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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Another method to represent the relationship of the Fibonacci numbers is the Fibonacci Q matrix.
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
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.
We'll focus on other interesting identities of the Fibonacci numbers, one of which is the sum of the first n Fibonacci numbers.
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.
Electrical Engineer having an experience in the Gulf region for construction and engineering consultancy services. Recipient of various appreciation certificates from different International firms while working in the Gulf. I am learning my fourth language at the moment.
Highly interested in Electronics, Renewable Energy, Leadership, Entrepreneurship, and FX.
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