Transcript Geometric Numbers

WARM-UP
How many rectangles are inside of a 3x3 square?
There are 36 rectangles inside of a 3x3 square! Fourteen of those are squares.
SQUARE NUMBERS
If m dots can be arranged into a square, the number m is known as a square number.
See if the following numbers can be arranged into squares.
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3
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4
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8
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9
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12
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16
Can you find other square numbers?
SQUARE NUMBERS
Exactly like a multiplication chart, we can use the same idea for square numbers!
Notice how the square numbers line up along the diagonal…
TRIANGULAR NUMBERS
If m dots can be arranged into a right triangle, then m is a triangular number.
Here are some triangular numbers with their diagrams…
TRIANGULAR NUMBERS
Notice how the even and odd numbers alternate…
TRIANGULAR NUMBERS
Triangular numbers represent the sum of consecutive numbers.
For example, the 4th triangular number = 4 + 3 + 2 + 1 = 10.
The 100th triangular number is the sum of 1 + 2 + … + 99 + 100 = 5050
…In fact, there’s an interesting story about the sum from 1 to 100 but it unfortunately
doesn’t have anything else to do with triangular numbers…research how Gauss
added these numbers as a kid if you’re interested. It’s cute!
TRIANGULAR NUMBERS
Interesting theorems
The Tetractys