You give a computer n points. It finds ONE polynomial that passes through all of them. That's interpolation — fitting a smooth curve to your data using the simplest tool in mathematics: polynomials. Sounds foolproof. It isn't. The red curve uses equally spaced points across the interval. At low degree, it looks fine. But as you add more points, something breaks. The polynomial starts thrashing wildly at the edges — exploding away from the true function even as it fits every single point perfectl
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You give a computer n points. It finds ONE polynomial that passes through all of them. That's interpolation — fitting a smooth curve to your data using the simplest tool in mathematics: polynomials. Sounds foolproof. It isn't. The red curve uses equally spaced points across the interval. At low degree, it looks fine. But as you add more points, something breaks. The polynomial starts thrashing wildly at the edges — exploding away from the true function even as it fits every single point perfectl
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