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Derivation and Visualization of the Binomial Theorem

International Journal of Computers for Mathematical Learning, 2000
The binomial theorem presents us with the opportunity to weave many different mathematical strands into one lesson. It has a fascinating history — the study of which leads to a better understanding of how mathematics evolved. In this paper, we have involved computer graphics, geometry, algebra and combinatorics in the derivation of the binomial theorem.
Peter Flusser, Guillermo A. Francia
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A treatise on the binomial theorem

2017
This dissertation discusses four problems taken from various areas of combinatorics— stability results, extremal set systems, information theory, and hypergraph matchings. Though diverse in content, the unifying theme throughout is that each proof relies on the machinery of probabilistic combinatorics. The first chapter offers a summary.
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Induction; the Binomial Theorem

1979
The first part of the course deals with the integers ℤ and the natural numbers ℕ. You know how to add and subtract, multiply and divide integers, and you know when one integer is bigger than another; we shall not review these things. One property of the integers which does need review is the principle of induction.
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A Codeword Proof of the Binomial Theorem [PDF]

The College Mathematics Journal, 2003
Proof. Consider an alphabet consisting of r ordinary letters and one special letter, say ∗. We count the number of possible codewords of length n in two ways. First, since there are a total of 1 + r symbols available and there are n slots to fill, the Multiplication Principle shows that the number of codewords is (1 + r)n.
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Fields with the Simple Binomial Theorem

Mathematics Magazine, 1989
(1989). Fields with the Simple Binomial Theorem. Mathematics Magazine: Vol. 62, No. 1, pp. 52-57.
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The Binomial Theorem [PDF]

The American Mathematical Monthly, 1896
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Newton’s Discovery of the General Binomial Theorem

The Mathematical Gazette, 1961
Newton was the greatest mathematician of the seventeenth century. Today, almost three centuries afterwards, we are just beginning to realize the full extent and variety of his achievement. Much of his mathematical work has never been published (though it ranges far through the fields of projective geometry and general point-correspondences to number ...
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The Binomial Theorem Tastes the Rainbow

The Mathematics Teacher, 1998
An advertisement for Skittles1, a small candy available in cherry, lemon, orange, grape, and lime, invites us to “taste the rainbow” and asks “how many flavor combinations can you find?” This commercial offers an excellent opportunity to introduce concepts of mathematical modeling and an application of the binomial theorem. I use this lesson as a hands-
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An Alternate Proof of the Binomial Theorem

The American Mathematical Monthly, 2016
(2016). An Alternate Proof of the Binomial Theorem. The American Mathematical Monthly: Vol. 123, No. 9, pp. 940-940.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Nature Machine Intelligence, 2021
Lu Lu, Pengzhan Jin, Guofei Pang
exaly