ASTRON 2B03 Lecture Notes - Topographic Map, Hypercube, Knot Theory
25 Sep 2013
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Size - finite or not: evidence that it is expanding at an ever-increasing speed, does not answer if it is finite or not. If the summation of angles is more than 180, even incredibly in a small way, that means that there is some sort of curve. Different size triangles add up to different 180s. On flat spaces, 180 is accurate yes. But, on curved spaces, it is a little more than 180, depending on size. Realized small triangles wouldn"t give him anything significant: measured a triangle on different mountains. By combining horizontal and vertical directions, you can get anywhere in the plane 2 dimensions. Use it as a definition of dimension. Life in 2 dimensions: just like a flat plane many limitations. How are we going to think about 4 dimensions : In 4 dimensions , you can take out the 3-d knot and make it a circle.
