🔍 Euler Characteristic Discovery
Discover a hidden mathematical pattern that many shapes share in common. To start click on button for the shape you wish to explore in order to view it, then count its vertices (corners), edges, and faces (flat sides).
🔢 Shape Investigation Table
Fill in the missing numbers as you explore each shape. Can you find a mathematical relationship that works for all shapes?
| Shape | Vertices (V) | Edges (E) | Faces (F) | V + E + F |
|---|---|---|---|---|
| ? | ||||
| ? | ||||
| ? | ||||
| ? | ||||
| ? |
🤔 Investigation Tips
- Vertices are the pointy corners where edges meet
- Edges are the lines where two faces meet
- Faces are the flat surfaces (including the bottom!)
- Try rotating the shape to see all sides
- Use the Pattern Discovery Calculator to test different mathematical relationships
- Look for a formula that gives the same result for every shape!
🔗 Pattern Hunt Challenge
These three shapes are related - one builds from the next. Explore them in order and see if your formula works:
| Related Shapes | V | E | F | V + E + F |
|---|---|---|---|---|
| ? | ||||
| ? | ||||
| ? |
Think about it: What happens to the numbers when we add a pyramid? Does your formula still give the same result?
🎯 The Big Discovery
Once you find a mathematical relationship that works for all shapes, you've made an amazing discovery! This pattern holds true for all convex polyhedra (3D shapes with flat faces).