MAS6318 Journal Book
Advanced Algebra and Geometry Book by Courteney Zboyan
Table of Contents
- Ch.1 Module 1 Examples from Lecture
- Circles in a Square #1
- Circles in a Square #2
- Circles in a Square #3
- Circles in a Square #4
- Circles in a Square #5
- Module 1 Exercise: Golden Ratio
- Basic Theorems #1
- Basic Theorems #2
- Basic Theorems #3
- Basic Theorems #4
- Basic Theorems #5
- Ch.2 Module 1 Workbook Exercises
- Workbook Exercise 1.1
Circles in a Square #1
Instruction
Created 4x4 square with segment tool. Created circle with radius on top side using that tool. Created the tangent segment BF. Displayed all the various required segment lengths using the segment tool. The result is a 3-4-5 triangle.
Construction
Circles in a Square #2
Instructions
The radii of the larger circle centered at A are both 4 in distance (segments AD and AF). The radii of the smaller circle centered at E are all 1 in distance (segments CE, FE, and GE). Thus, there is a 3-4-5 triangle, when we add up segments BG & GE to get 3, then side AB equals 4, and AF & FE to get 5
Construction
Circles in a Square #3
Instruction
Again, made a 4x4 square with two circles of radius 4 on each of left and right sides. Then, used circle at center with set radius tool to position a circle at (2,1.5) with radius 1.5[br]I displayed various segment lengths and emphasized certain shapes. A "3-4-5 triangle" is made at half the size with "1.5-2-2.5"
Construction
Circles in a Square #4
Instructions
Since a side AB of the square is 6, then a diagonal AH from the far opposite corner to the small tangent circle (with radius 1) center should be 7 and a diagonal BH to the near opposite corner should be 5. Again, circle tool and certain radius are very helpful here.
Construction
Circles in a Square #5
Instructions
Since side of square BC is 16, then displaced circle G has radius 1 such that GE is 15 with BG and GC are 17. Again, circle tool and certain radius are very helpful here. Segments and shapes were emphasized in color.
Construction
Module 1 Exercise: Golden Ratio
Instruction
Used polygon, midpoint, segment, and intersect tools to derive the golden ratio value of ~1.62[br]The, hid construction pieces besides for segment AB with Golden Ratio point G
Construction
Basic Theorems #1
Instructions
As given, 2 squared + 8 squared = (approx) 8.25 squared: 4 + 64 = 68 for all the triangles like AHE[br]This shows the Pythagorean Theorem: a^2 + b^2 = c^2
Construction
Basic Theorems #2
Construction
As given, 2 squared + 8 squared = (approx) 8.25 squared: 4 + 64 = 68 for all the triangles like AHF[br]This shows the Pythagorean Theorem: a^2 + b^2 = c^2 using the triangles in a different position
Construction
Basic Theorems #3
Instruction
This shows the Pythagorean Theorem: a^2 + b^2 = c^2 holds for right triangles. B is fixed while A and C are not.
Construction
Basic Theorems #4
Instructions
This shows the Pythagorean Theorem: a^2 + b^2 = c^2 for a 30-60-90 triangle
Construction
Basic Theorems #5
Instruction
This shows the Pythagorean Theorem: a^2 + b^2 = c^2 holds for a 45-45-90 triangle (which is easy to make).
Construction
Workbook Exercise 1.1
Instructions
(Two Circles and a Square)[br]Find the ratio of the radii of the 2 circles