Madame Polygon

Madame Polygon grew up in Tessellation.

She was the oldest of three sisters. Her family name was Polygon. Her younger sister was Hexa. Hexa was very good with hexagons. Her youngest sister was Octavia. Octavia lived in the dodecagon town hall. She ran the regional tile shop. You won't meet Hexa or Octavia today. They pop up later in Kit 13.

Madame Polygon's real name is Polly. The academy kids find this out later. They always love it. Polly joined the Polygon Council at twenty-six. The Council needed a spokesperson. For years, they had none. The old one was a heptagon. A very proper seven-sided shape. He just wanted to relax. He liked his seven-sided life. He would not come back.

The Council needed someone who could explain regular polygons to the world.

Polly was the perfect choice. She had spoken for polygons since she was seven.

This was normal in Tessellation. Kids there played with polygons. But Polly was extra good. Even for Tessellation. At seven, she taught her cousins. They were only four. She showed them pentagons and hexagons. They just wouldn't fit together. Not without gaps. The angles didn't make a full circle. Not where they touched.

At twelve, she could do math on a slate. She found the inside angle for any shape. It was a special formula: interior angle equals (n−2)·180° divided by n. She showed her younger cousins how it worked. You cut the shape into triangles. Just draw lines from one corner. It always made (n-2) triangles.

At sixteen, she knew even more. Only three shapes fit perfectly together. Triangles, squares, and hexagons. No gaps at all. Their angles fit exactly into a circle. She could draw all three tilings on a slate. Her chalk never left the slate.

The GeometryForge academy needed a teacher. Someone to teach shapes to kids. The Polygon Council picked Polly. Everyone agreed. Polly was twenty-seven. She had been spokesperson for one year. She said yes. She has taught there for fourteen years now.

Every morning, she comes to school. She wears her Council clothes. Fancy ones. She tells the children it's not showing off. It helps them learn. Her headdress has peacock feathers. Each feather eye is a tiny shape. A triangle. A square. A pentagon. A hexagon. A heptagon. An octagon. A nonagon. A decagon. A dodecagon. Nine shapes in all. You can count them.

Her dress has many shapes. Different ones. She carries a fan. It folds up small. With one flick, it opens wide. It becomes a perfect dodecagon. Twelve sides. She picked twelve sides on purpose. She says dodecagons are underrated.

The children love her. They draw her in their notebooks. They even try to make their own shape-fans.

In her classroom, she starts every first-day lesson the same way. She walks in. She puts her dodecagon-fan on the desk. She turns to face them. Her voice is big and dramatic. Like a Council meeting.

"The Council convenes. Each polygon has its angles, its symmetry, its place. Today we begin with the regular triangle. We will work our way up."

Then she teaches about the regular triangle. It has three sides. Inside angles are 60 degrees. Outside angles are 120 degrees. It can spin three ways. It fits together with other triangles. She teaches it slowly. Very grand. The children are confused at first. But they start to like it. By the end, they know many shapes. Triangle, square, pentagon, and hexagon. They can even say the interior-angle sum formula.

Lessons go on. Madame Polygon climbs the shape ladder. Pentagon. Hexagon. Heptagon. Octagon. She teaches about symmetry. She teaches about tiling. Why some shapes fit. Why some don't. She is patient. She is proper. She loves her job.

When children ask her if regular polygons are hard, Madame Polygon always says the same thing: