This is an excerpt from my math models textbook. It’s about Lagrange Polynomials which is a technique that lets you fit a polynomial to a set of any number of unique points (x_1,y_1) … (x_n,y_n) so long as all your x-values are different (otherwise it wouldn’t be a function, and couldn’t be a polynomial). The polynomial you’ll calculate will be the unique, lowest degree polynomial that passes through all points.

  • sirprize@lemm.ee
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    9 months ago

    Replace the words “Convince yourself” with “You can verify” and it might make more sense.

    • Leate_Wonceslace@lemmy.dbzer0.com
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      9 months ago

      No, I got that part, but I don’t think I understand the significance of the indexed y values and their relationships to the indexed x values. The criterion seems to suggest that P3(xn)=yn for each, but that strikes me as something that is defined as a constraint rather than something that is to be proved. Also, I woke up then and now so that might be playing a factor in my confusion.

      • sirprize@lemm.ee
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        9 months ago

        OK, you got it then, I believe. P3 is specifically built so that P3(xn)=yn for n from 1 to 4. The proof lies in its construction. I guess the sentence can be understood as “we know it works because we built it like that, however you may verify it yourself”

        • metiulekm
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          9 months ago

          I feel like the sentence also means “it’s kinda obvious when you think about it, so we won’t explain, but it’s actually important, so you probably should make sure you agree”.