4.1 (22 ratings)
3,077 students enrolled
Wishlisted Wishlist

Overview of the Fibonacci Sequence and its characteristics
4.1 (22 ratings)
3,077 students enrolled
Created by Mekhdi El Mussauy
Last updated 11/2016
English
Current price: \$10 Original price: \$35 Discount: 71% off
30-Day Money-Back Guarantee
Includes:
• 1 hour on-demand video
• Access on mobile and TV
• Certificate of Completion
What Will I Learn?
• Know who is Fibonacci
• Understand the growing rabbit population problem
• Know what is a Fibonacci sequence
• Understand how to perform mathematical induction
• Know the golden ratio
• Know the relationship between Fibonacci sequence and golden ratio
• Know Binet's Formula
• Know what is a Fibonacci Q matrix
• Understand Cassini identity
• Characteristics of the Fibonacci Sequence
View Curriculum
Requirements
• Willingness to learn
Description

The course will address the Fibonacci Sequence.

It will address who is Fibonacci and how is the sequence generated through recursion. We’ll see that different problems in life have solutions referred to Fibonacci Numbers (We’ll see an example related to climbing a stair case).

Moreover, we’ll learn about the Golden number (also known as Golden ratio or divine number). How divine is this divine number?!

Binet came up with a method to calculate the numbers in the Fibonacci Sequence non recursively. We'll investigate Binet's formula and how he came up with it.

Moreover, the course discusses the various characteristics of the sequence such as the Cassini's Identity. Cassini's identity presents an arithmetic relationship between various Fibonacci Numbers.

We'll investigate the formula to simply the sum of the first "n" Fibonacci numbers.

Who is the target audience?
• This course is meant for students who are not familiar with with Fibonacci Sequence and/or need students who are looking for a refresher on the sequence. Basic Mathematics is sufficient.
Students Who Viewed This Course Also Viewed
Curriculum For This Course
16 Lectures
59:28
+
Introduction
1 Lecture 01:20

This lesson is the introduction of the course. We'll present an outline of what will be discussed in the following lectures

Preview 01:20
+
Fibonacci Sequence
6 Lectures 24:15

This lecture will examine one of the Fibonacci Bamboozlements. This Bamboozlement will be explained in later lectures referring to an identity that we would derive called: Cassini's identity.

Preview 03:11

This lesson will give a brief description on who is Fibonacci, where he was born and raised. Moreover, we will address how he affected and touched the world and the LEGACY that he left behind.

Who is Fibonacci
02:03

This lecture examines the growing rabbit population. We all have heard the idiom: "breed like rabbits", we will prove that in numbers! We'll see how this growing rabbit population problem is related to Fibonacci Numbers. This lecture presents the Fibonacci sequence for us to address it formally in the next lecture.

Growing Rabbit Population Problem
06:30

The lecture will give the student the understanding to the Fibonacci Sequence. The Fibonacci Sequence can be derived from the recursive relationship which is presented. It can be derived from a formula derived by Binet called Binet's formula and addressed in the coming lectures.

Fibonacci Sequence
02:49

If the student needs a quick reminder on what is Mathematical Induction, it is advisable to give this lecture a look. We'll address what is mathematical induction and give an example. Mathematical induction is needed to solve the problem presented in the next lecture.

Preview 03:31

Different problems in life other than the growing rabbit population problem have a solution that is related to Fibonacci Sequence. We will investigate an example with a Fibonacci solution. Please have a look in the previous lecture for a quick refreshment on mathematical induction.

How many different ways to climb a "n" step stair case?
06:11
+
Golden Ratio
2 Lectures 08:52

What is the golden ratio? It is also known as the divine number. How divine is this number? Why is this number used in Forex? We will derive the golden number in this course and present the golden number conjugate as well.

Golden Ratio, What is it?
04:11

We will prove the relationship between the Fibonacci Sequence and the golden number. This relationship is so deep that even in Forex exchange the golden number is used under Fibonacci Retracement Method.

Relation between the Golden Ratio and the Fibonacci Sequence
04:41
+
Binet's Formula and Cassini's Identity and other characteristics
7 Lectures 25:01

We have presented a recursive method to derive the Fibonacci Sequence and it can be tiring and a waste of time in order to know big fibonacci numbers. Instead, Binet derived a formula on how to get the required Fibonacci numbers. We will present his derivation and the formula.

Binet's Formula
05:33

This lecture offers a quick refreshment for matrix algebra. Matrix additions and multiplications will be addressed here. It is advisable to have a quick look at this lecture to be refreshed.

Preview 02:45

Another method to represent the relationship of the Fibonacci numbers is the Fibonacci Q matrix.

Fibonacci Q matrix- What is it used for?
04:52

Cassini's identity illustrates the relation between consecutive Fibonacci Numbers. The identity will be useful to solve the Fibonacci Bamboozlement that we have presented in the beginning of the course. We will derive the identity and explain it in the lecture

Cassini's Identity
03:04

This lecture will explain the Fibonacci bamboozlement presented in the beginning of the course. We'll use the knowledge gained from the previous lecture about Cassini's identity.

Fibonacci Bamboozlement- Explained
01:19

We'll focus on other interesting identities of the Fibonacci numbers, one of which is the sum  of the first n Fibonacci numbers.

The sum of the first "n" Fibonacci Numbers
03:53

We'll focus on other interesting identities of the Fibonacci numbers, one of which is the sum of the square of the first n Fibonacci numbers.

The sum of the first "n" Fibonacci Numbers Squared
03:35