The aesthetics of numbers

The aesthetics of numbers

The beauty of nature cannot be measured. The beauty of nature is overflowing throughout the universe. The beauty of numbers is like the beauty of nature. The beauty of numbers is overflowing throughout the mathematical universe.

Now let's look at a mathematical aesthetic.

Have you ever written and added numbers?

For example write one to five in order and add them.

1 + 2 + 3 + 4 + 5 = 15

Now write numbers from one to ten and add them.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

Now try to write and add them in order from 1 to 100. What are you playing? Yes, it's a game. It's a game about discovering mathematical aesthetics.

Thus, when a teacher asked a student to add, the student added very easily. Who is that student? The student's name is Gauss. He was called the Emperor of Mathematics.

Do you think that student would be a quick math student? Not so. The student understands the beauty of this number sequence in its aesthetics.

Now you too understand this wonder and beauty.

Didn't we add one to five first? Let's see how to sum it up using a simple mathematical method.

Does our series end in sequence 5? Now you take the number six next to the five. Now multiply these two numbers you have taken, five and six. Have you multiplied? 30 Got the answer? Now divide this thirty by two. Have you figured it out? Is the answer 15? This 15 is the sum of the numbers from one to five.

Now let's take the next sequence. Only add numbers from one to ten. The number next to ten is eleven. Now let's multiply these two numbers. 10 × 11 = 110. Let's divide this answer by two. 110 ÷ 2 = 55. This 55 itself is the sum we got.

Now we can add the numbers from one to 100 in the same way. Let's see where to answer using our method.

The number next to 100 is 101. Multiply both? 100 × 101 = 10100. Now divide 10100 by two? 10100 ÷2 = 50500. This 50500 is the answer.

What is easier? That's right, we want to know how it comes, right? Only then can we understand the aesthetics of mathematics and its wonder.

First let's take the number sequence from one to five in ascending and descending order and add them as shown below.

Ascending Order	1	2	3	4	5
Descending Order	5	4	3	2	1
Total	6	6	6	6	6

 

Oh look, it all adds up to 6. How many 6s do we have now? Aren't there 5 six? Isn't 5 × 6 = 30? But didn't we add this series twice as ascending and descending order? All we need is the addition of the sequence once. Since we add twice, we divide by two. So let's divide 30 by two. Does division get 15? Isn't this an aesthetic? It is using this aesthetic that we easily find the sum of consecutive numbers from one.

Do the same for numbers one to ten. The answer will be correct. Do the same for numbers up to hundred. Will come right.

It goes without saying that if you want to remember this simply, you should make it into a formula.

To find the sum of numbers from one to n, we simply multiply n and the next number n + 1 and divide the sum by two.

So this is the formula for that

1 + 2 + 3 + 4 + 5 + … + n = (n(n+1)) / 2

What is right?

Tomorrow we will see how to find addition of odd numbers. There is a mathematical aesthetic and wonder to it.

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