Mathematics

What is a vertex? And how does algebra figure into geometry? This program examines all things angular, including acute, right, obtuse, straight, adjacent, complementary, supplementary, and vertical angles. Four theorems are also introduced, along with the reflexive, substitution, and transitive properties. A proof of the congruency of vertical angles is performed as well. (14 minutes)

This video describes how to calculate the area of rectangles and other shapes-both geometrical and irregular-and how to determine the volume of a rectangular solid. Dramatized segments and computer animations focus on calculating lawn dimensions at a sod farm; creatively redesigning a cereal box while retaining the original volume; and using the Pythagorean Theorem to work out the coverage area for a kitchen floor being tiled diagonally. (20 minutes)

This program considers the idea that circular motion must imply a force or component of a force toward the center of a circle, as in the Newtonian theory of how the Moon orbits the Earth. The reasons why bicyclists lean during turns, why roads are banked, and why car tires react as they do during a turn are investigated. (36 minutes)

What is the binomial probability that Mickey, a lounge lizard, will get a phone number? After presenting the five characteristics of binomial probability distribution and explaining the binomial probability formula-including a review of factorials-this program examines the mean, deviation, variation, and standard deviation of a binomial probability distribution. (21 minutes)

This program demonstrates how qualitative" bivariate data can be visualized by using a modification of the simple Bar Chart. Quantitative data is dealt with by developing the Dot Plot into the Scatter Diagram, which allows any correlation to show itself in a linear relation. The program explains how this correlation can be modeled by calculating a "Line of Best Fit," how to calculate 95% Confidence Bands, and how to calculate a summary measure for any correlation called the Correlation Coefficient. Finally, the program explains how to deal with data that indicates a curved Line of Best Fit by either finding a way of re-plotting to provide a linear correlation or, alternatively, how to calculate a curved Line of Best Fit. (20 minutes)"

In this program, geometry is combined with approximation to solve relatively complex problems involving shooting an arrow and landing an airplane on the deck of an aircraft carrier. Emphasizing the value of sketching as a visualization tool, the program also explains how the solution of the archery problem, through geometric inversion, can help solve the problem of a plane landing. (59 minutes)

Grade Level: 9+ Boost calculus confidence with this dynamic and engaging series that takes students through limits, graphing, derivatives, integrals and more. Fast-paced and full of information, this series will aid retention of key concepts with an easy-to-follow pace and repeated reviews of key concepts. Help your students grasp even the most perplexing functions!

This engaging ten-part set, adapted from the popular series developed for students to enhance their test-taking skills, combines serious academic content with a humorous presentation style to help make calculus more accessible. Each program skillfully employs elements such as clever mnemonics, high-tech computer graphics, and entertaining vignettes to boost retention and confidence while driving home core concepts through concise explanations and challenging problems. Modules include: • Functions and Limits • One-Sided Limits and Limits Involving Infinity • Continuity and Differentiability • Derivative Rules and Tangent Lines • Higher Derivatives and the Chain Rule • Curve Sketching • Extrema and Max/Min Word Problems • Position, Velocity, and an Introduction to Antiderivatives • Integration Techniques • Definite Integrals and Riemann Sums Joining the Standard Deviants Academic Team in the creation of this series are Jim Sandefur, Ph.D., and E. Ray Bobo, Ph.D., both of Georgetown University. Correlates to all applicable state and national standards. (4 hours 28 minutes)

Both elegant and sublime, fractal geometry has taught mathematicians and scientists to see things differently while quantifying a new level of order in the natural world. In this captivating program, visionary mathematician Benoit Mandelbrot tells his life story as it relates to his spatial approach to problem solving and his scientific achievements. Supported by the insights of Nobel Laureate Ivar Giaever and others, the documentary unifies the disparate periods of Mandelbrot's life around the recurring concept of iteration. Until fractal geometry became organized, my life had followed a fractal orbit," quips Dr. Mandelbrot. (57 minutes)"

After Denim Dog, General Rule, and other experts wrap up the subjects of continuity and discontinuity, this program introduces the derivative. Practical examples of derivatives are provided, along with insights into the concepts of tangent lines and slopes. The Derivative Definition is explained as well, reinforced by plenty of sample problems. (31 minutes)

This video describes how to identify points, plot ordered pairs on a graph, use map coordinates to find locations, and apply graphical break-even analysis to linear functions. Dramatized segments and computer animations illustrate ways to describe positions on a game board by using coordinates; program an industrial robot to assemble TVs in a factory; use a road map while traveling; and evaluate the impact of franchise costs and product prices on profit at a frozen yogurt bar company. (20 minutes)

Math is a universal language, but it also gives us insight into specific cultures throughout history. Founded on that idea, this eight-part series explores great civilizations and historical periods and the ways in which mathematics shaped them. Dynamic video footage and lively reenactments transport viewers into the midst of ancient societies, from China to South America, while engaging, easy-to-understand animation helps to clarify math concepts, number systems, and how these evolved. A Discovery Channel Production. 8-part series, 23-31 minutes each.

The Arabian peninsula produced one of history's greatest empires-and many of the calculation methods used today. This program illustrates the origins and evolution of the Islamic world through the fascinating lens of mathematics. Outlining the birth of human civilization in the Fertile Crescent and the ways in which Mohammad shaped Arabic society, the film shows how Arab scholars utilized Greek and Indian learning to create their own highly advanced systems for manipulating numbers and balancing equations. Viewers will encounter the work of al-Khwarizmi, the father of algebra, and several vital math concepts, including roots, squares, simple numbers, and al-mugabala, or reduction. A Discovery Channel Production. (31 minutes)

Unlike Greek and Arab mathematicians who absorbed knowledge from other cultures, the Chinese invented a numerical system almost entirely on their own. This program delves into the number symbols, sequences, and arithmetic methods developed during China's early dynastic periods, as well as subsequent innovations. Focusing on the Chinese counting board, the film shows how bamboo or ivory rods-and, later, the markings derived from them-were arranged in place value order and used in large-scale calculations. Students will also encounter the seminal book known as Jiuzhang Suanshu and the historical, mathematical, and archaeological significance of inscribed oracle shells and bones. A Discovery Channel Production. (26 minutes)

A pyramid's elegant simplicity belies the fact that early Egyptian builders used sophisticated mathematics throughout their work. This program guides viewers through fascinating intersections between math and Egyptology, examining construction techniques, writing methods, and numeric systems that arose in the ancient Nile Valley. Presenting animated illustrations of hieroglyphic number symbols, the film shows how the pyramid builders tackled problems of measurement and heavy lifting and how they aligned their structures to sacred stars. Students will also learn about the Egyptian concept of unit fractions and their two-column system for multiplication. A Discovery Channel Production. (29 minutes)