Simon has come up with a proof that Phi (the Golden Ratio) is an algebraic number (not transcendental). He proves it by showing that Phi can be the solution to a polynomial equation (which would be impossible if it was a transcendental number). Indeed, if you simplify Simon’s polynomial further, you can get x squared minus x equals one, which describes one of Phi’s remarkable qualities: the square of Phi (an infinite irrational fraction) equals exactly Phi plus 1. In fact, Simon has talked about this in his previous video (expressing Fibonacci sequence using Lucas Numbers):
During math lesson today, Simon’s teacher Sven pointed out that Simon seems to be looking at math problems with programmer’s eyes. Once he is presented with a new problem (in this case – polynomials), he doesn’t look for standard solutions, like other students do by solving similar tasks over and over again. What Simon does is trying to come up with his own algorithm to solve the problem, almost as if he was programming a computer to solve it. That’s why he may come over as inefficient and slow, as he sits there classifying all the components, drawing schematics and visual graphics to visualise the problem in a most elaborate way, instead of quickly applying a “strategy” someone else has taught him and moving on. And yet the question is, who understands the core of this polynomial better – a typical (high school) student, who is being trained to come up with a quick answer, or 7 year old Simon, slowly deconstructing the polynomial, creating his own algorithm and bursting with enjoyment while he’s at it? Luckily, passing a test and getting a good grade for being quick is not what Simon’s goal is at the moment. His goal is learning and understanding.
Last night, just before he fell asleep, he began talking to me about logarithms. He keeps surprising me with how easily he remembers complex concepts by understanding them, not by rote memorisation or ready-made strategies (that school originally tried to force upon him).
We also observe Simon applying algebra and trigonometry in real life, not only while coding but also when looking for an unknown variable or thinking about probabilities (like yesterday during his chemistry workshop). Math is not a school subject, he is trying to express life around him in mathematical formulas and when presented with new formulas, he never simply learns them by heart but spends time to take them apart piece by piece.
From today’s math lesson. Simon has started polynomials and insisted upon expressing them as a graph: