Algebra and Geometry: For the Enthusiastic Beginner

I am presently working on a book that will be titled “Algebra and Geometry for the Enthusiastic Beginner,” aimed at middle-school and high-school students (along with anyone else who wants to learn algebra and geometry). Like my other self-published books, it will be inexpensive. The completion date is probably two years away - I’m guessing the fall of 2023. But in the meantime I’ll periodically post some chapters in draft form. The book will include many examples and solved problems, so it should be great for self-study. It will also include lots of limericks. For now, here’s a draft of Chapter 6 on the Pythagorean theorem (the exercise solutions are at the end of the chapter):

Chapter 6 (Pythagorean theorem)

 The tentative list of chapters (which will be divided into two volumes) is:

  1. Background, Part 1
  2. Background, Part 2
  3. Algebra, Part 1
  4. Algebra, Part 2
  5. Geometry
  6. Pythagorean theorem
  7. Solving for x
  8. Functions and plotting
  9. Quadratic equations
  10. Triangles and cones
  11. Circles and spheres
  12. Miscellaneous topics
  13. Combinatorics
  14. Slopes
  15. Trigonometry 1
  16. Trigonometry 2
  17. Complex numbers 1
  18. Complex numbers 2