Download A Mathematical Space Odyssey: Solid Geometry in the 21st by Claudi Alsina, Roger Nelsen PDF

By Claudi Alsina, Roger Nelsen

Reliable geometry is the conventional identify for what we name at the present time the geometry of three-d Euclidean area. This ebook offers concepts for proving numerous geometric leads to 3 dimensions. specific consciousness is given to prisms, pyramids, platonic solids, cones, cylinders and spheres, in addition to many new and classical effects. A bankruptcy is dedicated to every of the next uncomplicated ideas for exploring area and proving theorems: enumeration, illustration, dissection, aircraft sections, intersection, generation, movement, projection, and folding and unfolding. The booklet contains a choice of demanding situations for every bankruptcy with strategies, references and a whole index. The textual content is geared toward secondary institution and faculty and collage lecturers as an creation to sturdy geometry, as a complement in challenge fixing classes, as enrichment fabric in a path on proofs and mathematical reasoning, or in a arithmetic path for liberal arts scholars.

Show description

Read or Download A Mathematical Space Odyssey: Solid Geometry in the 21st Century PDF

Similar topology books

When topology meets chemistry: A topological look at molecular chirality

During this brilliant topology textual content, the readers not just find out about knot thought, third-dimensional manifolds, and the topology of embedded graphs, but additionally their position in realizing molecular constructions. so much effects defined within the textual content are inspired through the questions of chemists or molecular biologists, even though they typically transcend answering the unique query requested.

Low-Dimensional Topology and Kleinian Groups, Volume 1 of the Proceedings of the Conference on the Topology in Low Dimension, Bangor, 1979

This quantity includes the complaints of a convention held on the college collage of North Wales (Bangor) in July of 1979. It assembles examine papers which replicate diversified currents in low-dimensional topology. The topology of 3-manifolds, hyperbolic geometry and knot concept end up significant subject matters.

Category Theory: Proceedings of the International Conference Held in Como, Italy, July 22-28, 1990

With one exception, those papers are unique and completely refereed examine articles on a number of purposes of classification idea to Algebraic Topology, common sense and laptop technology. The exception is a phenomenal and long survey paper through Joyal/Street (80 pp) on a starting to be topic: it supplies an account of classical Tannaka duality in this sort of means as to be available to the overall mathematical reader, and to supply a key for access to extra fresh advancements and quantum teams.

Additional resources for A Mathematical Space Odyssey: Solid Geometry in the 21st Century

Sample text

Gottfried Wilhelm Leibniz Mathematics is often said to be the study of patterns. Enumerative combinatorics is a branch of mathematics that counts the number of ways certain patterns can be formed. In combinatorial problems it is frequently advantageous to represent the patterns geometrically, as configurations of solids such as spheres, cubes, and so on. In many cases we have a sequence of configurations or patterns, and we seek to count the number of objects in each pattern in the sequence. We also exhibit examples where such a two-dimensional counting problem has a three-dimensional solution, and examples where a three-dimensional counting problem has a two-dimensional solution.

2n C 1/ D : 3 6 Pentagonal numbers and their sums Another class of figurate numbers is the set of pentagonal numbers Pn , which count the number of dots in pentagonal configurations. 8 we illustrate the first four pentagonal numbers. 3n 1/ : 2 34 CHAPTER 2. 8. 9a. 9. 4) 4 We can illustrate this with unit cubes as follows (the illustration is for n D 4/. 10a. 4. 10. 10b, which proves the result [Cupillari, 1989; Lushbaugh, 1965]. 1 shows how cannonballs were stored at Fort Monroe in Hampton Roads, Virginia, a Union military installation, in 1861.

Polyhedral sculpture Many modern abstract sculptures are polyhedral in form. One of the world’s largest is the Vegreville Pysanka (a Ukrainian Easter egg) in Vegreville, Alberta, Canada. It was constructed in 1975 to mark the centennial of the Royal Canadian Mounted Police. 21. The egg is a polyhedron with 2732 faces, 2208 congruent equilateral triangles and 524 non-convex equilateral hexagons in the shape of threepointed stars. The shape of the egg results from varying the angles in the stars.

Download PDF sample

Rated 4.87 of 5 – based on 7 votes