Hello, this is Andy. I’me here to tell you about a minor problem in the way the world is. Humor me, your well-adjusted benevolent author, and take a moment to look at the following pictures of shapes.
Aren’t these shapes just the neatest things? They’re so polite, perfectly tiling the imaginary, infinite plane they’re lying on.
Their corner angles piece together so neatly, leaving nothing showing of the mathematical void behind them.
Now, bear with me in considering the shape of the common waffle:
Notice something wrong? Not only are we resorting to putting square indents in a circular object, they don’t even fill the box they’re in properly! Everything about waffles screams “TILE AN INFINITE PLANE WITH ME,” yet Big Breakfast refuses to heed the call of efficient packaging. They’re playing a dangerous game.
In 1611, Johannes Kepler proposed a theoretical maximum density for packing spheres in 3D space. Regardless of how they were arranged in a box, he said, you will never fill more than 74% of your total box volume. His theorem went unproven until 1996, when Thomas Hales made a computer test every arrangement of spheres for two years and announced his results: Kepler was right.
I stand here, in the year of our Lord 2019, 408 years after Kepler’s famous sphere-packing conjecture, and announce a similar waffle packing conjecture. In the case of a circular waffle with square syrup pockets, the problem is similar but not analogous to the circle packing problem. The maximum packing density of regular circles is about 90%, which is pretty good. However, I think in this day and age, we can easily do better.
Take this square pocketed, square waffle. Put this in a square box like the one featured above and you have a perfect volume density of 100%. However, there’s no beauty in this approach. If I were to manufacture these waffles, I would gain an 11% advantage over those poor folks at Eggos by cutting out the corner reprocessing section of my waffle factory, but I would be selling square waffles for square customers. That’s not the people whose breakfasts I want to fuel!
I want the new generation, the modern consumers who want organic things to fuel their wholesome, mentally aware lives as they develop websites and meditate.
My solution: the hexagonal waffle, with hexagonal pockets.
Imagine seeing a hexagonal box of Hexxos, perfectly tiling the mathematically infinite shelves of a grocery store near you, filled 100% the way with waffle. The sky is a bright baby blue outside. The birds are chirping. Climate change is no more. “That’ll be 4 dollars, ma’am.” You pay with hexagonal coins.