Tag: Fibonacci
Simon’s Fibonacci Music Pesano Periods
Simon writes: I have composed a piece of music based on the Fibonacci sequence, using modular arithmetic (I assigned numbers from 0-6, the remainders after ÷ by 7, to notes … Continue reading Simon’s Fibonacci Music Pesano Periods
Fun with Brilliant’s Computer Courses
“Mom, how long would it take a supercomputer running at 10^15 additions per second to calculate the 1000th Fibonacci number?” Simon has learned this problem from the new course he … Continue reading Fun with Brilliant’s Computer Courses
A Fun Fibonacci Puzzle
Here is a fun math trick! Simon and Neva have made a 8 x 8 cm square (with an area of 64 cm²) and cut it into four pieces, turning … Continue reading A Fun Fibonacci Puzzle
Induction as mathematical proof
Simon explains: “Induction is a mathematical term, type of mathematical proof, if you have a couple of base cases (n base cases), then the inductive hypothesis implies that for the … Continue reading Induction as mathematical proof
Rational Approximations for Phi
“If I get the next two digits right, I’ll be ecstatic!” Simon says, as he hurries on with a φ (Phi) approximation algorithm using Fibonacci numbers. He keeps dividing every following … Continue reading Rational Approximations for Phi
Working on a proof outside
Simon saw this proof on the Numberphile channel.
Simon’s proof that every Fibonacci number is a sum of its neighbouring Lucas numbers divided by 5
This has probably been proven before, but Simon likes to come up with his own proof. Here he uses proof by induction, that is a proof that proves that some … Continue reading Simon’s proof that every Fibonacci number is a sum of its neighbouring Lucas numbers divided by 5
A trick with Lucas and Fibonacci numbers
Simon came up with this trick today and had Neva solve his riddle: any Fibonacci number is equal to the sum of its surrounding Lucas numbers divided by 5. And … Continue reading A trick with Lucas and Fibonacci numbers
A Cool Number Guessing Trick! Or Brown’s Criterion in Processing
This is a fun number guessing trick, based on powers of 2 and the Fibonacci sequence, that even little kids can enjoy. You don’t have to know anything about the … Continue reading A Cool Number Guessing Trick! Or Brown’s Criterion in Processing
Playing the Fibonacci Sequence on the Piano
Inspired by a Numberphile video, where Simon learned the technique to express the Fibonacci sequence in musical notes.
Simon’s Fibonacci function and Fibonacci counter in p5.js
Simon came up with this Fibonacci function while taking a walk downtown: f(0) = 0 f(1) = 1 f(n) = f(n-1)+f(n-2) When we got home, he used the function to … Continue reading Simon’s Fibonacci function and Fibonacci counter in p5.js
Geeks out of the box 