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Two students found an unexpected link between the Fibonacci sequence and the "pick-up sticks problem," a probability puzzle. For n random sticks, the probability that no three can form a triangle equals the reciprocal of the product of the first n Fibonacci numbers. This pattern, discovered through simulations by Arthur Sun and Edward Wang, was later proven mathematically. The connection stems from the fact that...

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The Sunlight Budget of Earth

Earth receives vast solar energy, mostly absorbed as heat or reflected to space. Only 0.5% is captured by photosynthesis, split between wild plants and phytoplankton. Human agriculture and solar power use 11% of what wild...

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Counting points on an elliptic curve

Counting points on elliptic curves can be done using three methods: brute force, checking x values, and Schoof's algorithm. Brute force takes O(p²) time, checking x values takes O(p log³ p), and Schoof's algorithm takes O(logᵏ...

How Can Math Protect Our Data?

Error-correcting codes protect digital data from corruption during transmission or storage. Stanford's Mary Wootters explains how these mathematical safeguards use strategic redundancy to detect and fix errors caused by various...