Presents an introduction to the study of projective geometry, including a definition and some analagous examples using the overhead projector. Illustrates the principle of duality, Desargues' theorem, Poppus' theorem, and Pascal's theorem. (TW)

Presents a technique for an inductive proof of a theorem from Pascal's triangle. (RP)

The use of DeMoivre's Theorem, the Binomial Theorem, and Pascal's Traingle in finding cos nx and sin nx is explained. (DT)

While helping proofread a book during my doctoral studies, I came across a chapter that included (among other things) a discussion of a set of problems and tasks involving the building of towers using only two (or three) colours of cubes (Maher & Ahluwali, 2014). Later that year, as I started my tenure track position at the University of…

Most students thinking mathematics is a difficult subject. This study aims to enhance students' motivation and efficiency in learning mathematics. This study developed 3D animation on the binomial theorem with historical stories of mathematics as the plot. It also examined the effect of animation on students' learning willingness and…

A table showing the first thirteen rows of Pascal's triangle, where the rows are, as usual numbered from 0 to 12 is presented. The entries in the table are called binomial coefficients. In this note, the authors systematically delete rows from Pascal's triangle and, by trial and error, try to find a formula that allows them to add new rows to the…

Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

This publication focuses on the work of one bright but math avoidant student in a writing seminar in mathematics. The introductory portion of the document explains the philosophy, goals, and activities of the seminar. The course is intended to provide opportunities for students in the humanities to experience mathematics as a discipline at once…

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play…

Pascal's Triangle is, without question, the most well-known triangular array of numbers in all of mathematics. A well-known algorithm for constructing Pascal's Triangle is based on the following two observations. The outer edges of the triangle consist of all 1's. Each number not lying on the outer edges is the sum of the two numbers above it in…

The Fibonacci sequence of Pascal's triangle is considered in pyramids and in the fourth and n dimensions. Four theorems are presented. (MNS)

The author gives a three dimensional analog of Pascal's Triangle as an exercise in heuristic thinking and an introduction to the multinomial theorem. The analog involves finding the number of shortest routes to various rooms in a cubical apartment house. (MN)

Pascal's Triangle is named for the seventeenth-century French philosopher and mathematician Blaise Pascal (the same person for whom the computer programming language is named). Students are generally introduced to Pascal's Triangle in an algebra or precalculus class in which the Binomial Theorem is presented. This article, presents a new method…

Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)