Computer Lab #1

1. Use a web browser to access the webpage http://www.research.att.com:80/~njas/sequences/

   With this webpage you can submit the initial segment of a sequence of integers, and search the huge database for a match and some references.

2. Use Geometer's Sketchpad to make some tilings of the plane with congruent triangles. Each triangle is rotated about the midpoint of each side to obtain its neighbor in the tiling. Try the same thing with various quadrilaterals.
3. Use Maple to find some summation formulas. Try
   sum(i,i=1..n);
   factor(sum(i,i=1..n));
   factor(sum(i^2,i=1..n));
   factor(sum(i^3,i=1..n));
   factor(sum(i^4,i=1..n));
   factor(sum(i^5,i=1..n));
   sum(1/i,i=1..infinity);
   sum(1/i^2,i=1..infinity);
   sum(1/i^3,i=1..infinity);
   sum(1/i^4,i=1..infinity);
4. Use Maple to construct the following objects:
   1. A cube.
   2. A square-based pyramid.
   3. An octahedron.
   4. A tetrahedron.
   5. A pyramid with a hexagonal base.
   Here are the instructions for drawing a square-based pyramid. See if you can figure out what the various commands are doing.

   with(plots);
   p1:=[1,1,0];
   p2:=[-1,1,0];
   p3:=[-1,-1,0];
   p4:=[1,-1,0];
   p5:=[0,0,1];
   pyramid:=[ [p1,p2,p3,p4], [p1,p2,p5], [p2,p3,p5], [p3,p4,p5], [p4,p1,p5] ];
   polygonplot3d(pyramid,scaling=constrained);

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