It includes 25 activities of learning fun, discovery and rediscovery of fundamental and basic concepts. The fun is there to provide learning ease and inspire simple thinking for problem-solving.

The classroom activities from the book cover the following topics: elements of geometry such as points, lines, and planes, angles, angle measurements, triangles, right triangles, the Pythagorean Theorem, quadrilaterals, polygons, areas and volumes, circles, construction classwork, areas and volumes of spheres, and optical exercises for enrichment and enhancing recall.

Solutions and answers are provided to serve as learning guides.

This book explores new and exciting ways with the Tangram puzzle. Many of the ideas are original both from the mathematical and artistic perspective. There are chapters on tessellating Tangrams, Tangram Mosaics and series of designs that exploit the precious nature of the tiles. A chapter is devoted to the creation of three dimensional objects and for the more mathematical mind there is a chapter on the representation of the designs using matrices. The book is full of remarkable illustrations, created by the author. If a picture is worth a thousand words then this book is a heavy tome.

"Circular Elliptics" is a new and radically different approach to the study of ellipses. It offers new insight into the relationships between the ellipse and the circle, through the concepts of "ellipticity" and the "elliptic family" with its parent circle.

In the process, a proof for an exact equation for the circumference of the ellipse is developed, and from this such measurements as slope, area, curvature and intersectional values arise.

Exploring the third dimension, relationships between a sphere and an ellipsoid of revolution are outlined. A final offering is an equation for the surface area of an ellipsoid of revolution.

This book shows Pythagorean Triples are in an infinite series, their relationship to prime numbers and equations of Euler's disproved conjecture. A very critical examination of culture in mathematics follows.

This book was written for high school students and teachers who love exploring beyond standard math curricula for a deeper understanding of the principles and applications of mathematics. It is also for anyone who loves the pursuit of a problem solution, including both professional and amateur mathematicians. The vehicle that transports us through this exploration is the study and solution of classical and advanced math problems.

As a high school math student, an engineer, a businessman and, ultimately, a high school math teacher, I collected and created math problems and solutions that can be used for advanced study. Some of the problems may be very familiar to you; some may not. A few may be quite easy to do; others will take more time. Included are classical proofs and their extensions that are often omitted in today's curricula.

Beyond the pure enjoyment of this exploration, we also attempt to find a "deeper understanding" of the math. We address four larger aspects of "understanding," namely: convention, evidence, perspective and connection. A portion of these aspects is addressed in the solutions, themselves. The rest is in comments, which come after the solutions. The comments range widely, including: additional points regarding the math itself, historical factoids, linguistics, suggestions for teachers, some personal experiences regarding the material, etc. Readers who only skim the problems and solutions might still find the applications and comments quite interesting.

It is hoped that this book will assist teachers and students alike in exploring the subject of mathematics in a new way, whether using material that is thousands of years old, or recently developed. Each problem can be used as a single assignment, done in a few minutes, or a term project that could require intuition, technique, research and/or fortitude (to plow through it). The material can be adapted for use in the standard classroom, subject to students' ability and the constrictions of uniform curricula. It is, perhaps, more applicable to classrooms with the freedom to experiment with project learning and with longer assignment periods. School math clubs or math teams might find this text a handy reference to hone skills, learn new techniques and satisfy the quest for more exciting material beyond the routine.

Although the primary focus here is the application of math principles to math problems, these studies are extended to interdisciplinary examples in the sciences, engineering, finance, social studies, etc. The subject material itself is organized into groups. There are twenty-two geometry/trigonometry problems, many of which are "classic proofs." Though some have been forgotten or ignored at large, they are offered here with some new ideas and approaches. There are ten algebra problems, all of which are extensions of a standard curriculum, and offer fresh insights when studied as a group. Statistics, the newest subject to be added to the high school curriculum, has three problems. And calculus, which is not always studied in high schools, has five problems.