Week 23 started out with the unit Solid Geometry and finished with me getting about a third of the way through the following unit Analytic Geometry. At the start of the week, the goal was to get through both units. I got called into work Thursday and Friday mornings which made tough to get through the second unit having lost that time. I’m proud of the effort I made to get as far as a did, however, as I tried to make up for those mornings by working through KA on Friday evening and Saturday morning, which I typically don’t do.

Solid Geometry started by introducing me to volume formulas for common polyhedrons (i.e. 3D, flat surfaced shapes). The shapes and their formulas I learned about are:

• Rectangular Prism
  • V = L * W * H
• Triangular Prism
  • V = L * W * H * ½
• Cylinder
  • V = (Pi) * r^2 * H
• Pyramid
  • V = L * W * H * 1/3
  • This seems to be for a square based pyramid. I’m not sure if the same formula applies to a triangular based pyramid.
• Cone
  • V = (Pi) * r^2 * H * 1/3
• Sphere
  • V = 4/3 * (Pi) * r^3

I went through a number of questions where I practiced finding the volume of these polyhedrons and also their surface area. I only found the surface area of rectangular and triangular prisms, cylinders and pyramids, however. I’m assuming I’ll learn how to find the surface area of cones and spheres later on.

I began the unit Analytic Geometry on Wednesday. So far in this unit I’ve worked on finding the midpoints of lines on a graph, finding the lengths of certain line segments of a line when given ratios between the distances of collinear points on that line, and using the distance formula (which is the Pythagorean Theorem) to find the length of lines. The notable things I learned on each of those three topics are:

• Midpoints
  • M.P. = (x’1 + x’2)/2, (y’1 + y’2)/2)
  • The commas should be read as “x-one plus x-two”, etc
  • Ex. the mid point of points (3, 5) (5, 4) is
    • M.P. = ((3 + 5)/2 , (5 + 4)/2)
    • M.P. = (8/2 , 9/2)
    • M.P. = (4, 4.5)
• Dividing Line Segments
  • “Find the point B on line segment AC such that the ratio of segment AB to BC is 3:1”
    • C = (-7, 1), B = (?), A = (9, 5)
    • BC = ¼ of the way to AC
      • B’x = (A’x – -C’x) * ¼ + C’x
        • = (9 – -7) * ¼ + -7
        • = 16 * ¼ + -7
        • = 4 + -7
        • B’x = (-3)
      • B’y = (A’y – C’y) * ¼ + C’y
        • = (5 – 1) * ¼ + 1
        • = 4 * ¼ + 1
        • = 1 + 1
        • B’y = 2
      • B = (-3, 2)
• Distance formula on a graph
  • d = {(x’2 – x’1)^2 + (y’2 – y’1)^2}
    • This is the same thing as the Pythagorean Theorem.
    • It’s used to find the length of a diagonal line on a graph.

Going through distance formula practice questions, I was able to get a much better grasp on, and began feeling much more comfortable working with square roots. I feel like I’ve got a stronger understanding of how/when to add, subtract, multiply, and factor square roots. Having felt semi intimidated seeing square roots in questions before, it’s nice to feel more confident working with them now. Based on seeing them more frequently lately, I think that feeling comfortable working with square roots is going to be important going forward.

This coming week, it would be nice to get through Analytic Geometry (320/900 M.P.) early on and make a solid dent in the following unit Circles (0/1700 M.P.). As I mentioned in my last post, my current short term goal is to get through the course High School Geometry by the end of Week 26. I assume it shouldn’t be too difficult to hit that goal, but I’ve also thought that about other goals I’ve made for myself in the past which I’ve fallen short of. Hopefully this time is different!