The beehive buzzed like a great, industrious heart. Inside, where the air smelled of honey and warm wax, a little bee named Mella was preparing for her big day. Today, she was to build her very first wax cell in a brand-new honeycomb. Her belly fluttered with excitement, and her tiny antennae quivered cheerfully.
"Here you are, Mella," said an older bee named Agatha, handing her a small, soft ball of yellow wax. "It's time for you to contribute to our shared home. Show us what you're made of."
Mella took the wax with reverence. It was warm and smelled like a summer meadow. With the ball in her mandibles, she flew to an empty spot in the honeycomb. She took a deep breath and set to work. But what shape should her cell be?
"I want it to be the most beautiful one!" she whispered to herself. "I'll make it round, like the sun or a drop of sweet nectar."
With great patience and skill, she began to shape the wax into a perfect circle. Wall by wall, it grew, and soon her very first cell was created. It was smooth, round, and Mella was immensely proud of it. She flew around it in admiration, looking forward to the day she would store pollen or a drop of honey inside.
Just then, her friend, a boy bee named Bruno, flew over. He had also received his first ball of wax. "Wow, Mella, that's beautiful! I'll build one just like it right next to you."
Bruno set to work and shaped his own round cell right next to Mella's. When he was finished, the two little bees looked at their work. Their cells touched at a single point, but a strange, pointy gap formed between them.
"That's odd," Mella frowned. "Look at that hole between us. Nothing can fit in there. It's wasted space!"
Soon, other young bees flew in and began to build their own round cells. The honeycomb slowly filled up, but empty, unused gaps yawned between each group of cells. It looked like a piece of holey cheese.
"This can't be right," Mella sighed in disappointment. "Our pantry will be full of holes, and we'll waste so much wax on cells that have empty space between them." She could see that much less honey would fit into the honeycomb this way.
She decided to undo her first attempt. She knocked down her beautiful round cell and worked the wax back into a ball. "A circle doesn't work. I have to think of something else. Something that will fit together perfectly."
She thought for a moment. She looked at the walls of the hive, which were straight. "What about a square?" it occurred to her. "Squares have straight sides. They should connect nicely."
With new determination, she began her second attempt. Shaping the wax into corners was a bit harder, but Mella was diligent. In a little while, a neat, square cell stood before her.
"Bruno, come and look!" she called to her friend. Bruno flew over and built his square right next to hers. And it worked! The walls fit together perfectly. No gaps. When other bees joined in, their squares formed a nice, regular grid.
"Hooray!" Mella exclaimed. "I've solved it!"
All the young bees enthusiastically clapped their wings for her. Just then, the old and wise bee, Agatha, flew over to them. She watched their work for a moment, smiling, but then she shook her head.
"It's a good idea, Mella," she praised her. "I see you are thinking and looking for solutions. That's very important. Squares do indeed fit together without any gaps."
"Then why don't you look pleased?" Mella asked.
"Because even though you're saving space, you're not saving wax," Agatha explained, pointing an antenna at one of the square cells. "Look how long the walls and how thick the corners must be to create one square. You use much more of our precious wax for such a structure than is necessary. And yet, you don't store that much more food inside."
Mella realized it. She was right. She had used much more wax to make the square than she had for the circle, but the space inside wasn't much larger. She was disappointed again. "So neither the circle nor the square is right. I'll probably never learn."
Agatha gently stroked her with a wing. "Oh, but you will learn. You have already figured out two important things. First, the shape must not create gaps. Second, it must be efficient so we don't waste a lot of wax. What if you tried to combine the advantages of both shapes? Imagine something that is a bit round, but at the same time has straight walls that fit together."
Mella pondered. Round and straight at the same time? How does that work?
Agatha smiled and, with her little leg, drew a strange shape in a thin layer of wax on the wall. It had six straight sides and six corners.
"What is that?" Mella asked curiously.
"We call this shape a hexagon," said Agatha. "It has six sides. Try it. It's the best shape nature has ever invented."
It seemed complicated to Mella, but she trusted the experienced bee. She took her ball of wax again and began to build. The first wall, the second, the third... slowly, one after the other. When she had built all six walls and joined them together, a perfect, symmetrical cell stood before her.
Bruno immediately started building his hexagonal cell next to hers. And that's when Mella saw the magic. One wall of Bruno's cell fit perfectly and completely against one wall of her cell. They became a shared wall. No gap, no extra walls needed.
"Aha!" Mella cried out with joy. "We're sharing a wall! That's how we save wax!"
"Exactly," Agatha nodded. "And when more bees join in, each new cell will share walls with its neighbors."
And so it was. The entire honeycomb began to fill with perfect hexagons that fit together like pieces of a puzzle. Not a single gap appeared, and the amount of wax used was the smallest possible. The strong and stable structure grew incredibly fast.
Mella was happy. Not only had she built her first cell, but she also understood why the hexagon is the very best shape. It wasn't magic; it was math and the cleverness of nature.
From that day on, Mella became one of the best builders in the hive. Whenever she saw a young bee hesitating over its first cell, she would fly to it and say with a smile: "It doesn't matter if you don't get it right the first time. Trying is the best way to learn anything. Come, I'll show you the secret of the six walls."
And you, children, can try it too. Take a piece of paper and a pencil and, with your parents' help, try drawing many circles next to each other. Do you see the gaps? Now try drawing squares. They fit together, don't they? And finally, try drawing hexagons. You will see what a beautiful and strong mosaic you can create, just like a honeycomb.