EmbeddingGemma 2: an open, lightweight multimodal embedding model
deepmind.google·6d ago
AI Engineering
Hacker News·Aug 21·5 min read
Every shape can be cut exactly in half with one straight line
TL;DR
A browser game called Bisecto demonstrates that any 2D shape can be divided into two equal-area parts with a single straight line, thanks to mathematical principles.
✦ Why It Matters
Explore mathematical concepts through interactive games to enhance understanding and engagement.
Key Takeaways
- Experiment with geometric shapes to visualize area division.
- Use the Intermediate Value Theorem in practical applications.
- Develop games that explore mathematical concepts interactively.
- Challenge assumptions about mathematical certainty versus human perception.
How It Works
The guarantee of equal-area division relies on the Intermediate Value Theorem, which ensures that as a line sweeps across a shape, the area on one side changes continuously. This means that there will always be a point where the areas on both sides of the line are equal, regardless of the shape's complexity.