By Barmak J.A., Minian E.G.

**Read Online or Download 2-Dimension from the Topological Viewpoint PDF**

**Similar geometry and topology books**

**Algebraic Geometry and Number Theory: In Honor of Vladimir - download pdf or read online**

Essentially the most inventive mathematicians of our instances, Vladimir Drinfeld bought the Fields Medal in 1990 for his groundbreaking contributions to the Langlands software and to the idea of quantum teams. those ten unique articles via in demand mathematicians, devoted to Drinfeld at the celebration of his fiftieth birthday, widely mirror the variety of Drinfeld's personal pursuits in algebra, algebraic geometry, and quantity concept.

**Get From Geometry to Quantum Mechanics: In Honor of Hideki Omori PDF**

This quantity consists of invited expository articles by way of famous mathematicians in differential geometry and mathematical physics which were prepared in party of Hideki Omori's fresh retirement from Tokyo collage of technological know-how and in honor of his basic contributions to those parts.

This easy-to-follow ebook deals a statistico-geometrical process for relationship historic megastar catalogs. The authors' medical tools show statistical homes of old catalogs and conquer the problems in their courting originated via the low accuracy of those catalogs. tools are verified on reliably dated medieval celebrity catalogs and utilized to the megastar catalog of the Almagest.

`For the quick destiny, besides the fact that, this e-book can be (possibly chained! ) in each college and school library, and, definite, within the library of each college that is rationale on enhancing its arithmetic educating. ' The Americal Mathematical per 30 days, December 1991 `This ebook may still make fascinating interpreting for philosophers of arithmetic, in the event that they are looking to detect how mathematical principles relatively improve.

**Additional info for 2-Dimension from the Topological Viewpoint**

**Example text**

9. 31 32 Figure 11: Some surfaces Problems 1. Take some strips and join the opposite ends of each strip together as follows: with no twists; with one twist (half-turn); this is called a M¨ obius strip; with two twists; with three twists. 2. Imagine that you are a two-dimensional being who lives in one of these four surfaces. To what extent can you tell exactly which one it is? 3. Now cut each of the above along the midline of the original strip. Describe what you get. Can you explain why? 4. What is the Euler number of a disk?

Here are the types of some of the patterns shown in section 31: 47 Figure 16: •; Figure 17: ∗2222; Figure 18: ∗∗; Figure 19: ∗◦. Figure 20: ∗632. Figure 21: 632. Apart from the spots and circles, these can be read directly from the pictures. The important thing to remember is that if two things are equivalent by a symmetry, then you only record one of them. A dodecahedron is very like a sphere. The orbifold corresponding to its symmetry group is a spherical triangle having angles π/5, π/3, π/2; so its symmetry group is ∗532.

A wave pattern is the next example. This pattern repeats horizontally, with no reflections or rotations. The wave pattern can be rolled up into a cylinder. It can be constructed by rolling up a strip of paper around a cylinder, and cutting a single wave, through several layers, with a sharp knife. When it is unrolled, the bottom part will be like the waves. When a pattern repeats both horizontally and vertically, but without reflections or rotations, the quotient orbifold is a torus. You can think of it by first rolling up the pattern in one direction, matching up equivalent points, to get a long cylinder.

### 2-Dimension from the Topological Viewpoint by Barmak J.A., Minian E.G.

by Steven

4.1