''Geometry and the Imagination'' is the English translation of the 1932 book by
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
and
Stefan Cohn-Vossen
Stefan Cohn-Vossen (28 May 1902 – 25 June 1936) was a mathematician, who was responsible for Cohn-Vossen's inequality and the Cohn-Vossen transformation is also named for him. He proved the first version of the splitting theorem.
He was also ...
.
The book was based on a series of lectures Hilbert made in the winter of 1920–21. The book is an attempt to present some then-current mathematical thought to "contribute to a more just appreciation of mathematics by a wider range of people than just the specialists." It differentiates between two tendencies in mathematics and any other scientific research: on the one hand, toward abstraction and logical relations, correlating the subject matter in a systematic and orderly manner, and on the other hand an intuitive approach, which moves toward a more immediate grasp of and a "live rapport" with the same material. Further he asserts that intuitive understanding actually plays a major role for the researcher as well as anyone who wishes to study and appreciate Geometry.
Contents
Topics covered by the chapters in the book include the
Leibniz formula for ,
configurations of points and lines with equally many points on each line and equally many lines through each point,
curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
and
non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...
,
mechanical linkages, the classification of
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
s by their
Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space ...
, and the
four color theorem
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions sh ...
.
[
]
Response
The Mathematical Association of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...
said about the book, "this book is a masterpiece — a delightful classic that should never go out of print".Physics Today
''Physics Today'' is the membership magazine of the American Institute of Physics. First published in May 1948, it is issued on a monthly schedule, and is provided to the members of ten physics societies, including the American Physical Society. I ...
called it "a readable exposition of modern geometry and its relation to other branches of mathematics". The Scientific Monthly
''The Scientific Monthly'' was a science magazine published from 1915 to 1957. Psychologist James McKeen Cattell, the former publisher and editor of ''The Popular Science Monthly'', was the original founder and editor. In 1958, ''The Scientific Mo ...
said about it "has been a classic for twenty years . . . Although it deals with elementary topics, it reaches the fringe of our knowledge in many directions".
References
{{Reflist
External links
''Geometry and the Imagination''
at the Internet Archive
The Internet Archive is an American digital library with the stated mission of "universal access to all knowledge". It provides free public access to collections of digitized materials, including websites, software applications/games, music, ...
1952 non-fiction books
Books about mathematics
1932 non-fiction books