By Irving Adler
More than a hundred routines with solutions and 2 hundred diagrams remove darkness from the textual content. academics, scholars (particularly these majoring in arithmetic education), and mathematically minded readers will take pleasure in this striking exploration of the function of geometry within the improvement of Western clinical thought.
Read or Download A New Look at Geometry (Dover Books on Mathematics) PDF
Best geometry & topology books
The outline for this booklet, Lectures on Vector Bundles over Riemann Surfaces. (MN-6), may be imminent.
Need assistance with Geometry? Designed to duplicate the prone of a talented inner most show, the recent and enhanced show in a Book's Geometry is at your provider! TIB's Geometry is an incredibly thorough, youngster validated and powerful geometry instructional. TIB’s Geometry comprises greater than 500 of the correct, well-illustrated, rigorously labored out and defined proofs and difficulties.
Additional resources for A New Look at Geometry (Dover Books on Mathematics)
Fire, he taught, is composed of units, each of which is a regular tetrahedron; air is composed of octahedra; water is composed of icosahedra; and earth is composed of cubes. The heavenly sphere is represented in the Pythagorean doctrine by a regular dodecahedron inscribed in it. The dodecahedron, discovered by Pythagoras, and used as a symbol of the heavenly sphere, was the prime secret of the Order of the Pythagoreans. Hippasus, a member of the Order, violated his oath of membership by revealing this secret to outsiders.
The corresponding statements that express the information given in the second and the third lines are related to each other in the same way, that is, each is the dual of the other. The corresponding statement that expresses the information given in the first line is its own dual. What we have observed here is a foretaste of a more general symmetry known as duality which we shall discuss in Chapter 10. The duality revealed in the table is not accidental. It corresponds to a significant geometric relationship: The centers of the faces of a regular polyhedron are the vertices of another regular polyhedron inscribed in it.
To associate a point of the plane with every complex number a + bi, we use this procedure: At the point a on the axis of real numbers draw the line that is perpendicular to the axis of real numbers. Associate a real number scale with the points on this vertical line in such a way that the unit of length on it is the same as on the axis of real numbers, and the positive half of the scale is above the axis of real numbers. Locate on the vertical line the point whose scale number on this line is b.