Classic Shapes - New Insights Circular and Oval Rings, Tractrix, Bicyclix, Exponentials, Logarithm, Parabola, Hyperbola, direct and inverse Power Functions, Catenary, Cycloid, Cardioid, Epi-and Hypo-Cycloids, Any-Cycloid, Involutes and Evolutes, Archimedian Spiral, Logarithmic Spiral, Pedal curves, Pascal's Limacon, Helix, Bernoulli's Lemniscate, Pursuit Curves, Cassinian Ovals, Trigonometric Functions; Sphere and Hollow Balls, Ellipsoid, Paraboloid, three types of Hyperboloids, PseudoSphere, Catenoid, Cycloidoid, Torus, Helicoids, Pursuitoid, Perseidoids, Kepleroids, etc... Plus many unknown yet Generalizations like AnyXponent, CycloTrix, etc...

"Bringing Nature Back to Math" Mamikon M. Geometric NATURE   Numerous Classical Geometric Figures are visual reflections of the most basic physical motion-related processes, and thus are so fundamental to all Natural Sciences and their Practical Applications. To analyze them, modern "almighty" Calculus has been developed historically, for over two millennia (started by Archimedes), which is extremely sophisticated, tedious, formalistic, and requires many special math-background disciplines, and even more years of study. But a simple and natural Approach to them has been unthinkably overlooked in history!... Mamikon's Method Following the very basic physical nature of these Classical Figures, this new, visual, and intuitive approach takes us elementarily to the roots of their understanding. With playful activities and manipulatives it can reach even kindergartens. No calculus, No formulas, No special background, No even calculations! We will solve them ALL in vivid, dynamic and insightful geometric ways. These Classical issues are about slopes, areas and volumes of various Shapes. We will "touchingly" Slice'N'Slide to ReShape them into the simplest forms - Ikons, and eventually into a rectangle or a box (the standard idea of finding areas/volumes). We will do so by following the natural way they are being generated, and discover their amazing intrinsic features and yet unknown inter-relationships. Mamikon's method works easily also for parts of all these Figures (indefinite integrals), extends to finding higher moments (gravity centers etc..), and even solves problems unsolved by calculus. Mamikon's method easily and naturally prompts us to "childish" generalizations of these classical figures, with new features, amazing relationships, and applications. By making the classical problems obvious, we also bring fundamental knowledge to everyone's eyes, hands, and hearts, to your joy and judgment. Mamikon's approach creates LOVELY Attitude of all students to so "hated" Math, as his life-long experience has demonstrated from K to Professors. It involves hands-on indoor and outdoor activities, interactive computer games, puzzles, coloring books, "excursions" to Nature, "intuitive" history, and new look at victorious applications in engineering, construction, and in other Sciences.Mamikon's method has own Philosophy, Psychology, Pedagogy, Heuristics. CONTENTS ( Cakulus versus Calculus )