# All The Formulas You Need To Know For Math Ii Pascal’s Triangle and Square Numbers

You are searching about All The Formulas You Need To Know For Math Ii, today we will share with you article about All The Formulas You Need To Know For Math Ii was compiled and edited by our team from many sources on the internet. Hope this article on the topic All The Formulas You Need To Know For Math Ii is useful to you.

Muc lục nội dung

## Pascal’s Triangle and Square Numbers

Below are the first rows of Pascal’s triangle:

1 1

1 2 1

1 3 3 1

1 4 6 4 1

15 10 10 5 1

16 15 21 15 6 1

The numbers in bold are the third diagonal when Pascal’s triangle is drawn in the center. These are the triangular numbers, made from the sums of consecutive integers (eg 15 = 1 + 2 + 3 + 4 + 5), and from these we can form the square numbers. All we have to do is add consecutive numbers of these and we get the square numbers. To get the first square number, we need to add a 0 to the top of 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 the squared numbers by taking the differences of numbers at two separate places on the fourth diagonal of Pascal’s triangle. The fourth diagonal goes 1, 4, 10, 20 35… , and the differences you get are 1-0 = 1, 4-0 = 4, 10-1 = 9, 20-4 = 16, 35-10 = 25 and so on.

To understand why you get square numbers by adding consecutive triangular numbers, you can use several methods. First, if you know that the formula for the nth number in the triangle is (n^2 + n)/2, then the number in the previous triangle is n less than this one, since it is the same sum of numbers but with ( n-1) and not n as the last number you add. If we add these two numbers, 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 this method was not to your liking, we can also show this result pictorially. Triangle numbers get their name from the fact that you can make them by adding up the number of points that make different sized triangles, and square numbers from the number of points that make squares of different sizes. So all we have to do is make a square from two point triangles. If you try this with coins or counters, or on paper, and make right-angled triangles, you should find that you can make a square from two triangles, but one must be a smaller counter on each of its sides. Okay, so it wasn’t such a rigorous method of proving it, but it was a lot easier than doing a lot of algebra, right?

## Question about All The Formulas You Need To Know For Math Ii

If you have any questions about All The Formulas You Need To Know For Math Ii, please let us know, all your questions or suggestions will help us improve in the following articles!

The article All The Formulas You Need To Know For Math Ii was compiled by me and my team from many sources. If you find the article All The Formulas You Need To Know For Math Ii helpful to you, please support the team Like or Share!

Rate: 4-5 stars
Ratings: 3341
Views: 43504362

## Search keywords All The Formulas You Need To Know For Math Ii

All The Formulas You Need To Know For Math Ii
way All The Formulas You Need To Know For Math Ii
tutorial All The Formulas You Need To Know For Math Ii
All The Formulas You Need To Know For Math Ii free
#Pascals #Triangle #Square #Numbers

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

Bài viết đã được tạo 3573

## Activities To Help Children Write Math Problems In Straigiht Line Should Children Be Allowed to Earn Money?

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

Trở lên trên