# 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