Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Law of large numbers wikipedia , lookup
Positional notation wikipedia , lookup
Ethnomathematics wikipedia , lookup
Infinitesimal wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Surreal number wikipedia , lookup
Bernoulli number wikipedia , lookup
Large numbers wikipedia , lookup
Real number wikipedia , lookup
Location arithmetic wikipedia , lookup
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. • 3 • 4 • 8 • 9 • 12 • 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