MATH 427, Fall 2025
FOUNDATIONS OF GEOMETRY
(Euclidean and various non-Euclidean geometries
and their development from postulate systems.)

Syllabus - Extra credit problems - Conformal disc model

• Мidterm: Fri, Nov 14, in class, 5 problems:
  • 2 theorems from the list (possibly with related definitions):
    11.1, 11.5, 11.9, 11.10, 12.8, 12.9, 13.3, 13.6, 13.10;
  • 2 problems from HWA 09--11 (possibly with related definitions);
  • 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.

• HWA-11, due 11:15, Mon, Nov 10.
  • Read and understand: Chapter 13.
  • Exercises: 13.1, 13.9, 13.15, 13.17.
  • Constructions:
    • Common perependicular,
    • Bolyai’s construction.
  • Start to think about the second midterm --- skim thru chapters 11--13, prepare at least one question.
• HWA-10, due 11:15, Mon, Nov 3.
  • Skim thru: Chapters 12 and 10.
  • Read and think: Chapter 13.
  • Exercises: 11.13, 12.21, 12.23.
  • Constructions:
    • Inversion,
    • Inversions,
    • Perpedicular circle 1,
    • Perpedicular circle 2.
• HWA-09, due 11:15, Mon, Oct 27.
  • Read and understand: Chapter 11.
  • Read and think: Chapter 12.
  • Exercises: 11.4, 11.14, 12.1.
  • Constructions:
    • Perpendicular,
    • Center,
    • Copy of circle,
    • Tangent to circle,
• Q-08, due 23:59, Wed, Oct 22.
• HWA-08, due 11:15, Mon, Oct 20.
  • For full credit, do 10 of the following 12 constructions:
    • ⅜π,
    • 2:3,
    • Copy of angle,
    • Side-median-side,
    • Tangent circle 2,
    • Minimal sum 2,
    • Concentric circles 2,
    • Parallel cut,
    • Inscribed square 2,
    • Equilateral triangles,
    • Minimal perimeter 1,
    • OX·OZ = OY².

• You can retake the exam until Wed, Oct 29. (A maximum of two scores will be counted.) Reserve 60 min in advance; no cheat sheet this time.
• Midterm, Fri Oct 17, in class, 5 problems:
  • 2 theorems from the list (possibly with related definitions):
    2.4, 2.7, 2.12, 2.14,
    3.6, 3.10, 3.13,
    4.1, 4.2, 4.4,
    5.2, 5.6, 5.8, 5.13, 5.20, 5.22,
    6.6,
    7.1, 7.2, 7.8, 7.9, 7.13, 7.18,
    8.1, 8.3, 8.6, 8.11, 8.15, 8.16;
  • 2 problems from HWA 01--07 (possibly with related definitions);
  • 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.
• I will print for you the list of axioms, plus you may ask for something else (in advance).
• Extra office hours: Thu, Oct 16, 19:00--19:50 psu.zoom.us/my/anton.petrunin.

• HWA-07, due 11:15, Mon, Oct 13.
  • Read and understand: Chapter 8.
  • Exercises: 7.23, 8.5, 8.14.
  • Constructions:
    • Segment trisection,
    • Inscribed triangle,
    • Tangent line 2,
    • Incircle.
  • Start to think about midterm exam --- skim thru the covered material, prepare at least one question.
• HWA-06, due 11:15, Mon, Oct 6.
  • Read and understand: Chapters 6 and 7.
  • Read and think: Chapter 8.
  • Exercises: 6.7, 6.10, 7.4.
  • Constructions:
    • Tangent circle 3,
    • Tangent line 1,
    • Inscribed equilateral triangle,
    • Parallel line.
• HWA-05, due 11:15, Mon, Sep 29.
  • Read and understand: Chapters 5 and 6.
  • Read and think: Chapter 7.
  • Exercises: 5.21, 5.23b, 6.3.
  • Constructions:
    • Perpendicular 1,
    • Minimal sum 1,
    • Bisected perpendicular 1,
    • Bisected line.
• HWA-04, due 11:15, Mon, Sep 22.
  • Read and understand: Chapters 4 and 5.
  • Read and think: Chapter 6.
  • Exercises: 4.3, 4.8, 5.3.
  • Register at geogebra.org and do the following constructions.
    (Once you see "Well done", make a screenshot and upload it to CANVAS.)
    • Angle-side-angle,
    • Angle-side-side,
    • Segment bisection,
    • Center of circle.
• HWA-03, due 11:15, Mon, Sep 15.
  • Read and understand: Chapters 3.
  • Read and think: Chapter 4.
  • Exercises: 1.17, 3.3, 3.14, 3.15, 3.21.
• HWA-02, due 11:15, Mon, Sep 8.
  • Read and understand: Chapter 2.
  • Read and think: Chapter 3.
  • Exercises: 1.3(a), 1.15(a), 1.16, 2.5, 2.11, 2.9.
• HWA-01, due 11:15, Fri, Aug 29.
  • Read and understand: Chapter 1.
  • Read and think: Chapter 2.
  • Exercises: 1.2, 1.4, 1.5, 1.10, 1.13.
    (Scan to pdf and upload to CANVAS.)