What We've Done

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The lists below provide an outline of the in-class activities we have completed in this program.

We are attempting to provide pdf files of the worksheets or other handouts from class, and there are also links here to other pages in the wiki which should help you review the content of what has been presented in class. Feel free to add more content, review, and example pages to the wiki and link them here when appropriate.

Your portfolio should display work related to the items listed here.

Contents

[edit] Week 1

[edit] Monday

  1. The Geometry of Space: Triangles and Coordinate Systems (We just did the triangles part on Monday.)
  2. Pythagorean Theorem worksheet (This will be uploaded later.)
  3. Discussed the concern with scale: some things work well at a small scale but don't work at all when they are a lot bigger.

[edit] Wednesday

  • TbnO: One-dimensional; Two-dimensional; Three-dimensional
The content of this is the second half of the The Geometry of Space worksheet.
  • Sum of the angles of a triangle
  • Brief discussion of chapter 2 of Simply Einstein
Key idea: Principle of relativity in one sentence: "The laws of physics are the same for all."
  • Continued work on Pythagorean Theorem worksheet: error analysis
  • Wiki workshop (56KB pdf file)
  • Mapping practice sheet and quiz (This will be uploaded later.)
  • Self-assessment form

[edit] Week 2

[edit] Monday

  • TbnO: Midpoints of a quadrilateral form a parallelogram
  • Continued work on mapping practice sheet and quiz: distance as an invariant
  • Distance formula
  • Discussed issues and expectations for peer feedback on truth papers
  • Brief lecture: Overview of Special Relativity (26KB pdf file)
  • Brief lecture: Why Geometry?
How can human-sized triangles, circles, and such be measured to find out about the size of Earth or the distance to Moon?
  • Similar triangles

[edit] Wednesday

Worksheet: Speed Practice‎ (46KB pdf file)
Hound of the Baskervilles
Simply Einstein chapters 3-4
Worksheet: Week 2: Position and Distance‎ (37KB pdf file)
Self-assessment form

[edit] Week 3

[edit] Monday

  • TbnO: Stars move
  • Postulate 1 and Mauney's Postulate
  • Review of speed
  • Demonstrations: wave, medium, wave speed
  • Question: What medium does light (or any electromagnetic wave) travel through?
  • Seminar

[edit] Wednesday

  • TbnO: Wine bottle theorem
  • Exam 1
  • Proposition 1 and Mauney's Postulate
  • Seminar
  • Self-assessment form

[edit] Week 4

[edit] Monday

  • TbnO: The speed of light is a universal constant
  • Special Relativity Consequence #1: The speed of light can be used to convert units of distance to units of time.
Light travels 1 meter per meter or 1 second per second or 1.
Worksheet: Skills 9 and 10 (41KB pdf file)
Worksheet: Parallel lines, transversals, and angles‎ (56KB pdf file)
  • Proof that the sum of the angles of a triangle is a line or a straight angle
  • Special Relativity Consequence #2: The time between two events is not always the same as measured by different observers.

[edit] Wednesday

  • Parable of the Surveyor
  • Special Relativity: Invariance of the Spacetime Interval
  • Activity: Two dimensional and three dimensional sets
  • Seminar: Flatland, Part 1 and Simply Einstein chapter 8
  • Proofs: Propositions A, B, and C
  • Self-assessment form

[edit] Week 5

[edit] Monday

  • ObnT: It's noon!
  • Difference between proof and measurement
  • More work on Propositions A, B, and C
  • Clock synchronization
Worksheet: Clock synchronization‎ (39KB pdf file)
  • Seminar: Truth paper and Simply Einstein
  • Worksheet: Area formulas

[edit] Wednesday

  • TbnO: The area of all triangles with the same base and same height is the same
  • Proving the Pythagorean Theorem
  • Activity: Simulation of radioactive decay using dice
  • Sample problem using the spacetime interval
  • Muons on Mt. Washington - video of experimental evidence which supports the predictions of special relativity
  • Seminar: Flatland
  • Self-assessment form

[edit] Week 6

[edit] Monday

  • TbnO: Any triangle inscribed in a circle which uses a diameter as one of its sides is a right triangle.
  • Preaching: The realm of truth (for intellectuals in ancient Greece)
  • Announcements: Truth paper part 2 due Wednesday. Exam next Monday!
  • Workshop: Proof of the Pythagorean Theorem
  • Workshop: Spacetime Levels 1-3
Worksheet‎ (59KB pdf file)
  • Seminar: Truth paper and muon experiment

[edit] Wednesday

  • Announcements
  • Workshop: Pythagorean Theorem; non-Euclidean geometry
  • Workshop: Spacetime Levels 3-4
  • Seminar: Plato's Republic
  • Self-assessment form

[edit] Week 7

[edit] Monday

  • Speech by Richard Dawkins from CBC radio's show called Ideas
  • Exam 2
  • Discussion questions about special relativity
  • Taxicab geometry

[edit] Wednesday

  • Continuation of speech by Richard Dawkins
  • More taxicab geometry
  • The time stretch factor in special relativity
Workshop: Length contraction‎ (70KB pdf file)
  • Seminar on Simply Einstein and relativity
  • Self-assessment form

[edit] Week 8

[edit] Monday

[edit] Wednesday

  • TbnO: A circle is as infinite as a line
  • Set theory and paradoxes
  • Seminar: Goedel's incompleteness theorem
  • Special relativity: Train paradox
  • Self-assessment form

[edit] Week 9

[edit] Monday

  • Holiday!

[edit] Wednesday

  • More on the paradoxes of set theory and Goedel's proof
  • More on the train paradox and
  • Seminar: Descartes' Dream
  • Portfolio prompts