Utilizes the problem of determining the number of different ice cream cones and cups that can be made from a choice of 31 flavors to investigate the concepts of combinations and permutations. Provides a set of six related problems with their answers. (MDH)

The transformation assigning to every point its inverse with respect to a circle with given radius and center is called an inversion. Discusses inversion with respect to points, circles, angles, distances, space, and the parallel postulate. Exercises related to these topics are included. (MDH)

Uses the context of rock climbing to discuss the science concept of friction. Presents the mathematics equations that describe the concept. Examines the physics of different rock climbing situations encountered and equipment used. A series of related problems with answers is provided. (MDH)

Presents a series of challenges, problems, and examples to demonstrate the principle of mathematical induction and illustrate the many situations to which it can be applied. Applications relate to Fibonacci sequences, graph theory, and functions. (MDH)

Describes "Bop," a game that considers solely the sequence of letters. Words are determined to be equivalent if different letters of one word become different letters in the other word in exactly the same order. Examples of four-, five-, and six-letter words and BOProblems are provided. (MDH)

Presents six learning activities dealing with planetary motion, the launching of satellites, and Halley's comet, all of which utilize the three laws of Johannes Kepler. These three laws are discussed in detail, and answers to the activities are provided. (KR)

Presents illustrated examples that promote problem solving through the student's consideration of a visible predicament from a three-dimensional viewpoint rather than the typical planar perspective. Includes six student exercises involving rays, circles, quadrilaterals, and hexagons, with hints and solutions provided. (JJK)

Describes the importance of estimation in science for planning projects, conducting experiments, and developing theories. Defines order of magnitude. Provides explicit mathematical equations and calculations to estimate answers for seven provocative physics problems. Includes nine additional open-ended problems with hints and solutions. (PR)

The game "Pythagoras" is an adaptation of the tangram puzzle. Describes the process of finding all the possible convex polygons with seven sides to prove that the solution to a given puzzle shape of seven sides difficult to find was not possible. (MDH)

Challenges the readers comprehension of mathematical induction by presenting four examples of arguments that misrepresent the concept. Discusses the reasons why the arguments lead to false conclusions. (MDH)

Presents six learning exercises that introduce students to the mathematics used to control and track spacecraft attitude. Describes the geocentric system used for Earthbound location and navigation, the celestial sphere, the spacecraft-based celestial system, time-dependent angles, observer-fixed coordinate axes, and spacecraft rotational axes.…