Fall 2019 Notes.pdf - MATH 228 Fall 2019 Professor Thomas...

This preview shows page 1 - 5 out of 43 pages.

The preview shows page 3 - 5 out of 43 pages.
©2019 An Li. All rights reserved.1MATH 228 Fall 2019Professor Thomas FoxContentsLecture 1Wednesday, September 4, 2019..................................................................4History.........................................................................................................................4Lecture 2Friday, September 6, 2019...........................................................................5Lecture 3Monday, September 9, 2019........................................................................7The “converse” of a theorem.......................................................................................7Converse of Thales I................................................................................................7Congruent triangles..................................................................................................8Lecture 4Wednesday, September 11, 2019................................................................8Subdividing polygons..................................................................................................8Regular polygons.........................................................................................................8Tiling floor with regular polygons.............................................................................9Lecture 5Friday, September 13, 2019.......................................................................10Parallels.....................................................................................................................10Euclid’s five axioms...................................................................................................10Lecture 6Monday, September 16, 2019....................................................................11The most famous theorem: Pythagorean theorem....................................................12Lecture 7Wednesday, September 18, 2019..............................................................13Lecture 8Friday, September 20, 2019.......................................................................14Centers of a triangle..................................................................................................15Circumcenter.........................................................................................................15Lecture 9Monday, September 23, 2019....................................................................16Incenter..................................................................................................................16Centroid.................................................................................................................16Lecture 10Wednesday, September 25, 2019............................................................17Quiz 1 review (Part 1)Monday, September 30, 2019.................................................17Homework 3, #13......................................................................................................17About the quiz...........................................................................................................18
2©2019 An Li. All rights reserved.How to draw a bisector with a compass?.................................................................18Quiz 1 review (Part 2)Wednesday, October 2, 2019..................................................18Homework 6, #5........................................................................................................19Lecture 11Monday, October 7, 2019........................................................................19Back to Thales II........................................................................................................19Lecture 12Wednesday, October 9, 2019...................................................................21Altitude of a triangle...................................................................................................21Lecture 13Friday, October 11, 2019..........................................................................23Thales (continued).....................................................................................................23Cyclic quadrilaterals...............................................................................................23Back to orthocenter...............................................................................................23Lecture 14Wednesday, October 16, 2019.................................................................24Lecture 15Friday, October 18, 2019..........................................................................25Homework 7, Problem 19..........................................................................................25Lecture 16Monday, October 21, 2019......................................................................26Lecture 17Wednesday, October 23, 2019.................................................................26Four-dimensional space............................................................................................26Lecture 18Friday, October 25, 2019..........................................................................27Lecture 19Monday, October 28, 2019......................................................................28Lecture 20Wednesday, October 30, 2019.................................................................29Lecture 21Friday, November 1, 2019........................................................................30Lecture 22Monday, November 4, 2019.....................................................................31Nine-point circle, revisited.........................................................................................31Lecture 23Wednesday, November 6, 2019...............................................................32Lecture 24Friday, November 8, 2019........................................................................33Lecture 25Wednesday, November 13, 2019.............................................................34Regular polyhedra.....................................................................................................34Lecture 26Friday, November 15, 2019......................................................................35Recall: The “shadow” of a polyhedron......................................................................35Lecture 27Monday, November 18, 2019...................................................................37Lecture 28Wednesday, November 20, 2019.............................................................37
©2019 An Li. All rights reserved.3Lecture 29Friday, November 22, 2019......................................................................38Ceva’s Theorem........................................................................................................39Lecture 30Monday, November 25, 2019...................................................................39Back to the nine-point circle......................................................................................39Ceva’s Theorem (revisited)........................................................................................40Menelaus...................................................................................................................40Lecture 31Wednesday, November 27, 2019.............................................................40Lecture 32Friday, November 29, 2019......................................................................41Homework 11............................................................................................................41Problem 5...............................................................................................................41Lecture 33Monday, December 2, 2019.....................................................................42Problem 8...............................................................................................................42Lecture 34Tuesday, December 3, 2019....................................................................43Recall: Menelaus.......................................................................................................43
4©2019 An Li. All rights reserved.Lecture 1Wednesday, September 4, 2019HistoryFor 200 years, geometry was done without graphs nor equations.Real mathematicians see a picture when they see an equation.Unfortunately today, it is just the algebra.This course is about thinking math in pictures and not equations.Geometry begins with Greek philosopher Thales (~600 BC).It is possible that not every triangle in the entire world has its angles sum up to 180°.He asked, “How do you know it’s true?”Measuring is not feasible, because firstly, there is an error with measuring instrumentsand we cannot simply measure every single triangle in the world.

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 43 pages?

Upload your study docs or become a

Course Hero member to access this document

Term
Fall
Professor
Thomas Fox
Tags

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture