What Is The Formula For Area Of A Right Triangle Pascal’s Triangle and Square Numbers

You are searching about What Is The Formula For Area Of A Right Triangle, today we will share with you article about What Is The Formula For Area Of A Right Triangle was compiled and edited by our team from many sources on the internet. Hope this article on the topic What Is The Formula For Area Of A Right Triangle is useful to you.

Pascal’s Triangle and Square Numbers

Below are the first few lines of Pascal’s triangle:

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 21 15 6 1

The numbers in bold are the third diagonal when Pascal’s triangle is drawn in the middle. These are triangle numbers made from the sums of consecutive whole numbers (eg 15 = 1 + 2 + 3 + 4 + 5) and we can form square numbers from them. We only need to add the consecutive numbers from them and we get square numbers. To get the first square number, we need to add 0 to the list:

0, 1, 3, 6, 10, 15, 21…

0 + 1 = 1 = 1^2

1 + 3 = 4 = 2^2

3+ 6 = 9 = 3^2

6 + 10 = 16 = 4^2

10 + 15 = 25 = 5^2

15 +21 = 36 = 6^2

By the way, you can also get square numbers if you take the differences of the numbers on the 4th diagonal of Pascal’s triangle two places apart. The fourth diagonal is 1, 4, 10, 20 35… and the differences are 1-0 = 1, 4-0 = 4, 10-1 = 9, 20-4 = 16, 35-10 = 25, and so on.

You can use different methods to understand why the addition of consecutive triangle numbers produces square numbers. First, if you know that the formula for the nth triangle number is (n^2 + n)/2, then the previous triangle number is n less than that because it is the same sum of numbers but (n-1) and not n as the last one the number you add. If we add these two numbers together, we get

(n^2 + n)/2 + (n^2 + n)/2 – n

= (1/2)n^2 + n/2 + (1/2)n^2 + n/2 – n

= n^2 + n – n

= n^2

If you did not like this method, we can also show this result graphically. Triangle numbers get their name from the fact that you can create them by adding up the number of points that make up a triangle of different sizes, and square numbers from the number of points that make up squares of different sizes. So all you need to do is make a square out of the two triangles of points. If you try this with coins or counters or on paper and make right triangles, you should find that you can make a square out of two triangles, but one has to be one counter smaller on each side. Okay, so it wasn’t a rigorous method to prove it, but it was a lot easier than doing a lot of algebra, wasn’t it?

Video about What Is The Formula For Area Of A Right Triangle

You can see more content about What Is The Formula For Area Of A Right Triangle on our youtube channel: Click Here

Question about What Is The Formula For Area Of A Right Triangle

If you have any questions about What Is The Formula For Area Of A Right Triangle, please let us know, all your questions or suggestions will help us improve in the following articles!

The article What Is The Formula For Area Of A Right Triangle was compiled by me and my team from many sources. If you find the article What Is The Formula For Area Of A Right Triangle helpful to you, please support the team Like or Share!

Rate Articles What Is The Formula For Area Of A Right Triangle

Rate: 4-5 stars
Ratings: 1785
Views: 61494444

Search keywords What Is The Formula For Area Of A Right Triangle

What Is The Formula For Area Of A Right Triangle
way What Is The Formula For Area Of A Right Triangle
tutorial What Is The Formula For Area Of A Right Triangle
What Is The Formula For Area Of A Right Triangle free
#Pascals #Triangle #Square #Numbers

Source: https://ezinearticles.com/?Pascals-Triangle-and-Square-Numbers&id=7320648

Bài viết đã được tạo 1450

Bài liên quan

Bắt đầu nhập từ khoá bên trên và nhấp enter để tìm kiếm. Nhấn ESC để huỷ.

Trở lên trên