MATH 471, GEOMETRY FOR TEACHERS
(Problem solving oriented introduction
to Euclidean and non-Euclidean geometries.)

Syllabus - Extra credit problems - Euclidea

• Lecture 04, due 15:35, Fri, May 2, in class.
  Prepare a demo lecture on a geometry topic of your choice. Make sure each person chooses a different topic, and keep your lecture exactly 15 minutes long.
• HWA-14, due 15:35, Mon, Apr 29. (Upload all to CANVAS.)
  • Skim thru Chapters 19.
  • Exercises: 19.9(a), 19.13, and these constructions.
• Construction set 10.
• HWA-13, due 15:35, Mon, Apr 21. (Upload all to CANVAS.)
  • Skim thru chapters 12 and 13.
  • Exercises: 12.1, 12.11*, 12.21*, 13.11 13.12.
  • Draw* an equilateral h-triangle with angle smaller than \(\tfrac\pi4\).
    *Draw it by hand or use this applet.
  • If you have time, watch few moments from Hyperbolica walkthru, starting at 7:32, 12:43, 26:40 (spherical world), 1:22:45, and 1:29:07.
• Construction set 09.
• Quiz 12, due midnite, Wed, Apr 16. (Upload it to CANVAS.)
• HWA-12, due 15:35, Mon, Apr 14. (Upload all to CANVAS.)

• Мidterm: Fri, Apr 11, in class, 5 problems:
  • 2 theorems from the list (possibly with related definitions):
    8.1, 8.3, 8.5, 8.9, 8.13, 8.14, 20.12, 20.14, 20.22, 9.1, 9.2 (only-if part), 9.13, 11.4;
  • 2 HW problems from the list (possibly with related definitions):
    8.8, 8.12, 8.17, 20.13, 20.20, 20.21, 20.24, 9.6, 9.12, 9.18, 11.2, 11.3, 11.6.
  • one new problem.
• You may prepare and use a cheat sheet --- one sided standard paper size, include diagrams and formulas, but no words. Do not make it cryptic.
• Extra office hour: Thu, Apr 10, 19:00, psu.zoom.us/my/anton.petrunin.

• HWA-11, due 15:35, Mon, Apr 7. (Upload all to CANVAS.)
  • Read Chapter 11.
  • Exercises: 11.2, 11.3, 11.6, 11.12, 11.13.
• Lecture 03, Fri, Apr 4, in class.
  The lecture should be no longer than 15 minutes.
  You should receive a message with one of the following topics:
  1. Congruent trianges: list the congruence conditions (without proofs), make necessary comments, and discuss one application (4.5, 5.2, 8.13, or your choice) with a proof.
  2. Similar triangles: list the similarity conditions (without proofs), make necessary comments, and discuss one application (6.8, 6.9, 7.11, or your choice) with a proof.
  3. The area method: describe the theorems used in the area method (without proofs), make necessary comments, and discuss one application (8.9, 20.21, 20.24, or your choice) with a proof.
  4. The method of the additional circle: describe the theorems used in the method of the additional circle (without proofs), make necessary comments, and discuss one application (the problem in 9D, 9.18, or your choice) with a proof.
• HWA-10, due 15:35, Mon, Mar 31. (Upload all to CANVAS.)
  • Read Chapter 9.
  • Exercises: 9.6, 9.12, 9.17, 9.18, 9.7.
  • Extended hint for 9.17.
• Construction set 08.
• Quiz 09, due midnite, Wed, Mar 26. (Upload it to CANVAS.)
• HWA-09, due 15:35, Mon, Mar 24. (Upload all to CANVAS.)
  • Read Chapter 20.
  • Exercises: 20.4, 20.13, 20.20, 20.21, 20.24.
• Construction set 07.
• HWA-08, due 15:35, Mon, Mar 17. (Upload all to CANVAS.)
  • Read chapters 8 and 20.
  • Exercises: 8.8, 8.12, 8.17, 20.5, 20.13.
• Construction set 06, due Tue Mar 18.
  Create a GeoGebra applet and upload the link to CANVAS.
  You should receive a message with the selected problems.
  Exapmples:
  • Simpson line + walk-thru.
  • Line thru midpoints and the intersection of bisectors + walk-thru.
• HWA-07, due 15:35, Mon, Mar 03. (Upload all to CANVAS.)
  • Check the following solutions, mark errors (if they exist), and indicate the reason. Solution 1, Solution 2, Solution 3.
  • Set a timer for 20 minutes and do as many exercises from this constriction set as possible. (The grade will be the same if you do at least one exercise.)

