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The Fibonacci sequence, commonly represented as Fn, is defined as a series of infinite numbers that follow a certain pattern. In other words, the Fibonacci sequence is a series of numbers that starts with 0 and 1, and then the next number in the sequence is equal to the sum of the two numbers before or preceding it. The Fibonacci sequence can be written using the following equation:
Fn = (Fn-1) + (Fn-2)..
n represents a number in the sequence and,
F represents the Fibonacci number value.
Fibonacci Sequence Formula
The Fibonacci sequence formula for Fn is defined using a recursive formula. It can be determined by placing F0 = 0, F1 =1. Therefore, the Fibonacci sequence formula is given as:
Fn = Fn- 1 + Fn-2 , where the value of n is greater than 1 (n > 1)
Example Of Fibonacci Sequence
This Fibonacci example will clear up all your concepts of the topic at no time.
Let the Fibonacci sequence be = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 54, 88
Here, the 3rd term is 1 and this is found by adding the 1st and 2nd term (i.e., 0 + 1 = 1).
- By adding the 2nd and 3rd terms, we get the 4th term i.e. 2 (1+1 = 2)
- By adding the 3rd and 4th terms, we get the 5th term i.e. 3(1+2) and so on.
- Similarly, the next term after 81 can be found by adding 54 and 88.
Therefore, the next term in the sequence will be 142.
Applications of Fibonacci Sequence
Fibonacci sequence is observed in different fields. It is found in nature music, and even in the human body. Following are some of the applications of the Fibonacci sequence:
- It is used in coding including computer algorithms, and interconnecting parallel, and distributed systems.
- It is used in different fields of science including quantum mechanics, cryptography, high-energy physical science, etc.
- It is used to represent many human parts such as one nose, one trunk, one head, etc. Then there are pairs including ears, hands, legs, and eyes.
Know About Acute Triangle and Its Amazing Facts
The acute triangle, also known as the acute-angled triangle, is a type of triangle in which all the three internal angles of the triangle are acute. This implies that all the three interior angles of an acute-angle triangle are less than 90 degrees.
Types of Acute Triangle
The three different types of acute triangle are:
- Equilateral acute triangle
- Isosceles acute triangle
- Scalene acute triangle
Let’s discuss all three types in brief:
- Equilateral Acute Triangle – Equilateral acute triangle, also known as the equiangular triangle is a type of triangle in which all the three internal angles of the triangle measure 60 degrees.
- Isosceles Acute Triangle: Isosceles acute triangle, is a type of triangle in which two angle measures equal, just like its two sides are equal.
- Scalene Acute Triangle: Scalene acute triangle, is a type of triangle in which three interior angles are unequal. This implies that all the three internal angles of the scalene acute triangle measure less than 90 degrees.
Area Of An Acute Triangle
The area of an acute triangle is found by using the formula: ½ x Base x Height
Note: If measures of all the three sides of an acute triangle are given, then the area of an acute triangle can be found using Heron’s formula.
The perimeter Of Acute Triangle
The perimeter of an acute triangle is the sum or total of the length of all its three sides. Hence, if the length of the sides of the acute triangle is given as x, y, and z units, then its perimeter is calculated as”
Acute Triangle Perimeter Formula = (x + y + z) units.
Facts About Acute Triangle
- The sum of all the three angles of the acute triangle is equal to 180 degrees (angle sum property)
- A given triangle can never be a right-angled triangle and an acute-angled triangle at the same time.
- A given triangle can never be an obtuse-angled triangle and an acute-angled triangle at the same time.
Hope you have understood the topics Learn Fibonacci sequence and acute triangle curated by subject experts at Cuemaths.