Hexagon Weave

Quite a few years ago there was some furor in the tennis world regarding tennis racquets. New ones had entered the market, including a larger-than-normal size, and various folks thought the sport was being fouled.

However, they apparently were legal according to the rules of the game. While I haven't paid much attention since, to see if they have locked down some racquet-variety rules, to prevent similar problems in the future, I did happen to notice that the main reason the new racquets had been introduced was because of something known as "the sweet spot", the best part of the racquet for controlling a tennis ball.

A larger sweet spot means a better chance to control the ball, provided you actually make the racquet meet the ball while playing the game.

Well, an Idea came to me: What If The Strings Of The Racquet Formed An Array Of Hexagons Instead Of Squares? See, hexagons are more naturally circular than squares, so it might logically follow that such an array would fit/grip the curved ball-surface better, and therefore equate with a larger sweet spot.

The only problem is, every intersection of a grid of hexagons has exactly 3 lines connecting to it. A grid of squares has 4 lines connecting at each intersection, and a grid of triangles (I THINK I saw a racquet once that was strung with a grid of triangles) has 6 lines connecting at each intersection.

It seems physically impossible, at first glance, to weave a grid of hexagons. After all if every string that enters an intersection must exit again, then you have to have an even total number of lines at each intersection, and a hexagon grid still has only 3.

Note that there are ways to cheat. See the first link, which actually yields a grid of triangles and hexagons.

Nevertheless, I thought of a way, and no, it does not involve big fat knots at every intersection. What you do is visualize the grid of hexagons as having two parallel strings at every line where you would normally see just one string. This means that each intersection can have 3 strings going into it (half of each parallel pair), plus those same 3 strings going out (the other half of each parallel pair).

All that remains to be done is to figure out how to lace them AT the intersection. And, no, it STILL is not a knot! See the second link, showing 3 connected rings. If you imagined that the outside of each ring was cut, and they were made of string, you could pull their connection point tightly together, and they would stay well-connected. You could also pull on the strings such that they would be approaching that intersection at 120- degree angles, exactly like the intersection of 3 hexagons.

So all you have to do, to make a Hexagon Weave, is to ensure that EVERY intersection connects like that one. Which turns out to be slightly more complicated. The parallel strings have to cross each other allong every one of the straight-side lengths of the hexagon array.

Nevertheless, It Appears To Be Workable In Theory. When the strings are all pulled taut, a true grid of hexagons should be produced. Perhaps a tennis racquet featuring a Hexagon Weave can be made yet! Note that ordinary weavings don't pull all the strings taut, and so something like a "doily" would look more like a mass of tangled strings than a nice hexagon pattern. Still, there are a few possibilities, after the example of "fish- net stockings". Since said netting is under tension when worn, its threads are taut. Which means "chicken-wire stockings" should be quite possible....

I've created an image (3rd link). You may have to load it into an image viewer and enlarge it to see the intersection details. But you should be able to see that the green strings zigzag mostly horizontally, always crossing on top of the blue strings; the red strings zigzag from upper-right to lower-left, always crossing on top of the green strings, and the blue strings zigzag from upper-left to lower-right, always crossing on top of the red strings.