Once upon a time, there was a kite named Kitey who loved to fly high in the sky. Kitey was a special kite because it was shaped like a hexagon. One day, Kitey was feeling curious about its own shape and decided to learn more about it.

Kitey flew down to visit its friend, a mathematician named Mathis. Mathis explained to Kitey that the longest side of a hexagon was called the hypotenuse and that the height of a hexagon was the distance from the top to the bottom. Kitey was amazed to learn all these new things about its own shape.

Next, Mathis showed Kitey something even more interesting. He drew an incircle inside Kitey's hexagonal shape. The incircle was a circle that was tangent to all six sides of the hexagon. Kitey was fascinated by this and wanted to learn more.

Mathis then introduced Kitey to the concept of inversion. An inversion was when a shape was flipped over a certain point. Mathis demonstrated this by flipping the incircle over its center. Kitey was amazed by how the incircle transformed into a new shape called an involute.

Finally, Mathis showed Kitey how the leg of a kite could be represented as a line segment connecting two points on the involute. Kitey was thrilled to learn that its own legs were a part of such a complex shape.

From that day on, Kitey was even more proud of its hexagonal shape and loved to show off its knowledge to all its kite friends. The end.

Reflections

1. What shape was Kitey?
2. What did Kitey learn about its shape from Mathis?
3. What is an incircle?
4. What is an inversion?
5. What did the incircle turn into after the inversion?
6. What did Kitey learn about its legs?
7. How did Kitey feel after learning all this new information?
8. Can you think of any real-life examples of hexagons or incircles?