Patterns of Pascal's triangle
1. The sides of the triangle are all 1's
4. The sums of the horizontal rows are all powers of 2. (2¹, 2², 2³, 2⁴, 2⁵...)
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2. The next diagonal layer is made up of consecutive natural counting numbers.
(1, 2, 3, 4, 5...) 5. On the second diagonal layer, if you square any of the numbers, it will be equal to the number beside it, PLUS the number below, as shown in the picture.
Ex: 6² = 16 + 21 = 36 5² = 10 + 15 = 25 |
3. The 3rd diagonal layer is made up of triangular numbers.
They are a sequence of numbers that represent the number of dots needed to form different sizes of triangles. See below: 6. Pascal's triangle is symmetrical! The numbers on one side of the triangle are a mirror-image of the other side.
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These are just a taste of the patterns of Pascal's triangle! There so many more to explore be amazed by.