• Midterm, Fri Feb 28, in class, 5 problems:
  • 2 theorems from the list (possibly with related definitions):
    2.2, 2.5, 2.13, 4.1, 4.2, 4.4, 4.5, 5.2, 5.5, 5.10, 5.15, 5.17, 6.4, 7.1, 7.3, 7.8, 7.12, 7.17, 8.1, 8.3.
  • 2 HW problems from the list (possibly with related definitions):
    1.4, 2.14, 4.3, 4.6, 4.7, 5.3, 5.4, 5.7, 5.12, 5.16, 5.18, 5.19, 5.20, 6.5, 6.8, 6.9, 7.7, 7.10, 7.14, 7.15, 7.20, 7.21, 8.4.
  • one new problem.
• You may prepare and use a cheat sheet --- one sided standard paper size, include diagrams and formulas, but no words. Do not make it cryptic.
• Extra office hour: Thu, Feb 27, 21:00, psu.zoom.us/my/anton.petrunin.

• Quiz 06, due midnite, Wed, Feb 26.
  You should receive a message with the selected problems.
• Lecture 02, due 15:35, Тue, Feb 25.
  You should receive a message with a selection of theorem.
  You will need to state the theorem, make the necessary remarks, provide a proof (not necessarily complete, but in that case, explain where it is incomplete), and, if time allows, give an example of its application. Record it in ZOOM and upload the link to CANVAS.
  The lecture should be no longer than 10 minutes.
• HWA-06, due 15:35, Mon, Feb 24.
  • Read Chapters 7 and 8.
  • Exercises: 7.14, 7.15, 7.20, 7.21, 8.4.
  • Start to think about the midterm exam --- skim thru the covered material and prepare questions.
• Construction set 05.
• Lecture 01, due 15:35, Wed, Feb 19.
  You should receive a message with a selection of construction problems.
  Your lecture should be useful to someone---find such a person or imagine one. In the lecture, you should:
  • Formulate the problem,
  • Explain how to come up with the right idea for solving it,
  • Demonstrate that the solution works, and
  • Explain why it works.
  Record your lecture in ZOOM and upload the link to CANVAS.
  The lecture should be no longer than 5 minutes.
  For better results, consider asking other student(s) to participate and ask questions.
• HWA-05, due 15:35, Mon, Feb 17.
  • Read Chapters 6 and 7.
  • Exercises: 6.5, 6.8, 6.9, 7.7, 7.10.
• Construction set 04.
• HWA-04, due 15:35, Mon, Feb 10.
  • Read Chapters 5 and 6.
  • Exercises: 5.12, 5.16, 5.18, 5.19, 5.20.
  • Soon, I will ask you to record a short lecture on one of the constructions in ZOOM; it should be approximately like this one, but shorter. Please watch it and make sure you can do something similar.
• Construction set 03.
• HWA-03, due 15:35, Mon, Feb 3.
  • Read sections A--E in Chapter 5.
  • Exercises: 5.1, 5.3, 5.4, 5.7, 5.9. (Scan to PDF and upload to CANVAS.)
• Construction set 02.
• HWA-02, due 15:35, Mon, Jan 27.
  • Skim thru Chapter 3; make sure that your intuition agrees with 3.7, 3.9, 3.10, 3.12, and 3.17.
  • Read Chapter 4.
  • Exercises: 3.13, 4.3, 4.6, 4.7, 4.8. (Scan to PDF and upload to CANVAS.)
• Construction set 01.
• HWA-01, due 15:35, Fri, Jan 17.
  • Read the 2nd chapter (using the 1st chapter as a reference).
  • Exercises: 1.4, 1.5, 1.13, 2.12, 2.14; scan to PDF and upload to CANVAS.
  • Test construction --- get to "Well done", make a screenshot, and upload it to CANVAS. This part will not be graded; it is to ensure that you can run these applets on your computer. (Spend no more than 3 minutes on it.)