specification claims refers to at least one of something selected from the group consisting of A, B, C . . . and N, the text should be interpreted as requiring only one element from the group, not A plus N, or B plus N, etc.

Summary:
An interlocking tile system comprises tiles that has a body, interlocking cap structure with a first surface and a second surface; a first curved portion connecting the first surface with a radius of R 1  to the second engaging surface with a radius of R 2 , wherein R 1 &gt;R 2 ; and a stem supporting the cap structure. The cap is a mushroom-like shape. Such configuration of the connector aids in installation by lessening instances of binding and align and guide the caps into their corresponding receiving areas. The tiles are preferably square, and are connected along all four sides.