Squared numbers
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The document discusses properties of squared and triangular numbers. It notes that subtracting a squared number from its successor results in the numbers 3, 5, 7, 9, etc. And that adding two successive triangular numbers always results in a squared number, such as 1 + 3 = 4, 3 + 6 = 9, and 6 + 10 = 16.
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Squared numbers
- 1. Information collected by Anda
- 2. These numbers can be arranged to look like squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, …
- 3. A curious property appears when we subtract a squared number from its successor : 4 – 1 = 3 9 – 4 = 5 16 – 9 = 7 25 – 16 = 9, … The drawing shows you why!
- 4. These numbers can be arranged to look like triangles: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …
- 5. A curious property appears when we add two successive trianghular numbers: the result is always a squared number! 1 + 3 = 4 3 + 6 = 9 6 + 10 = 16 10 + 15 = 25, …
- 6. A curious property appears when we add two successive trianghular numbers: the result is always a squared number! 1 + 3 = 4 3 + 6 = 9 6 + 10 = 16 10 + 15 = 25, …