*Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house. *

**Robert A. HEINLEIN**

Welcome to the blog **Math1089 – Mathematics for All**.

I’m glad you came by. I wanted to let you know I appreciate your spending time here on the blog very much. I do appreciate your taking time out of your busy schedule to check out **Math1089**!

Numbers are beautiful, but arranging them in a particular way is more interesting. In this blog post, we will consider the **first sixteen natural numbers** and arrange them in a particular way to see the beauties in them. In fact, we will arrange them in a square to see the beauties of number relations.

A magic square is an arrangement of *n*^{2} numbers into an *n* × *n* square array such that:

- the sum of the elements of each row;
- the sum of the elements in each column;
- the sum of the elements along each diagonal

are the same. When the elements are not specified, it is conventional for them to be the first *n*^{2} (strictly) positive integers. Consider the following magic square of order 4 due to Moessner.

Following the definition of a magic square, we have

the sum of the elements of each row are same:

12 + 13 + 1 + 8 = 34;

6 + 3 + 15 + 10 = 34;

7 + 2 + 14 + 11 = 34;

9 + 16 + 4 + 5 = 34.

the sum of the elements of each column are same:

12 + 6 + 7 + 9 = 34;

13 + 3 + 2 + 16 = 34;

1 + 15 + 14 + 4 = 34;

8 + 10 + 11 + 5 = 34.

the sum of the elements along each diagonal are same:

12 + 3 + 14 + 5 = 34;

8 + 15 + 2 + 9 = 34.

In addition to the above properties, the following are a few additions.

**The sums of the cubes of the entries on the diagonals of Moessner’s order 4 magic square are equal.**

12

^{3}+ 3^{3}+ 14^{3}+ 5^{3}= 1728 + 27 + 2744 + 125

=

4624;

and

9

^{3}+ 2^{3}+ 15^{3}+ 8^{3}= 729 + 8 + 3375 + 512

=

4624

Your suggestions are eagerly and respectfully welcome! See you soon with a new mathematics blog that you and I call **“****Math1089 – Mathematics for All!**“.

If i want a magic square with

15, 9, 19, 49 as entries in the first row, how do i get them?

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