Triangular Numbers & Fibonacci Numbers
Hi there. This patterning math post features triangular numbers and Fibonacci numbers.
Sections
- Triangular Numbers
- Fibonacci Numbers
- The Golden Ratio From Fibonacci Numbers
Triangular Numbers
To start, here is an image which features triangular numbers.
The first number is 1, the second number is 3 where the number 2 is added to 1. Adding 3 to the second number gives 6 and adding 4 to 6 gives the fourth triangular number. The pattern continues where the number that is added increases by one.
As you can see triangular numbers are based on the sequence:
1, 2, 3, 4, 5, 6, 7, ...Finding The N-th Triangular Number Formula
Let the variable N represents the N-th triangular number. To find the N-th triangular number you can use the formula:
Example One
The seventh triangular number can be found with N = 7 in the formula.
Example Two
The hundredth triangular number can be found with N = 100 in the formula.
Fibonacci Numbers
There is a neat pattern where the next number in a sequence of numbers depends on the last two numbers. This Fibonacci sequence of numbers is as follows:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...In the number sequence we start with the numbers 1 and 1 as the first two terms. The next number in the sequence consists of adding the last two numbers together.
A more mathematical version would be as follows:
The Golden Ratio Approximation From Fibonacci Numbers
Interesting
Patterns like this just shows the beauty of mathematics , glad to see people love mathematics here on steemit