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Oct.5 - 2B03.docx

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Laura Parker

Oct. 5 – 2B03 05/10/2011 9:32:00 AM Guest Lecture Major mathematical questions about the universe:  Shape of the universe – fixed or evolving?  Size - finite or not. o Evidence that it is expanding – at an ever-increasing speed. o Does not answer if it is finite or not.  Dimensions Positive Curvature  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. Gauss  Realized small triangles wouldn’t give him anything significant. o Measured a triangle on different mountains.  People use this method w/ stars. What is a dimension:  Different definitions All curves are one-dimensional By combining horizontal and vertical directions, you can get anywhere in the plane – 2 dimensions.  Hollow spheres for ex, nothing insides. Power of scaling  use it as a definition of dimension Analogy  Life in 2 dimensions o Just like a flat plane – many limitations. Our universe could be a cyclinder.  Radius – several billion light years.  Could also be donut shaped. Learning properties of dimensions  Intuitive level and the mathematical level. How are we going to think about 4 dimensions :  Level
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