In continuing from the last post on Post’s Machine by V. A. Uspenskii (sometimes Uspensky) we come to another volume by him titled Pascals’s Triangle.
The reader who is not familiar with Pascal’s triangle should be warned that it is not a geometric triangle with three angles and three sides. What we call Pascal’s triangle is an important numerical table, with the help of which a number of computation problems may be solved. We shall examine some of these problems and shall incidentally touch upon the question of what “solving a problem” can mean in general.
This exposition requires no preliminary knowledge beyond the limits
of the eighth-grade curriculum, except for the definition of and notation for the zeroth power of a number. That is, one must know that any non-zero number, raised to the zeroth power, is considered (by definition!) to be equal to unity: a0 = 1 for a ≠ 0.
The book was published by Mir in the Little Mathematics Library in 1976. But earlier in the West many books from this series were translated and published by University of Chicago Press under the series Popular Lectures in Mathematics. This particular title was translated from the Russian by David J, Soonke and Timothy McLarnan and was published in 1974.
You can get the book here.
All credits to the original uploader.
The contents are us under:
1. A Problem from the Eighth Olympiad 1
2. What It Means to Solve a Problem 5
3. Pascal’s Triangle 9
4. Pascal’s Operation 17
5. Binomial Coefficients 22
6. The Number of Subsets of a Given Set 26
7. The Connection with Factorials 32