Discrete geometry | Wikipedia audio article
Channel: wikipedia tts
Date: 04/10/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Discrete_geometry


00:00:49 1 History
00:01:26 2 Topics in discrete geometry
00:01:36 2.1 Polyhedra and polytopes
00:02:26 2.2 Packings, coverings and tilings
00:03:43 2.3 Structural rigidity and flexibility
00:04:10 2.4 Incidence structures
00:05:40 2.5 Oriented matroids
00:06:14 2.6 Geometric graph theory
00:06:48 2.7 Simplicial complexes
00:07:23 2.8 Topological combinatorics
00:08:15 2.9 Lattices and discrete groups
00:09:37 2.10 Digital geometry
00:10:13 2.11 Discrete differential geometry
00:11:03 3 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9276576567807017
Voice name: en-AU-Wavenet-B


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.  Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth.  The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object.
Discrete geometry has a large overlap with convex geometry and computational geometry, and is closely related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology.