This text is the fifth and final in the series of educational books
written by Israel Gelfand with his colleagues for high school students.
These books cover the basics of mathematics in a clear and simple
format - the style Gelfand was known for internationally. Gelfand
prepared these materials so as to be suitable for independent studies,
thus allowing students to learn and practice the material at their own
pace without a class.
Geometry takes a different approach to presenting basic geometry for
high-school students and others new to the subject. Rather than
following the traditional axiomatic method that emphasizes formulae and
logical deduction, it focuses on geometric constructions. Illustrations
and problems are abundant throughout, and readers are encouraged to draw
figures and "move" them in the plane, allowing them to develop and
enhance their geometrical vision, imagination, and creativity. Chapters
are structured so that only certain operations and the instruments to
perform these operations are available for drawing objects and figures
on the plane. This structure corresponds to presenting, sequentially,
projective, affine, symplectic, and Euclidean geometries, all the while
ensuring students have the necessary tools to follow along.
Geometry is suitable for a large audience, which includes not only
high school geometry students, but also teachers and anyone else
interested in improving their geometrical vision and intuition, skills
useful in many professions. Similarly, experienced mathematicians can
appreciate the book's unique way of presenting plane geometry in a
simple form while adhering to its depth and rigor.
"Gelfand was a great mathematician and also a great teacher. The book
provides an atypical view of geometry. Gelfand gets to the intuitive
core of geometry, to the phenomena of shapes and how they move in the
plane, leading us to a better understanding of what coordinate geometry
and axiomatic geometry seek to describe."
- Mark Saul, PhD, Executive Director, Julia Robinson Mathematics
Festival
"The subject matter is presented as intuitive, interesting and fun. No
previous knowledge of the subject is required. Starting from the
simplest concepts and by inculcating in the reader the use of
visualization skills, [and] after reading the explanations and working
through the examples, you will be able to confidently tackle the
interesting problems posed. I highly recommend the book to any person
interested in this fascinating branch of mathematics." - Ricardo Gorrin, a student of the Extended Gelfand Correspondence
Program in Mathematics (EGCPM)
