Solid Mensuration By Richard Earnhartrar
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Review of Solid Mensuration: Understanding the 3D Space by Richard Earnhart
Solid Mensuration: Understanding the 3D Space is a book by Richard Earnhart that covers various topics related to plane and solid geometry. The book aims to help students develop their spatial visualization skills and apply them to solve problems involving two-dimensional and three-dimensional figures. The book also provides numerous examples, exercises, and solutions to reinforce the concepts and principles discussed.
The book is divided into 11 chapters, each focusing on a specific type of geometric figure or topic. The first chapter introduces the basic concepts and definitions of plane geometry, such as polygons, angles, congruence, similarity, and area. The second chapter deals with circles and circular regions, including arcs, sectors, segments, chords, tangents, and inscribed and circumscribed figures. The third chapter covers triangles and their properties, such as the Pythagorean theorem, trigonometric ratios, law of sines, law of cosines, Heron's formula, and special triangles. The fourth chapter discusses quadrilaterals and their properties, such as parallelograms, rectangles, squares, rhombuses, trapezoids, kites, and cyclic quadrilaterals. The fifth chapter explores other types of polygons and their properties, such as regular polygons, pentagons, hexagons, octagons, decagons, dodecagons, and n-gons.
The sixth chapter marks the transition from plane geometry to solid geometry by introducing the concepts of space and dimension. It also discusses the different types of solids and their classifications based on their faces, edges, vertices, bases, cross-sections, and symmetry. The seventh chapter focuses on prisms and cylinders and their properties, such as lateral area, total area, volume, right prisms, oblique prisms, right cylinders, oblique cylinders, frustums of prisms and cylinders. The eighth chapter covers pyramids and cones and their properties,
such as lateral area, total area, volume,
right pyramids,
oblique pyramids,
right cones,
oblique cones,
frustums of pyramids
and cones.
The ninth chapter deals with spheres
and spherical regions,
including great circles,
small circles,
zones,
lunes,
sectors,
segments,
caps,
and spherical wedges.
The tenth chapter discusses other types of solids
and their properties,
such as polyhedra,
platonic solids,
archimedean solids,
torus,
ellipsoid,
paraboloid,
hyperboloid,
and helix.
The eleventh chapter covers some advanced topics
in solid geometry,
such as Euler's formula,
theorems of Pappus-Guldin,
Cavalieri's principle,
and surface area
and volume of solids of revolution.
The book is well-written
and easy to follow.
The author uses clear
and concise language
to explain the concepts
and principles of solid mensuration.
The book also provides
many illustrations
and diagrams
to help the reader visualize
the geometric figures
and their properties.
The book also offers
a variety of examples
and exercises
to test the reader's understanding
and application of the topics covered.
The book also includes
a comprehensive answer key
to all the exercises
at the end of each chapter.
Overall,
Solid Mensuration: Understanding the 3D Space
is a useful
and informative book
for students who want to learn more about plane
and solid geometry.
The book covers a wide range of topics
and provides a solid foundation
for further study in mathematics
or engineering.
The book is also suitable for teachers
who want to supplement their lectures
with additional materials
or exercises. aa16f39245