"The roads by which we come to know the heavens are almost as wonderful as the heavens themselves." — Johannes Kepler, Astronomia Nova (1609)

Today we embark on an adventure through the hidden world of polygons and then follow them right off the page, into our third dimension, and up into the night sky. We will walk beside a stargazer who asked one of the strangest questions in history, started with a gloriously wild guess, but by refusing to let go of the question changed our knowledge of the world forever.

By the end of class you won't just learn to derive a theorem.

You'll be hopefully leaving with: a question of your own.

What we will learn

What you will embody as math leaders:

1. To Seek
2. To Observe

What you will learn mathematically:

1. The sum of exterior angles of ANY polygon equals 360° and the closed path theorem
2. Why only exactly five Platonic solids can exist.

What you will learn computationally:

1. The power of "loops" and iteration
2. Spatial and 3D Modelling

Kepler's initial guess: the five Platonic solids nested between the spheres of the six known planets (Mysterium Cosmographicum, 1596).

Prelude: What is Mathematics? (5 mins)

Every adventurer checks the map before setting out. Ours begins with a question that has no wrong answers:

What is mathematics… to you?

Shout it out, scribble it down, Is it numbers? rules? puzzles? homework? 😅 We'll keep every answer safe and we will return to them at the very end.

Starting Your Adventure (5 mins)

First, you'll need to learn 3 magical commands.

Join your class in PaperLand at https://dojo.paperland.sg/welcome.

Enter your name and press enter.

On the left side of your magical screen, you'll see ancient text. Select it all and banish it with the delete key.

On the right side, you'll discover your Command Deck with powerful commands!

Cast your first command by clicking fw to move your arrowhead forward — watch it glide 50 units through the darkness!

In the left code editor, change fw 50 to fw 100 and observe the more powerful magic!

Now cast your second command, rt, to pivot your arrowhead to the right. It turns 30 degrees clockwise! Try changing rt 30 to rt 120 for an even sharper turn!

<aside> 💡 You can also type these magic commands instead of just clicking. Press the enter key in the left code editor to create a new line, then type fw 100 to command your arrow forward again. </aside>

Finally, master the third command, lt — a left turn of 30 degrees.