Math 116: Symmetry and Shape
Guide for Exam 2

The second midterm is on Wednesday, April 1, during the regular class period.

The following is a chapter by chapter guide intended to help you organize the material we have covered as you study for your exam. It is only intended to serve as a guideline, and may not explicitly mention everything that you need to study. Also note that while chapters not listed here will not explicitly be tested, you may require information from them in order to solve problems related to the material listed below.

Please start by taking a look at class notes and the material that we discussed in class. Then review all relevant textbook sections and homework problems for the chapters given below, and make sure you can solve all of them.

Ch 1.1. Measurement:

  1. Know how to find the area and perimeter of a figure made up of rectangular, circular or right triangular pieces, such as the ones in Problem 10 and 14.
  2. Know the statement of the Pythagorean Theorem and how to apply it.

Ch 1.2. Polygons:

  1. Know how polygons are defined and named, especially for n-gons where n=3,4,5,6,8,10,12,20.
  2. Identify different types of triangles (ie, equilateral, isosceles, scalene) and quadrilaterals (ie, squares, rectangles, parallelograms, rhombuses, trapezoids).
  3. Know what it means for a polygon to be convex (or not).
  4. Be able to find the sum of the vertex angles of an arbitrary (ie, not necessarily regular) polygon by dividing it up into triangles.
  5. Be able to find each vertex angle, the center and the central angle of a regular polygon.

Ch 4.1. Regular and Semiregular Tilings:

  1. Know the definitions of regular and semiregular tilings, and system used to label them.
  2. You should know all of the possible regular tilings (although you do not need to remember every possible semiregular tiling).
  3. Know how to sketch a given regular or semiregular tiling.
  4. Given a regular or semiregular tiling, you should be able to draw the dual tiling, and identify the vertex angles of the dual tiles.

Ch 4.2. Irregular Tilings:

  1. Know how to identify and sketch irregular tilings.
  2. Be able to describe and identify the following transformations and create examples of tiles formed using them:
    1. parallel translation
    2. glide reflection
    3. midpoint rotation
    4. side rotation

Ch 2.2. Celtic Knots:

  1. Be able to find the appropriate grid of dots for a knot with specified dimensions, and draw this knot.
  2. Be able to find the number of strands and position of loose ends based on dimensions, and be able to determine dimensions that would give a specified number of strands or position of loose ends.
  3. Know how to draw a celtic knot on a grid with bars.

Ch 7.1. Prisms and Pyramids:

  1. Know the definitions of the terms polyhedron, prism and pyramid.
  2. Be able to classify prisms and pyramids as right or skew, and as regular or irregular.
  3. Be able to sketch a net of a specified polyhedron.
  4. Know how to find the volume of prisms, pyramids, cones, cylinders and spheres.
  5. You should be able to identify the shape of cross-sections of solids.

Ch 7.2. Platonic Solids:

  1. You should know how many Platonic solids there are, and be able to name them all.
  2. You should be able to label these solids in the same way that we labelled regular tilings (for example, 3.3.3.3).
  3. Know what it means for a polyhedron to be convex and the Euler characteristic (ie, #vertices - #edges + #faces) of convex polyhedra.
  4. Know what we mean by the dual of a polygon, and know the duals of each of the Platonic solids in particular.

Ch 5.1. Two Dimensional Symmetry:

  1. You should know what we mean by reflection symmetry and rotational symmetry.
  2. You should be able to identify lines of reflection, and angles of rotation of a given figure.

Maintained by ynaqvi and last modified 03/26/15