Geometry

1. The "Big Book" Offline Foundations

Since OpenStax doesn't have a Geometry book (yet), these are the best OER (Open Educational Resource) alternatives we could find that exist as single, downloadable PDFs.

• CK-12 Geometry (FlexBook 2.0): This is the most "modern" equivalent to OpenStax. It is Creative Commons licensed. You can download the entire book as a PDF. It includes "discovery" prompts that fit your style.

  • Why it fits: It covers high school geometry comprehensively and includes units on 3D symmetry.

• Elementary Geometry for College Students by Alexander and Koeberlein. It is available as a full-book PDF download and is very rigorous.

• Geometry: A Guided Inquiry (by Chakerian et al.)—it is the gold standard for "deriving the rules yourself." If the official version isn't free, look for their "Open Source Edition" or look-alikes like "Inquiry-Based Geometry" by McLean.

2. Supplemental Reading Materials for Deriving the Rules (Textbooklet Material)

Suggested reading and exercises

• The Kerala School & Pi: To teach the Madhava-Gregory-Leibniz series, look for the paper "Madhava's Pi-Series in the Modern Context" 

  • Derivation Suggestion: Have students draw a circle inside a square, then "cut" the corners of the square to make an octagon, then a 16-gon. Have them calculate the perimeter at each step. This is how the Kerala mathematicians (and Archimedes) derived the limits of pi.

• The Tau Manifesto: Download the PDF version from tauday.com. It is a short, polemic, and highly readable "booklet" on why C / r (Circumference over Radius) is more fundamental than C / d (Circumferenceover Diameter).   

• Coordinate Shifts: For the Cartesian-to-Polar derivation, look at "Street-Fighting Mathematics" by Sanjoy Mahajan (MIT Press, Open Access). It teaches how to solve complex problems through "guessing" and "symmetry".

3. Engineering & 3D Geometry Connection (Rods, Balls, & Arches)

For students studying fields like Mechanical Engineering or Reticular Chemistry, these resources bridge the gap between shapes and structures.

• The Physics of Arches: Search for "Statics for Engineering Technology" (Open Library). It explains Compression (the force holding stone arches together) and Tension.

  • Keystone Activity: Use magnetic "rods and balls" visual aid to build a "V-shape" and ask students why it falls. Then have them build a triangle. They will "derive" that a triangle is the only rigid polygon.

• Tetrahedrons & Reticular Chemistry: 

  • The Resource: Look for the "Reticular Chemistry Structure Resource (RCSR)" database

  • The Activity: Have students build a Tetrahedron (4 balls, 6 rods). Then ask them to link them together to fill space. They will quickly realize they can't fill all space with just tetrahedrons (they’ll need octahedrons too)—this is the "geometry gap" that defines many crystal structures.

4. Visual & Hands-On (The Mosaic Tiles)

To use those wooden tiles for higher-level math:

• Tessellations and Symmetries: Look for "Symmetry, Shape, and Space".

• Aperiodic Tilings (Penrose Tiles): These are patterns that never repeat. You can print "Penrose Tile Templates" (kites and darts) for them to cut out or match with their wooden blocks. This connects geometry directly to Quasicrystals (another Nobel-winning topic).

5. Summary Checklist for Your Offline Bundle

To make this work for your students, I recommend downloading these specific files and "bundling" them into a single folder on the device:

1. Full Textbook: CK-12 Geometry PDF (as the "Big Book").

2. The Tau Manifesto PDF (for the Pi debate).

3. A "Penrose Tile" Template PDF (for the mosaic toys).

4. "Introduction to Reticular Chemistry" (Intro chapters): Look for Professor Yaghi’s open-access review papers on "Metal-Organic Frameworks" (MOFs).

5. The "Yuktibhasa" summary: A 2-page PDF explaining the Kerala School’s derivation of infinite series.