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A Review of A New Course in Geometry by Walker and Miller
A New Course in Geometry by Andrew Walker and James Millar is a classic textbook that was first published in 1954. The book covers various topics in Euclidean and non-Euclidean geometry, such as congruence, similarity, parallelism, circles, polygons, area, volume, coordinate geometry, transformations, trigonometry, and spherical geometry. The book also includes many problems and exercises with answers.
The book is written in a clear and concise style, with an emphasis on the logical development of geometric concepts and methods. The book aims to foster the students' interest and appreciation of geometry, as well as their ability to solve problems systematically. The book is suitable for high school and college students who have a basic knowledge of algebra and geometry.
The book has received positive reviews from readers who praised its comprehensive coverage, rigorous proofs, and engaging examples. Some readers also noted that the book is challenging but rewarding, and that it helps them develop their geometric intuition and skills. The book is considered to be one of the best books on geometry ever written.
A New Course in Geometry by Walker and Miller is available in paperback format from various online retailers. The book has 494 pages and an ISBN of 8125012494.
Geometry is not only a fascinating subject, but also a useful one. Geometry has many applications in various fields of science, engineering, art, and everyday life. Some examples of geometry applications are:
Using the Pythagorean theorem to find the distance between two points or the length of a diagonal in a rectangle[^3^].
Using trigonometry to find the height of a building, the angle of elevation of a plane, or the speed of a Ferris wheel.
Using coordinate geometry to graph equations, find slopes and intercepts, and determine parallelism and perpendicularity of lines[^2^].
Using circle geometry to find arc lengths, sector areas, inscribed angles, and tangents.
Using transformations to create patterns, tessellations, and fractals.
Using solid geometry to find volumes and surface areas of prisms, cylinders, cones, and spheres.
To learn more about geometry and its applications, there are many online resources available. One of them is GeoGebra[^1^], a free interactive geometry tool that allows users to create and explore geometric constructions and graphs. GeoGebra also offers tutorials, activities, and games for different levels and topics of geometry. Another resource is Khan Academy[^2^], a free online learning platform that offers videos, exercises, quizzes, and articles on various geometry concepts and skills. Khan Academy also provides personalized feedback and progress tracking for learners.
Geometry is not only a useful and fascinating subject, but also a very ancient one. Geometry's origins go back to approximately 3000 BC in ancient Egypt[^3^], where it was used for practical purposes such as surveying, construction, and astronomy. The ancient Egyptians developed some remarkable geometric principles and formulas, such as the Pythagorean theorem, the formula for the area of a circle, and the formula for the volume of a frustum of a pyramid.
The word geometry comes from the Greek words geo (earth) and metron (measurement), and it was the Greeks who elevated geometry to an abstract and rigorous science. The most influential Greek geometer was Euclid, who wrote the Elements, a comprehensive treatise on plane and solid geometry that is considered one of the most influential books of all time[^1^]. Euclid's geometry was based on a set of axioms, or self-evident truths, from which he derived hundreds of logical theorems by deductive reasoning.
Geometry continued to develop and flourish in various cultures and civilizations, such as India, China, Persia, and Arabia. In the Middle Ages, geometry was studied by Islamic scholars who preserved and translated the works of the Greeks and also made original contributions. In Europe, geometry was revived by the Renaissance artists and architects who were inspired by the classical forms and proportions. Geometry also played a key role in the scientific revolution of the 17th century, when it was used to describe the laws of nature and motion. 248dff8e21