Explore the websites below, then use what you learn to answer the following questions.
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Oregon State University:
Blaise Pascal history
Montclair State University, college of science and mathematics:
Pascal's triangle history
Mathforum: Using Pascal's triangle to find binomial coefficients Mathforum: Triangle expanded to row 15
Mathforum: Interactive demonstration of number patterns
Montclair State University, college of science and mathematics:
Explanation of number patterns
Shodor: Interactive demonstration of multiples in the triangle
University of Massachusetts:
Fractal generator/demonstrations http://www.math.umass.edu/~mconnors/fractal/generate/pascal.html |
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1. How old was Pascal when he died? 2. What country was he from?
3. Mathematicians from which two countries investigated the triangle before Pascal?
4. Give at least two ways the triangle is used.
5. What other contributions to math and science did Pascal make?
6. Expand (x + 1) to the 10th power using Pascal's Triangle
7. What are the triangular numbers?
8. How do you construct a sequence of triangular numbers? That is, how do you find the next consecutive number from the previous one? List the first ten in the sequence.
9. Demonstrate how to use Pascal's triangle to evaluate 2 to the 12th power.
10. Describe the hockey stick pattern, and give an example.
11. Increase row depth to 15 or more and investigate multiples of 2 - 9.
What patterns do you notice?
12. Print out this page and follow the directions online. Turn it in with your answers to questions 1 - 11 |