Polynomial Hack: Identify a Polynomial from Just Two Inputs // скачать в хорошем качестве

Polynomial Hack: Identify a Polynomial from Just Two Inputs //

A polynomial is a mathematical object built from only addition, subtraction, and multiplication. As such, we can express them using only positive integer powers (and, technically, the zero power for constants), and they can be evaluated everywhere. In a single variable, the polynomial can be categorized by degree, and that degree is simply the greatest single power of any of the terms. Subscribe: https://bit.ly/polymathematic | Enable ALL push notifications 🔔 Usually, to fully determine a polynomial, we need one more input than whatever the degree is. So, for a first degree polynomial, that is for a line, we need two points to determine the equation of that line. For a second degree polynomial, we would need three points, and so on. BUT! Under a specific condition, we can actually fully determine ANY degree polynomial from just two inputs. That condition is that the coefficients of the terms of the polynomial all be non-negative integers. If that condition is true, we can be very clever about our two inputs for the polynomial, and we can use that information to fully determine its equation. I originally saw this on a r/math thread (comment here:   / ius9d8b  , which also led to this John Cook blog post (https://www.johndcook.com/blog/2012/0..., through he computes f(1) and f(f(1)) instead, which leads to some slightly different results (that is, sometimes the result is ambiguous). Like I said in the video, I actually didn't think much of it at first, but when I saw this video (  / the.virtual.math.lab  ) on the Virtual Math Lab TikTok channel, I realized it was much cooler than I first thought! You can see more video from the Virtual Math Lab channel on both TikTok and YouTube (https://www.youtube.com/channel/UCiJ9.... Finally, if you'd like to play the game yourself, check out this graph in Desmos: https://bit.ly/guessthepolynomial. #polynomialhack #SoME2 #polynomials #algebra #algebrahack #mathtrick #mathemagic Follow Tim Ricchuiti: TikTok:   / polymathematic   Twitter:   / poly_mathematic   Instagram:   / polymathematicnet   Reddit:   / polymath-matic   Facebook:   / polymathematic   Watch more Math Videos: Math Minis:    • Math Mini   Math Minutes:    • Math Minutes   Number Sense:    • Number Sense (UIL / PSIA)   MATHCOUNTS:    • MATHCOUNTS   SoME2 SoME3?