nth degree polynomials inside square.


y=8x48x2+1y=8x^4 - 8x^2 +1

The two pictures are examples of third and fourth degree polynomials 'just fitting' inside a square of side length 2 and centered about the origin. These surprisingly have integer coefficients.

What can be said about polynomials of a higher degree?

Here are degrees 2-5:




16x520x3+5x16x^5-20x^3+5x (By trial and error)

It is easy to show that the coefficients must sum to 1 and it appears the leading coefficient increases by powers of 2

Note by Chris Sapiano
1 year ago

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See Chebyshev Polynomials.

Pi Han Goh - 1 year ago

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Interesting that there is this connection, why is this so?

Elijah L - 1 year ago

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I guess it's just a corollary of Chebyshev polynomials. I can't verbally explain this.

Pi Han Goh - 1 year ago

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