Finding the Fibonacci Numbers: A Similar Formula

In this series of posts about the Fibonacci sequence , a very famous sequence of numbers within mathematics, we have just concluded showing how you can take the recursive formula (which uses previous values of to compute the next values) and turn that formula into an exact formula that can skip right over the previousContinue reading “Finding the Fibonacci Numbers: A Similar Formula”

Finding the Fibonacci Numbers: The Formula

This is the third post in a series about an exact formula for the Fibonacci numbers, , which are defined by the initial values and the recurrence relation . We have made a lot of progress towards our goal. We discovered a connection between , the golden ratio , and the Fibonacci sequence by findingContinue reading “Finding the Fibonacci Numbers: The Formula”

Finding the Fibonacci Numbers: Getting Our Bearings

This is the second in a series of posts discussing a quite elegant and interesting problem in the history of mathematics. We have previously defined the Fibonacci numbers using the starting point and defining for every larger value of . This set up is often called a recursive formula, since we use the same processContinue reading “Finding the Fibonacci Numbers: Getting Our Bearings”

Finding the Fibonacci Numbers: The Problem

The 1202 mathematics textbook Liber Abaci is arguably one of the most important contributions to the development of the scientific and cultural systems we have in the world today, especially for Western society. Written by Leonardo of Pisa, known colloquially by the name Fibonacci, this text introduced to the Western world important notations and mathematicalContinue reading “Finding the Fibonacci Numbers: The Problem”

Critical Thinking Toolkit: External and Internal Contradictions

When developing critical thinking skills, learning to recognize falsehood is as important as learning to recognize truth. This is important for many reasons. Recognizing falsehood helps you realize when you are making mistakes, when others might be making mistakes or using confusing language, and can help you find out the truth by process of elimination.Continue reading “Critical Thinking Toolkit: External and Internal Contradictions”

The Quadratic Formula (Solution)

Having discussed the motivation of why something like a “quadratic formula” is a useful thing to discover and understand, I’d like to work through some of the ideas that might lead one to discover a quadratic formula. Reducing the Number of Unknowns Remember that the equation we care about is , with (so that thisContinue reading “The Quadratic Formula (Solution)”

The Quadratic Formula (Problem)

This problem is something that is pretty well known from our high school education – the quadratic formula. In a follow-up post, I will present the solution through a shortened version of the process by which a mathematician might have gone about finding a solution. Equations are among the most important objects in mathematics. InContinue reading “The Quadratic Formula (Problem)”

Evaluating a Premise: Don’t be a “Mere Skeptic”

This is the last of the initial series of discussions I am putting forward about evaluating premises in an argument – or more colloquially, evaluating anything that somebody tells you is true. We’ve gone through a variety of nuances so far – about properly evaluating probabilities, when people do and do not need to justifyContinue reading “Evaluating a Premise: Don’t be a “Mere Skeptic””

Current Happenings and Future Plans for the Blog

Life has been quite hectic lately. It’s increasingly difficult to find time to write on the blog. I should have more time to write a few weeks from now, and once that time comes I should be able to make progress on a lot of the ideas I’ve been wanting to develop here. For theContinue reading “Current Happenings and Future Plans for the Blog”