Have you ever wondered what mathematicians mean when they talk about a “beautiful” math proof?

“Beauty in mathematics is seeing the truth without effort.”

“There’s something striking about the economy of the counselor’s construction. He drew a single line, and that totally changed one’s vision of the geometry involved.

“Very often, there’s a simple introduction of something that’s not logically within the framework of the question — and it can be very simple — and it utterly changes your view of what the question really is about.”

CREDITS: Castle photo (top) by Rachel Davis via Unsplash. “A Mathematical Fable” via YouTube. Story told by Barry Mazur. Animation by Pete McPartlan. Video by Brady Haran for Numberphile.

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Wonderful video, thank you for sharing this. If I had access to videos like this in high school (or earlier), math would have been so much fun, rather than drudgery with little point.

I always wondered in geometry class WHY we should care about the angles of a triangle. This video shows a practical use in terms kids can understand. There is also a great children’s book available – What’s Your Angle Pythagoras? that tells a story of a young Pythagoras using his famous theory to help his father: https://www.charlesbridge.com/products/whats-your-angle-pythagoras

I believe some textbooks now teach geometry beginning with symmetry, similarity, and transformations. It’s a beautiful approach, and more intuitive for many students.