Tag Archives: formula

A simple proof of the quadratic formula

Posted on December 23, 2019 by Brent

If you’re reading this blog you have probably memorized (or used to have memorized) the quadratic formula, which can be used to solve quadratic equations of the form But do you know how to derive the formula? Usually the derivation … Continue reading →

Posted in algebra, proof | Tagged , , , , | 3 Comments

Golden numbers are Fibonacci

Posted on March 19, 2016 by Brent

This post is fourth in a series, proving the curious fact that is a Fibonacci number if and only if one (or both) of or is a perfect square; we call numbers of this form golden numbers. Last time, I … Continue reading →

Posted in arithmetic, computation, famous numbers, fibonacci, proof | Tagged , , , , , | 2 Comments

Fibonacci numbers are golden

Posted on February 28, 2016 by Brent

Recall that a “golden number” (this is not standard terminology) is a number such that one (or both) of or is a perfect square. In this post, I’ll explain Gessel’s proof that every Fibonacci number is golden. First, we need … Continue reading →

Posted in arithmetic, computation, famous numbers, fibonacci, proof | Tagged , , , , , | 1 Comment

Testing Fibonacci numbers: the proofs

Posted on February 27, 2016 by Brent

In my last post I stated this surprising theorem: is a Fibonacci number if and only if one of is a perfect square. If one of is a perfect square, then let’s say that is a “golden number” (a nod, … Continue reading →

Posted in arithmetic, computation, famous numbers, fibonacci, proof | Tagged , , , | 1 Comment

Testing Fibonacci numbers

Posted on February 26, 2016 by Brent

From a recent post on Brian Hayes’ blog, bit-player, I learned the following curious fact: is a Fibonacci number if and only if either or is a perfect square. Recall that the Fibonacci numbers begin where each number is the … Continue reading →

Posted in arithmetic, computation, famous numbers, fibonacci | Tagged , , , | 8 Comments