You can easily visualize a multiplication if you think of numbers as length and width and the product as area. Many of these complicated mathematical properties can be easily understood when we visualize them; something we are going to call ‘Visual Proof’. Here we will try to visually prove the theorem on sum of first n odd numbers.

### The Theorem

The theorem states that the “sum of the first N odd natural numbers is always a perfect square and is equal to N^2”.

This can be proved in a number of ways but, there is also a proof without words.

### The Visual Proof

Start from the lower left corner. The first blue dot is **1**. Then we have **3** green dots surrounding it. Next we have **5** blue dots. Then **7, 9, 11** and **13**. As you can see, these dots are the series of first 7 odd numbers.

Try to visualize them in parts. When you see the group of first blue dot and the next 3 green dots, you find out that it is a **2 X 2** square. Now add the next 5 blue dots. You can see that it is a **3 X 3** square. Now add the next 7 green dots and it looks like a **4 X 4** square and so on.

### Watch the animated Visual Proof in the video at top

#### Transcript of the video

*Let us see, if, we can add, these numbers, in a way, that, they always form, a square. *

*One.** It’s a square. **1,2,3. Again a square. **1,2,3,4,5. Again a square. **1,2,3,4,5,6,7. Again a square. **And so on. *

*Here is a, quick visualization, of the same thing. **Hope you enjoyed, how, mathematics can be put in a way, that you can, see, what’s going inside the theorem.*

### More Fun Learning

This is a fun place to learn so if you love math jokes and riddles; you can find them here.

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